idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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1,401 | tanh activation function vs sigmoid activation function | Generally speaking, $\tanh$ has two main advantages over a sigmoid function:
It has a slightly bigger derivative than the sigmoid (at least for the area around 0), which helps it to cope a bit better with the “vanishing gradients” problem of deep neural networks. Here is a plot of the derivatives of both functions:
... | tanh activation function vs sigmoid activation function | Generally speaking, $\tanh$ has two main advantages over a sigmoid function:
It has a slightly bigger derivative than the sigmoid (at least for the area around 0), which helps it to cope a bit better | tanh activation function vs sigmoid activation function
Generally speaking, $\tanh$ has two main advantages over a sigmoid function:
It has a slightly bigger derivative than the sigmoid (at least for the area around 0), which helps it to cope a bit better with the “vanishing gradients” problem of deep neural networks.... | tanh activation function vs sigmoid activation function
Generally speaking, $\tanh$ has two main advantages over a sigmoid function:
It has a slightly bigger derivative than the sigmoid (at least for the area around 0), which helps it to cope a bit better |
1,402 | Does an unbalanced sample matter when doing logistic regression? | Balance in the Training Set
For logistic regression models unbalanced training data affects only the estimate of the model intercept (although this of course skews all the predicted probabilities, which in turn compromises your predictions). Fortunately the intercept correction is straightforward: Provided you know, ... | Does an unbalanced sample matter when doing logistic regression? | Balance in the Training Set
For logistic regression models unbalanced training data affects only the estimate of the model intercept (although this of course skews all the predicted probabilities, whi | Does an unbalanced sample matter when doing logistic regression?
Balance in the Training Set
For logistic regression models unbalanced training data affects only the estimate of the model intercept (although this of course skews all the predicted probabilities, which in turn compromises your predictions). Fortunately t... | Does an unbalanced sample matter when doing logistic regression?
Balance in the Training Set
For logistic regression models unbalanced training data affects only the estimate of the model intercept (although this of course skews all the predicted probabilities, whi |
1,403 | Does an unbalanced sample matter when doing logistic regression? | The problem is not that the classes are imbalanced per se, it is that there may not be sufficient patterns belonging to the minority class to adequately represent its distribution. This means that the problem can arise for any classifier (even if you have a synthetic problem and you know you have the true model), not ... | Does an unbalanced sample matter when doing logistic regression? | The problem is not that the classes are imbalanced per se, it is that there may not be sufficient patterns belonging to the minority class to adequately represent its distribution. This means that th | Does an unbalanced sample matter when doing logistic regression?
The problem is not that the classes are imbalanced per se, it is that there may not be sufficient patterns belonging to the minority class to adequately represent its distribution. This means that the problem can arise for any classifier (even if you hav... | Does an unbalanced sample matter when doing logistic regression?
The problem is not that the classes are imbalanced per se, it is that there may not be sufficient patterns belonging to the minority class to adequately represent its distribution. This means that th |
1,404 | Does an unbalanced sample matter when doing logistic regression? | Think about the underlying distributions of the two samples. Do you have enough sample to measure both sub- populations without a massive amount of bias in the smaller sample?
See here for a longer explanation.
https://statisticalhorizons.com/logistic-regression-for-rare-events | Does an unbalanced sample matter when doing logistic regression? | Think about the underlying distributions of the two samples. Do you have enough sample to measure both sub- populations without a massive amount of bias in the smaller sample?
See here for a longer ex | Does an unbalanced sample matter when doing logistic regression?
Think about the underlying distributions of the two samples. Do you have enough sample to measure both sub- populations without a massive amount of bias in the smaller sample?
See here for a longer explanation.
https://statisticalhorizons.com/logistic-re... | Does an unbalanced sample matter when doing logistic regression?
Think about the underlying distributions of the two samples. Do you have enough sample to measure both sub- populations without a massive amount of bias in the smaller sample?
See here for a longer ex |
1,405 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | Ross describes three versions of this "paradox" in the Example 6a in his textbook. In each version, 10 balls are added to the urn and 1 ball is removed at each step of the procedure.
In the first version, $10n$-th ball is removed at the $n$-th step. There are infinitely many balls left after midnight because all balls... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | Ross describes three versions of this "paradox" in the Example 6a in his textbook. In each version, 10 balls are added to the urn and 1 ball is removed at each step of the procedure.
In the first ver | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
Ross describes three versions of this "paradox" in the Example 6a in his textbook. In each version, 10 balls are added to the urn and 1 ball is removed at each step of the procedure.
In the first vers... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
Ross describes three versions of this "paradox" in the Example 6a in his textbook. In each version, 10 balls are added to the urn and 1 ball is removed at each step of the procedure.
In the first ver |
1,406 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | Hurkyl (in an answer) and Dilip Sarwate (in a comment) give two common deterministic variants of this puzzle. In both variants, at step $k$, balls $10k-9$ through $10k$ are added to the pile ($k=1,2,...$).
In Hurkyl's variation, ball $k$ is removed. In this variant, in can be definitively argued that there are no b... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | Hurkyl (in an answer) and Dilip Sarwate (in a comment) give two common deterministic variants of this puzzle. In both variants, at step $k$, balls $10k-9$ through $10k$ are added to the pile ($k=1,2, | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
Hurkyl (in an answer) and Dilip Sarwate (in a comment) give two common deterministic variants of this puzzle. In both variants, at step $k$, balls $10k-9$ through $10k$ are added to the pile ($k=1,2,.... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
Hurkyl (in an answer) and Dilip Sarwate (in a comment) give two common deterministic variants of this puzzle. In both variants, at step $k$, balls $10k-9$ through $10k$ are added to the pile ($k=1,2, |
1,407 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | Enumaris' answer is perfectly right on the diverging limits problem. Nevertheless, the question can actually be answered in an unambiguous way. So, my answer will show you precisely where the zero balls solution goes wrong, and why the intuitive solution is the correct one.
It is true, that for any ball $n$, the proba... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | Enumaris' answer is perfectly right on the diverging limits problem. Nevertheless, the question can actually be answered in an unambiguous way. So, my answer will show you precisely where the zero bal | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
Enumaris' answer is perfectly right on the diverging limits problem. Nevertheless, the question can actually be answered in an unambiguous way. So, my answer will show you precisely where the zero ball... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
Enumaris' answer is perfectly right on the diverging limits problem. Nevertheless, the question can actually be answered in an unambiguous way. So, my answer will show you precisely where the zero bal |
1,408 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | This argument is focused on the tendency for infinite sets and sequences to behave in unitnuitive ways. This is no more surprising than the Hilbert Hotel. In such a case, you will indeed have taken out an infinite number of balls, but you will have put an infinite number in. Consider the Hilbert Hotel in reverse. Y... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | This argument is focused on the tendency for infinite sets and sequences to behave in unitnuitive ways. This is no more surprising than the Hilbert Hotel. In such a case, you will indeed have taken | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
This argument is focused on the tendency for infinite sets and sequences to behave in unitnuitive ways. This is no more surprising than the Hilbert Hotel. In such a case, you will indeed have taken o... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
This argument is focused on the tendency for infinite sets and sequences to behave in unitnuitive ways. This is no more surprising than the Hilbert Hotel. In such a case, you will indeed have taken |
1,409 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | I think it helps to remove the superfluous temporal component of the problem.
The more basic variant of this paradox is to always remove the lowest numbered ball. For ease of drawing, I will also only add two balls at each step.
The procedure describes how to fill out an infinite two-dimensional grid:
.*........
..**..... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | I think it helps to remove the superfluous temporal component of the problem.
The more basic variant of this paradox is to always remove the lowest numbered ball. For ease of drawing, I will also only | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
I think it helps to remove the superfluous temporal component of the problem.
The more basic variant of this paradox is to always remove the lowest numbered ball. For ease of drawing, I will also only ... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
I think it helps to remove the superfluous temporal component of the problem.
The more basic variant of this paradox is to always remove the lowest numbered ball. For ease of drawing, I will also only |
1,410 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | Several posters have been concerned the computations in Ross may not be rigorous. This answer addresses that by proving the existence of a probability space where all sets of outcomes considered by Ross are indeed measurable, and then repeats the vital parts of Ross's computations.
Finding a suitable probability space
... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | Several posters have been concerned the computations in Ross may not be rigorous. This answer addresses that by proving the existence of a probability space where all sets of outcomes considered by Ro | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
Several posters have been concerned the computations in Ross may not be rigorous. This answer addresses that by proving the existence of a probability space where all sets of outcomes considered by Ros... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
Several posters have been concerned the computations in Ross may not be rigorous. This answer addresses that by proving the existence of a probability space where all sets of outcomes considered by Ro |
1,411 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | This answer aims to do four things:
Review Ross's mathematical formulation of the problem, showing how it follows directly and unambiguously from the problem description.
Defend the position that Ross's paradoxical solution is both mathematically sound and relevant to our understanding of the physical world, whether... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | This answer aims to do four things:
Review Ross's mathematical formulation of the problem, showing how it follows directly and unambiguously from the problem description.
Defend the position that R | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
This answer aims to do four things:
Review Ross's mathematical formulation of the problem, showing how it follows directly and unambiguously from the problem description.
Defend the position that Ro... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
This answer aims to do four things:
Review Ross's mathematical formulation of the problem, showing how it follows directly and unambiguously from the problem description.
Defend the position that R |
1,412 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | On the one hand, you could try to explain it like this: "think of the
probability of any ball i being on the urn at 12 P.M. During the
infinite random draws, it will eventually be removed. Since this holds
for all balls, none of them can be there at the end".
I don't find this argument convincing. If this argum... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | On the one hand, you could try to explain it like this: "think of the
probability of any ball i being on the urn at 12 P.M. During the
infinite random draws, it will eventually be removed. Since t | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
On the one hand, you could try to explain it like this: "think of the
probability of any ball i being on the urn at 12 P.M. During the
infinite random draws, it will eventually be removed. Since th... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
On the one hand, you could try to explain it like this: "think of the
probability of any ball i being on the urn at 12 P.M. During the
infinite random draws, it will eventually be removed. Since t |
1,413 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | The problem is either ill-formed or not in first-order logic.
Root cause: execution of the "last" step will write an infinite number of digits on a ball, causing that step to take itself an infinite time to execute.
The ability to execute an infinite process with an infinite step implies the ability to solve all first-... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | The problem is either ill-formed or not in first-order logic.
Root cause: execution of the "last" step will write an infinite number of digits on a ball, causing that step to take itself an infinite t | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
The problem is either ill-formed or not in first-order logic.
Root cause: execution of the "last" step will write an infinite number of digits on a ball, causing that step to take itself an infinite ti... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
The problem is either ill-formed or not in first-order logic.
Root cause: execution of the "last" step will write an infinite number of digits on a ball, causing that step to take itself an infinite t |
1,414 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | What's the best explanation we can give to them to solve these
conflicting intuitions?
Here's the best answer, and it has very little to do with probabilities. All balls have numbers, let's call them birth numbers. The birth numbers start from B1, B2, B3... and go to infinity, because we really never stop. We get cl... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | What's the best explanation we can give to them to solve these
conflicting intuitions?
Here's the best answer, and it has very little to do with probabilities. All balls have numbers, let's call th | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
What's the best explanation we can give to them to solve these
conflicting intuitions?
Here's the best answer, and it has very little to do with probabilities. All balls have numbers, let's call the... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
What's the best explanation we can give to them to solve these
conflicting intuitions?
Here's the best answer, and it has very little to do with probabilities. All balls have numbers, let's call th |
1,415 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | I want to make a reformulation that is as easy as possible to make the answer of 0 more intuitive, starting from the simplified example that balls are not removed randomly, but ball $n$ is removed at the $n$-th step.
Consider this: I put all balls into the urn at the beginning. In step 1, I take out ball 1. In step 2, ... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | I want to make a reformulation that is as easy as possible to make the answer of 0 more intuitive, starting from the simplified example that balls are not removed randomly, but ball $n$ is removed at | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
I want to make a reformulation that is as easy as possible to make the answer of 0 more intuitive, starting from the simplified example that balls are not removed randomly, but ball $n$ is removed at t... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
I want to make a reformulation that is as easy as possible to make the answer of 0 more intuitive, starting from the simplified example that balls are not removed randomly, but ball $n$ is removed at |
1,416 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | Let x be the number of balls that have been removed and y be the number of balls remaining. After each cycle y=9x. As x>0, y>0. There will be infinitely many balls in the urn at 12PM.
The reason that solutions based on probabilities lead to difficulties is that the probabilities from infinite series are tricky. ET Jayn... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | Let x be the number of balls that have been removed and y be the number of balls remaining. After each cycle y=9x. As x>0, y>0. There will be infinitely many balls in the urn at 12PM.
The reason that | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
Let x be the number of balls that have been removed and y be the number of balls remaining. After each cycle y=9x. As x>0, y>0. There will be infinitely many balls in the urn at 12PM.
The reason that s... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
Let x be the number of balls that have been removed and y be the number of balls remaining. After each cycle y=9x. As x>0, y>0. There will be infinitely many balls in the urn at 12PM.
The reason that |
1,417 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | It's worth reading amoeba's answer that is just excellent and clarifies the problem very much. I don't exactly disagree with his answer but want to point out that the solution of the problem is based on a certain convention. What is interesting is that this sort of problem shows that this convention, while often used, ... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | It's worth reading amoeba's answer that is just excellent and clarifies the problem very much. I don't exactly disagree with his answer but want to point out that the solution of the problem is based | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
It's worth reading amoeba's answer that is just excellent and clarifies the problem very much. I don't exactly disagree with his answer but want to point out that the solution of the problem is based o... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
It's worth reading amoeba's answer that is just excellent and clarifies the problem very much. I don't exactly disagree with his answer but want to point out that the solution of the problem is based |
1,418 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | The aim of this post is to argue for the OPs last option that we need a better formulation. Or at least, Ross proof is not as clear cut as it may seem at first, and certainly, the proof is not so intuitive that is in a good position to be in an introduction course for theory of probability. It requires much explanation... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | The aim of this post is to argue for the OPs last option that we need a better formulation. Or at least, Ross proof is not as clear cut as it may seem at first, and certainly, the proof is not so intu | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
The aim of this post is to argue for the OPs last option that we need a better formulation. Or at least, Ross proof is not as clear cut as it may seem at first, and certainly, the proof is not so intui... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
The aim of this post is to argue for the OPs last option that we need a better formulation. Or at least, Ross proof is not as clear cut as it may seem at first, and certainly, the proof is not so intu |
1,419 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | OK, I'll try again.
The answer is that the paradox is purely mathematical. Enumaris's and cmaster's answer's tell what is going on in one way, but this is another way to see the problem. The problem is how we deal with probabilities with infinities, as Jaynes has written about (see my other attempted answer for details... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | OK, I'll try again.
The answer is that the paradox is purely mathematical. Enumaris's and cmaster's answer's tell what is going on in one way, but this is another way to see the problem. The problem i | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
OK, I'll try again.
The answer is that the paradox is purely mathematical. Enumaris's and cmaster's answer's tell what is going on in one way, but this is another way to see the problem. The problem is... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
OK, I'll try again.
The answer is that the paradox is purely mathematical. Enumaris's and cmaster's answer's tell what is going on in one way, but this is another way to see the problem. The problem i |
1,420 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | I believe that this example supports "if the premise is false then the conditional is true"
In this universe, there are no infinite urns and no infinite collection of balls. It is impossible to split time into arbitrarily small pieces.
Thus Sheldon Ross is right to say that the urn is empty at 12:00. Students who say... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | I believe that this example supports "if the premise is false then the conditional is true"
In this universe, there are no infinite urns and no infinite collection of balls. It is impossible to split | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
I believe that this example supports "if the premise is false then the conditional is true"
In this universe, there are no infinite urns and no infinite collection of balls. It is impossible to split ... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
I believe that this example supports "if the premise is false then the conditional is true"
In this universe, there are no infinite urns and no infinite collection of balls. It is impossible to split |
1,421 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | I support the opinion that the problem is ill-posed. When we consider something transfinite we often have to use a limit. It seems that here it is the only way. Since we distinguish different balls, we have an infinite-dimensional process $$(X_{t,1}, X_{t,2},...),$$
where $t=-1,-1/2,-1/4,...$ stands for the time, $X_... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | I support the opinion that the problem is ill-posed. When we consider something transfinite we often have to use a limit. It seems that here it is the only way. Since we distinguish different balls, w | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
I support the opinion that the problem is ill-posed. When we consider something transfinite we often have to use a limit. It seems that here it is the only way. Since we distinguish different balls, we... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
I support the opinion that the problem is ill-posed. When we consider something transfinite we often have to use a limit. It seems that here it is the only way. Since we distinguish different balls, w |
1,422 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | Recently several comments by Wilhelm, Wolfgang Mückenheim, caused me to reconsider certain formulations in my answer. I am posting this as a new answer mainly because the different approach of this answer, not arguing about the teaching of this problem, but instead about the paradox being invalid.
Wilhelm discusses in ... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | Recently several comments by Wilhelm, Wolfgang Mückenheim, caused me to reconsider certain formulations in my answer. I am posting this as a new answer mainly because the different approach of this an | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
Recently several comments by Wilhelm, Wolfgang Mückenheim, caused me to reconsider certain formulations in my answer. I am posting this as a new answer mainly because the different approach of this ans... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
Recently several comments by Wilhelm, Wolfgang Mückenheim, caused me to reconsider certain formulations in my answer. I am posting this as a new answer mainly because the different approach of this an |
1,423 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | The problem as stated is a variant of a conditionally convergent sum. That is, the sum is indeterminate depending on how the addition is performed; in what order the terms are summed. In general, if $\Sigma_{n=0}^\infty x_n$ converges but $\Sigma_{n=0}^\infty |x_n|$ is divergent, then convergence is conditional and n... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | The problem as stated is a variant of a conditionally convergent sum. That is, the sum is indeterminate depending on how the addition is performed; in what order the terms are summed. In general, if | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
The problem as stated is a variant of a conditionally convergent sum. That is, the sum is indeterminate depending on how the addition is performed; in what order the terms are summed. In general, if $... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
The problem as stated is a variant of a conditionally convergent sum. That is, the sum is indeterminate depending on how the addition is performed; in what order the terms are summed. In general, if |
1,424 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | More intuition than formal education, but:
If the intervals to midnight are halving, we never reach midnight... we only approach asymptotically; so one could argue that there is no solution.
Alternatively, depending on the phrasing:
as there are infinite intervals of +10 balls the answer is infinite
as there are infin... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | More intuition than formal education, but:
If the intervals to midnight are halving, we never reach midnight... we only approach asymptotically; so one could argue that there is no solution.
Alternati | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
More intuition than formal education, but:
If the intervals to midnight are halving, we never reach midnight... we only approach asymptotically; so one could argue that there is no solution.
Alternativ... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
More intuition than formal education, but:
If the intervals to midnight are halving, we never reach midnight... we only approach asymptotically; so one could argue that there is no solution.
Alternati |
1,425 | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left? | Rewrite: Jan 16, 2018
Section 1: Outline
The fundamental results this post are as follows:
The halfway ball has a probability of about $0.91$ of remaining in the limit as the step goes to $\infty$ - this is both a real world observation and is derived mathematically.
The derived function has a domain of the rationals... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma | Rewrite: Jan 16, 2018
Section 1: Outline
The fundamental results this post are as follows:
The halfway ball has a probability of about $0.91$ of remaining in the limit as the step goes to $\infty$ - | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How many balls are left?
Rewrite: Jan 16, 2018
Section 1: Outline
The fundamental results this post are as follows:
The halfway ball has a probability of about $0.91$ of remaining in the limit as the step goes to $\infty$ - ... | At each step of a limiting infinite process, put 10 balls in an urn and remove one at random. How ma
Rewrite: Jan 16, 2018
Section 1: Outline
The fundamental results this post are as follows:
The halfway ball has a probability of about $0.91$ of remaining in the limit as the step goes to $\infty$ - |
1,426 | Why does the Lasso provide Variable Selection? | Let's consider a very simple model: $y = \beta x + e$, with an L1 penalty on $\hat{\beta}$ and a least-squares loss function on $\hat{e}$. We can expand the expression to be minimized as:
$\min y^Ty -2 y^Tx\hat{\beta} + \hat{\beta} x^Tx\hat{\beta} + 2\lambda|\hat{\beta}|$
Keep in mind this is a univariate example, wit... | Why does the Lasso provide Variable Selection? | Let's consider a very simple model: $y = \beta x + e$, with an L1 penalty on $\hat{\beta}$ and a least-squares loss function on $\hat{e}$. We can expand the expression to be minimized as:
$\min y^Ty | Why does the Lasso provide Variable Selection?
Let's consider a very simple model: $y = \beta x + e$, with an L1 penalty on $\hat{\beta}$ and a least-squares loss function on $\hat{e}$. We can expand the expression to be minimized as:
$\min y^Ty -2 y^Tx\hat{\beta} + \hat{\beta} x^Tx\hat{\beta} + 2\lambda|\hat{\beta}|$... | Why does the Lasso provide Variable Selection?
Let's consider a very simple model: $y = \beta x + e$, with an L1 penalty on $\hat{\beta}$ and a least-squares loss function on $\hat{e}$. We can expand the expression to be minimized as:
$\min y^Ty |
1,427 | Why does the Lasso provide Variable Selection? | Suppose we have a data set with y = 1 and x = [1/10 1/10] (one data point, two features). One solution is to pick one of the features, another feature is to weight both features. I.e. we can either pick w = [5 5] or w = [10 0].
Note that for the L1 norm both have the same penalty, but the more spread out weight has... | Why does the Lasso provide Variable Selection? | Suppose we have a data set with y = 1 and x = [1/10 1/10] (one data point, two features). One solution is to pick one of the features, another feature is to weight both features. I.e. we can either | Why does the Lasso provide Variable Selection?
Suppose we have a data set with y = 1 and x = [1/10 1/10] (one data point, two features). One solution is to pick one of the features, another feature is to weight both features. I.e. we can either pick w = [5 5] or w = [10 0].
Note that for the L1 norm both have the s... | Why does the Lasso provide Variable Selection?
Suppose we have a data set with y = 1 and x = [1/10 1/10] (one data point, two features). One solution is to pick one of the features, another feature is to weight both features. I.e. we can either |
1,428 | Why does the Lasso provide Variable Selection? | I think there are excellent anwers already but just to add some intuition concerning the geometric interpretation:
"The lasso performs $L1$ shrinkage, so that there are "corners" in the constraint, which in two dimensions corresponds to a diamond. If the sum of squares "hits'' one of these corners, then the coefficient... | Why does the Lasso provide Variable Selection? | I think there are excellent anwers already but just to add some intuition concerning the geometric interpretation:
"The lasso performs $L1$ shrinkage, so that there are "corners" in the constraint, wh | Why does the Lasso provide Variable Selection?
I think there are excellent anwers already but just to add some intuition concerning the geometric interpretation:
"The lasso performs $L1$ shrinkage, so that there are "corners" in the constraint, which in two dimensions corresponds to a diamond. If the sum of squares "hi... | Why does the Lasso provide Variable Selection?
I think there are excellent anwers already but just to add some intuition concerning the geometric interpretation:
"The lasso performs $L1$ shrinkage, so that there are "corners" in the constraint, wh |
1,429 | Why does the Lasso provide Variable Selection? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
I recently created a blog post to compare ridge and la... | Why does the Lasso provide Variable Selection? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| Why does the Lasso provide Variable Selection?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
I recen... | Why does the Lasso provide Variable Selection?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
1,430 | Calculating optimal number of bins in a histogram | The Freedman-Diaconis rule is very robust and works well in practice. The bin-width is set to $h=2\times\text{IQR}\times n^{-1/3}$. So the number of bins is $(\max-\min)/h$, where $n$ is the number of observations, max is the maximum value and min is the minimum value.
In base R, you can use:
hist(x, breaks="FD")
For... | Calculating optimal number of bins in a histogram | The Freedman-Diaconis rule is very robust and works well in practice. The bin-width is set to $h=2\times\text{IQR}\times n^{-1/3}$. So the number of bins is $(\max-\min)/h$, where $n$ is the number of | Calculating optimal number of bins in a histogram
The Freedman-Diaconis rule is very robust and works well in practice. The bin-width is set to $h=2\times\text{IQR}\times n^{-1/3}$. So the number of bins is $(\max-\min)/h$, where $n$ is the number of observations, max is the maximum value and min is the minimum value.
... | Calculating optimal number of bins in a histogram
The Freedman-Diaconis rule is very robust and works well in practice. The bin-width is set to $h=2\times\text{IQR}\times n^{-1/3}$. So the number of bins is $(\max-\min)/h$, where $n$ is the number of |
1,431 | Calculating optimal number of bins in a histogram | If you use too few bins, the histogram doesn't really portray the data very well. If you have too many bins, you get a broken comb look, which also doesn't give a sense of the distribution.
One solution is to create a graph that shows every value. Either a dot plot, or a cumulative frequency distribution, which doesn't... | Calculating optimal number of bins in a histogram | If you use too few bins, the histogram doesn't really portray the data very well. If you have too many bins, you get a broken comb look, which also doesn't give a sense of the distribution.
One soluti | Calculating optimal number of bins in a histogram
If you use too few bins, the histogram doesn't really portray the data very well. If you have too many bins, you get a broken comb look, which also doesn't give a sense of the distribution.
One solution is to create a graph that shows every value. Either a dot plot, or ... | Calculating optimal number of bins in a histogram
If you use too few bins, the histogram doesn't really portray the data very well. If you have too many bins, you get a broken comb look, which also doesn't give a sense of the distribution.
One soluti |
1,432 | Calculating optimal number of bins in a histogram | Maybe the paper "Variations on the histogram" by Denby and Mallows will be of interest:
This new display which we term "dhist" (for diagonally-cut histogram) preserves the desirable features of both the equal-width hist and the equal-area hist. It will show tall narrow bins like the e-a hist when there are spikes in t... | Calculating optimal number of bins in a histogram | Maybe the paper "Variations on the histogram" by Denby and Mallows will be of interest:
This new display which we term "dhist" (for diagonally-cut histogram) preserves the desirable features of both | Calculating optimal number of bins in a histogram
Maybe the paper "Variations on the histogram" by Denby and Mallows will be of interest:
This new display which we term "dhist" (for diagonally-cut histogram) preserves the desirable features of both the equal-width hist and the equal-area hist. It will show tall narrow... | Calculating optimal number of bins in a histogram
Maybe the paper "Variations on the histogram" by Denby and Mallows will be of interest:
This new display which we term "dhist" (for diagonally-cut histogram) preserves the desirable features of both |
1,433 | Calculating optimal number of bins in a histogram | Did you see the Shimazaki-Shinomoto method?
Although it seems to be computationally expensive, it may give you good results. It's worth giving it a try if computational time is not your problem. There are some implementations of this method in java, MATLAB, etc, in the following link, which runs fast enough:
web-interf... | Calculating optimal number of bins in a histogram | Did you see the Shimazaki-Shinomoto method?
Although it seems to be computationally expensive, it may give you good results. It's worth giving it a try if computational time is not your problem. There | Calculating optimal number of bins in a histogram
Did you see the Shimazaki-Shinomoto method?
Although it seems to be computationally expensive, it may give you good results. It's worth giving it a try if computational time is not your problem. There are some implementations of this method in java, MATLAB, etc, in the ... | Calculating optimal number of bins in a histogram
Did you see the Shimazaki-Shinomoto method?
Although it seems to be computationally expensive, it may give you good results. It's worth giving it a try if computational time is not your problem. There |
1,434 | Calculating optimal number of bins in a histogram | I'm not sure this counts as strictly good practice, but I tend to produce more than one histogram with different bin widths and pick the histogram which histogram to use based on which histogram fits the interpretation I'm trying to communicate best. Whilst this introduces some subjectivity into the choice of histogram... | Calculating optimal number of bins in a histogram | I'm not sure this counts as strictly good practice, but I tend to produce more than one histogram with different bin widths and pick the histogram which histogram to use based on which histogram fits | Calculating optimal number of bins in a histogram
I'm not sure this counts as strictly good practice, but I tend to produce more than one histogram with different bin widths and pick the histogram which histogram to use based on which histogram fits the interpretation I'm trying to communicate best. Whilst this introdu... | Calculating optimal number of bins in a histogram
I'm not sure this counts as strictly good practice, but I tend to produce more than one histogram with different bin widths and pick the histogram which histogram to use based on which histogram fits |
1,435 | Calculating optimal number of bins in a histogram | If I need to determine the number of bins programmatically I usually start out with a histogram that has way more bins than needed. Once the histogram is filled I then combine bins until I have enough entries per bin for the method I am using, e.g. if I want to model Poisson-uncertainties in a counting experiment with ... | Calculating optimal number of bins in a histogram | If I need to determine the number of bins programmatically I usually start out with a histogram that has way more bins than needed. Once the histogram is filled I then combine bins until I have enough | Calculating optimal number of bins in a histogram
If I need to determine the number of bins programmatically I usually start out with a histogram that has way more bins than needed. Once the histogram is filled I then combine bins until I have enough entries per bin for the method I am using, e.g. if I want to model Po... | Calculating optimal number of bins in a histogram
If I need to determine the number of bins programmatically I usually start out with a histogram that has way more bins than needed. Once the histogram is filled I then combine bins until I have enough |
1,436 | Calculating optimal number of bins in a histogram | Please see this answer as a complementary of Mr. Rob Hyndman's answer.
In order to create histogram plots with exact same intervals or 'binwidths' using the Freedman–Diaconis rule either with basic R or ggplot2 package, we can use one of the values of hist() function namely breaks. Suppose we want to create a histogram... | Calculating optimal number of bins in a histogram | Please see this answer as a complementary of Mr. Rob Hyndman's answer.
In order to create histogram plots with exact same intervals or 'binwidths' using the Freedman–Diaconis rule either with basic R | Calculating optimal number of bins in a histogram
Please see this answer as a complementary of Mr. Rob Hyndman's answer.
In order to create histogram plots with exact same intervals or 'binwidths' using the Freedman–Diaconis rule either with basic R or ggplot2 package, we can use one of the values of hist() function na... | Calculating optimal number of bins in a histogram
Please see this answer as a complementary of Mr. Rob Hyndman's answer.
In order to create histogram plots with exact same intervals or 'binwidths' using the Freedman–Diaconis rule either with basic R |
1,437 | Calculating optimal number of bins in a histogram | Conventional wisdom dictates that a "broken look' resulting from a histogram with many bins is undesirable. This clashes with the need to show individual outliers, digit preference, bimodality, data gaps, and other features. I believe that histograms need to be both summary and descriptive measures. For that reason ... | Calculating optimal number of bins in a histogram | Conventional wisdom dictates that a "broken look' resulting from a histogram with many bins is undesirable. This clashes with the need to show individual outliers, digit preference, bimodality, data | Calculating optimal number of bins in a histogram
Conventional wisdom dictates that a "broken look' resulting from a histogram with many bins is undesirable. This clashes with the need to show individual outliers, digit preference, bimodality, data gaps, and other features. I believe that histograms need to be both s... | Calculating optimal number of bins in a histogram
Conventional wisdom dictates that a "broken look' resulting from a histogram with many bins is undesirable. This clashes with the need to show individual outliers, digit preference, bimodality, data |
1,438 | Calculating optimal number of bins in a histogram | With so few data, what approaches should I take to calculating the number of bins to use?
FD or doane methods (see below) might be more suitable. Experience tells, this depends on the upstream task as well. If binning changes the inference or results of the upstream task. Then, one should find a stable/robust method t... | Calculating optimal number of bins in a histogram | With so few data, what approaches should I take to calculating the number of bins to use?
FD or doane methods (see below) might be more suitable. Experience tells, this depends on the upstream task a | Calculating optimal number of bins in a histogram
With so few data, what approaches should I take to calculating the number of bins to use?
FD or doane methods (see below) might be more suitable. Experience tells, this depends on the upstream task as well. If binning changes the inference or results of the upstream ta... | Calculating optimal number of bins in a histogram
With so few data, what approaches should I take to calculating the number of bins to use?
FD or doane methods (see below) might be more suitable. Experience tells, this depends on the upstream task a |
1,439 | Calculating optimal number of bins in a histogram | Another method is Bayesian Blocks from Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations by Scargle et al.
Bayesian Blocks is a dynamic histogramming method which optimizes one
of several possible fitness functions to determine an optimal binning
for data, where the bins are not necessar... | Calculating optimal number of bins in a histogram | Another method is Bayesian Blocks from Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations by Scargle et al.
Bayesian Blocks is a dynamic histogramming method which optim | Calculating optimal number of bins in a histogram
Another method is Bayesian Blocks from Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations by Scargle et al.
Bayesian Blocks is a dynamic histogramming method which optimizes one
of several possible fitness functions to determine an optimal... | Calculating optimal number of bins in a histogram
Another method is Bayesian Blocks from Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations by Scargle et al.
Bayesian Blocks is a dynamic histogramming method which optim |
1,440 | Calculating optimal number of bins in a histogram | The MDL histogram density estimation method has the following features:
variable width; the method is not constrained to histograms with fixed bin widths.
adaptive; the number of bins, and bin widths are determined based on data. Very few input parameters are required, and the parameters have little impact on the resu... | Calculating optimal number of bins in a histogram | The MDL histogram density estimation method has the following features:
variable width; the method is not constrained to histograms with fixed bin widths.
adaptive; the number of bins, and bin widths | Calculating optimal number of bins in a histogram
The MDL histogram density estimation method has the following features:
variable width; the method is not constrained to histograms with fixed bin widths.
adaptive; the number of bins, and bin widths are determined based on data. Very few input parameters are required,... | Calculating optimal number of bins in a histogram
The MDL histogram density estimation method has the following features:
variable width; the method is not constrained to histograms with fixed bin widths.
adaptive; the number of bins, and bin widths |
1,441 | Is it possible to train a neural network without backpropagation? | The first two algorithms you mention (Nelder-Mead and Simulated Annealing) are generally considered pretty much obsolete in optimization circles, as there are much better alternatives which are both more reliable and less costly. Genetic algorithms covers a wide range, and some of these can be reasonable.
However, in t... | Is it possible to train a neural network without backpropagation? | The first two algorithms you mention (Nelder-Mead and Simulated Annealing) are generally considered pretty much obsolete in optimization circles, as there are much better alternatives which are both m | Is it possible to train a neural network without backpropagation?
The first two algorithms you mention (Nelder-Mead and Simulated Annealing) are generally considered pretty much obsolete in optimization circles, as there are much better alternatives which are both more reliable and less costly. Genetic algorithms cover... | Is it possible to train a neural network without backpropagation?
The first two algorithms you mention (Nelder-Mead and Simulated Annealing) are generally considered pretty much obsolete in optimization circles, as there are much better alternatives which are both m |
1,442 | Is it possible to train a neural network without backpropagation? | Well, the original neural networks, before the backpropagation revolution in the 70s, were "trained" by hand. :)
That being said:
There is a "school" of machine learning called extreme learning machine that does not use backpropagation.
What they do do is to create a neural network with many, many, many nodes --with ra... | Is it possible to train a neural network without backpropagation? | Well, the original neural networks, before the backpropagation revolution in the 70s, were "trained" by hand. :)
That being said:
There is a "school" of machine learning called extreme learning machin | Is it possible to train a neural network without backpropagation?
Well, the original neural networks, before the backpropagation revolution in the 70s, were "trained" by hand. :)
That being said:
There is a "school" of machine learning called extreme learning machine that does not use backpropagation.
What they do do i... | Is it possible to train a neural network without backpropagation?
Well, the original neural networks, before the backpropagation revolution in the 70s, were "trained" by hand. :)
That being said:
There is a "school" of machine learning called extreme learning machin |
1,443 | Is it possible to train a neural network without backpropagation? | There are all sorts of local search algorithms you could use, backpropagation has just proved to be the most efficient for more complex tasks in general; there are circumstances where other local searches are better.
You could use random-start hill climbing on a neural network to find an ok solution quickly, but it wou... | Is it possible to train a neural network without backpropagation? | There are all sorts of local search algorithms you could use, backpropagation has just proved to be the most efficient for more complex tasks in general; there are circumstances where other local sear | Is it possible to train a neural network without backpropagation?
There are all sorts of local search algorithms you could use, backpropagation has just proved to be the most efficient for more complex tasks in general; there are circumstances where other local searches are better.
You could use random-start hill climb... | Is it possible to train a neural network without backpropagation?
There are all sorts of local search algorithms you could use, backpropagation has just proved to be the most efficient for more complex tasks in general; there are circumstances where other local sear |
1,444 | Is it possible to train a neural network without backpropagation? | You can use pretty much any numerical optimization algorithm to optimize weights of a neural network. You can also use mixed continous-discrete optimization algorithms to optimize not only weights, but layout itself (number of layers, number of neurons in each layer, even type of the neuron).
However there's no optimiz... | Is it possible to train a neural network without backpropagation? | You can use pretty much any numerical optimization algorithm to optimize weights of a neural network. You can also use mixed continous-discrete optimization algorithms to optimize not only weights, bu | Is it possible to train a neural network without backpropagation?
You can use pretty much any numerical optimization algorithm to optimize weights of a neural network. You can also use mixed continous-discrete optimization algorithms to optimize not only weights, but layout itself (number of layers, number of neurons i... | Is it possible to train a neural network without backpropagation?
You can use pretty much any numerical optimization algorithm to optimize weights of a neural network. You can also use mixed continous-discrete optimization algorithms to optimize not only weights, bu |
1,445 | Is it possible to train a neural network without backpropagation? | You can also use another network to advise how the parameters should be updated.
There is the Decoupled Neural Interfaces (DNI) from Google Deepmind. Instead of using backpropagation, it uses another set of neural networks to predict how to update the parameters, which allows for parallel and asynchronous parameter upd... | Is it possible to train a neural network without backpropagation? | You can also use another network to advise how the parameters should be updated.
There is the Decoupled Neural Interfaces (DNI) from Google Deepmind. Instead of using backpropagation, it uses another | Is it possible to train a neural network without backpropagation?
You can also use another network to advise how the parameters should be updated.
There is the Decoupled Neural Interfaces (DNI) from Google Deepmind. Instead of using backpropagation, it uses another set of neural networks to predict how to update the pa... | Is it possible to train a neural network without backpropagation?
You can also use another network to advise how the parameters should be updated.
There is the Decoupled Neural Interfaces (DNI) from Google Deepmind. Instead of using backpropagation, it uses another |
1,446 | Is it possible to train a neural network without backpropagation? | As long as this is a community question , I thought I would add another response. "Back Propagation" is simply the gradient descent algorithm. It involves using only the first derivative of the function for which one is trying to find the local minima or maxima. There is another method called Newton's method or New... | Is it possible to train a neural network without backpropagation? | As long as this is a community question , I thought I would add another response. "Back Propagation" is simply the gradient descent algorithm. It involves using only the first derivative of the fun | Is it possible to train a neural network without backpropagation?
As long as this is a community question , I thought I would add another response. "Back Propagation" is simply the gradient descent algorithm. It involves using only the first derivative of the function for which one is trying to find the local minima... | Is it possible to train a neural network without backpropagation?
As long as this is a community question , I thought I would add another response. "Back Propagation" is simply the gradient descent algorithm. It involves using only the first derivative of the fun |
1,447 | Assessing approximate distribution of data based on a histogram | The difficulty with using histograms to infer shape
While histograms are often handy and mostly useful, they can be misleading. Their appearance can alter quite a lot with changes in the locations of the bin boundaries.
This problem has long been known*, though perhaps not as widely as it should be -- you rarely see it... | Assessing approximate distribution of data based on a histogram | The difficulty with using histograms to infer shape
While histograms are often handy and mostly useful, they can be misleading. Their appearance can alter quite a lot with changes in the locations of | Assessing approximate distribution of data based on a histogram
The difficulty with using histograms to infer shape
While histograms are often handy and mostly useful, they can be misleading. Their appearance can alter quite a lot with changes in the locations of the bin boundaries.
This problem has long been known*, t... | Assessing approximate distribution of data based on a histogram
The difficulty with using histograms to infer shape
While histograms are often handy and mostly useful, they can be misleading. Their appearance can alter quite a lot with changes in the locations of |
1,448 | Assessing approximate distribution of data based on a histogram | Cumulative distribution plots [MATLAB, R] – where you plot the fraction of data values less than or equal to a range of values – are by far the best way to look at distributions of empirical data. Here, for example, are the ECDFs of this data, produced in R:
This can be generated with the following R input (with the a... | Assessing approximate distribution of data based on a histogram | Cumulative distribution plots [MATLAB, R] – where you plot the fraction of data values less than or equal to a range of values – are by far the best way to look at distributions of empirical data. Her | Assessing approximate distribution of data based on a histogram
Cumulative distribution plots [MATLAB, R] – where you plot the fraction of data values less than or equal to a range of values – are by far the best way to look at distributions of empirical data. Here, for example, are the ECDFs of this data, produced in ... | Assessing approximate distribution of data based on a histogram
Cumulative distribution plots [MATLAB, R] – where you plot the fraction of data values less than or equal to a range of values – are by far the best way to look at distributions of empirical data. Her |
1,449 | Assessing approximate distribution of data based on a histogram | A kernel density or logspline plot may be a better option compared to a histogram. There are still some options that can be set with these methods, but they are less fickle than histograms. There are qqplots as well. A nice tool for seeing if data is close enough to a theoretical distribution is detailed in:
Buja,... | Assessing approximate distribution of data based on a histogram | A kernel density or logspline plot may be a better option compared to a histogram. There are still some options that can be set with these methods, but they are less fickle than histograms. There ar | Assessing approximate distribution of data based on a histogram
A kernel density or logspline plot may be a better option compared to a histogram. There are still some options that can be set with these methods, but they are less fickle than histograms. There are qqplots as well. A nice tool for seeing if data is cl... | Assessing approximate distribution of data based on a histogram
A kernel density or logspline plot may be a better option compared to a histogram. There are still some options that can be set with these methods, but they are less fickle than histograms. There ar |
1,450 | Assessing approximate distribution of data based on a histogram | Suggestion: Histograms usually only assign the x-axis data to have occurred at the midpoint of the bin and omit x-axis measures of location of greater accuracy. The effect this has on the derivatives of fit can be quite large. Let us take a trivial example. Suppose we take the classical derivation of a Dirac delta but ... | Assessing approximate distribution of data based on a histogram | Suggestion: Histograms usually only assign the x-axis data to have occurred at the midpoint of the bin and omit x-axis measures of location of greater accuracy. The effect this has on the derivatives | Assessing approximate distribution of data based on a histogram
Suggestion: Histograms usually only assign the x-axis data to have occurred at the midpoint of the bin and omit x-axis measures of location of greater accuracy. The effect this has on the derivatives of fit can be quite large. Let us take a trivial example... | Assessing approximate distribution of data based on a histogram
Suggestion: Histograms usually only assign the x-axis data to have occurred at the midpoint of the bin and omit x-axis measures of location of greater accuracy. The effect this has on the derivatives |
1,451 | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | TL;DR: Unless you assume people are unreasonably bad at judging car color, or that blue cars are unreasonably rare, the large number of people in your example means the probability that the car is blue is basically 100%.
Matthew Drury already gave the right answer but I'd just like to add to that with some numerical ex... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | TL;DR: Unless you assume people are unreasonably bad at judging car color, or that blue cars are unreasonably rare, the large number of people in your example means the probability that the car is blu | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
TL;DR: Unless you assume people are unreasonably bad at judging car color, or that blue cars are unreasonably rare, the large number of people in your example means the probability that the car is blue is basically 100%.
Matthew Drury... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
TL;DR: Unless you assume people are unreasonably bad at judging car color, or that blue cars are unreasonably rare, the large number of people in your example means the probability that the car is blu |
1,452 | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | The correct answer depends on information not specified in the problem, you will have to make some more assumptions to derive a single, definitive answer:
The prior probability the car is blue, i.e. your belief that the car is blue given you have not yet asked anyone.
The probability someone tells you the car is blue ... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | The correct answer depends on information not specified in the problem, you will have to make some more assumptions to derive a single, definitive answer:
The prior probability the car is blue, i.e. | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
The correct answer depends on information not specified in the problem, you will have to make some more assumptions to derive a single, definitive answer:
The prior probability the car is blue, i.e. your belief that the car is blue g... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
The correct answer depends on information not specified in the problem, you will have to make some more assumptions to derive a single, definitive answer:
The prior probability the car is blue, i.e. |
1,453 | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | There's an important assumption that your 1000 opinions don't share a systematic bias. Which is a reasonable assumption here, but could be important in other cases.
Examples might be:
they all share a similar colorblindness (genetics in a population for example),
they all saw the car at night under orange sodium str... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | There's an important assumption that your 1000 opinions don't share a systematic bias. Which is a reasonable assumption here, but could be important in other cases.
Examples might be:
they all share | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
There's an important assumption that your 1000 opinions don't share a systematic bias. Which is a reasonable assumption here, but could be important in other cases.
Examples might be:
they all share a similar colorblindness (genetic... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
There's an important assumption that your 1000 opinions don't share a systematic bias. Which is a reasonable assumption here, but could be important in other cases.
Examples might be:
they all share |
1,454 | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | One reason you're getting different answers from different people is that the question can be interpreted in different ways, and it isn't clear what you mean by "probability" here. One way to make sense of the question is to assign priors and reason using Bayes' rule as in Matthew's answer.
Before asking for probabilit... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | One reason you're getting different answers from different people is that the question can be interpreted in different ways, and it isn't clear what you mean by "probability" here. One way to make sen | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
One reason you're getting different answers from different people is that the question can be interpreted in different ways, and it isn't clear what you mean by "probability" here. One way to make sense of the question is to assign pr... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
One reason you're getting different answers from different people is that the question can be interpreted in different ways, and it isn't clear what you mean by "probability" here. One way to make sen |
1,455 | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | Simple practical answer:
The probability can easily range from 0% to 100% depending on your assumptions
Though I really like the existing answers, in practice it basically boils down to these two simple scenarios:
Scenario 1: People are assumed to be very good at recognizing blue when it is blue ... 0%
In this case, th... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | Simple practical answer:
The probability can easily range from 0% to 100% depending on your assumptions
Though I really like the existing answers, in practice it basically boils down to these two simp | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
Simple practical answer:
The probability can easily range from 0% to 100% depending on your assumptions
Though I really like the existing answers, in practice it basically boils down to these two simple scenarios:
Scenario 1: People a... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
Simple practical answer:
The probability can easily range from 0% to 100% depending on your assumptions
Though I really like the existing answers, in practice it basically boils down to these two simp |
1,456 | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | You need to develop some framework of estimation. Some questions you might ask are
How many colors are there? Are we talking two colors? Or all the colors of the rainbow?
How distinct are the colors? Are we talking blue and orange? Or blue, cyan, and turquoise?
What does it mean to be blue? Are cyan and/or ... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | You need to develop some framework of estimation. Some questions you might ask are
How many colors are there? Are we talking two colors? Or all the colors of the rainbow?
How distinct are the c | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
You need to develop some framework of estimation. Some questions you might ask are
How many colors are there? Are we talking two colors? Or all the colors of the rainbow?
How distinct are the colors? Are we talking blue and or... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
You need to develop some framework of estimation. Some questions you might ask are
How many colors are there? Are we talking two colors? Or all the colors of the rainbow?
How distinct are the c |
1,457 | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | An exact, mathematical, true/false probability cannot be computed with the information you provide.
However, in real life such information is never available with certainty. Therefore, using our intuition (and where all my money would go if we were betting), the car is definitely blue. (some believe this is not statis... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | An exact, mathematical, true/false probability cannot be computed with the information you provide.
However, in real life such information is never available with certainty. Therefore, using our intu | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
An exact, mathematical, true/false probability cannot be computed with the information you provide.
However, in real life such information is never available with certainty. Therefore, using our intuition (and where all my money woul... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
An exact, mathematical, true/false probability cannot be computed with the information you provide.
However, in real life such information is never available with certainty. Therefore, using our intu |
1,458 | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | I would not eat feces based on the fact that billion of flies can't be wrong. There might dozens of other reasons why 900 people out of 1000 might have been cheated to think the car is blue. After all, that's the base of magical tricks, luring people into thinking something removed from reality.
If 900 people out of 10... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | I would not eat feces based on the fact that billion of flies can't be wrong. There might dozens of other reasons why 900 people out of 1000 might have been cheated to think the car is blue. After all | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
I would not eat feces based on the fact that billion of flies can't be wrong. There might dozens of other reasons why 900 people out of 1000 might have been cheated to think the car is blue. After all, that's the base of magical trick... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
I would not eat feces based on the fact that billion of flies can't be wrong. There might dozens of other reasons why 900 people out of 1000 might have been cheated to think the car is blue. After all |
1,459 | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | The questionee knows too little about how the poll was carried out in order to answer the question accurately. As far as he's concerned, the poll can suffer from several problems:
The people taking the poll could have been biased:
The car looked blue because of an optical illusion.
The color of the car was for some re... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | The questionee knows too little about how the poll was carried out in order to answer the question accurately. As far as he's concerned, the poll can suffer from several problems:
The people taking th | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
The questionee knows too little about how the poll was carried out in order to answer the question accurately. As far as he's concerned, the poll can suffer from several problems:
The people taking the poll could have been biased:
Th... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
The questionee knows too little about how the poll was carried out in order to answer the question accurately. As far as he's concerned, the poll can suffer from several problems:
The people taking th |
1,460 | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | What is the definition of "blue"?
Different cultures and languages have different notions of blue. IIRC, some cultures include green within their notion of blue!
Like any natural language word, you can only assume there is some cultural convention on when (and when not) to call things "blue".
Overall, color in language... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | What is the definition of "blue"?
Different cultures and languages have different notions of blue. IIRC, some cultures include green within their notion of blue!
Like any natural language word, you ca | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
What is the definition of "blue"?
Different cultures and languages have different notions of blue. IIRC, some cultures include green within their notion of blue!
Like any natural language word, you can only assume there is some cultur... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
What is the definition of "blue"?
Different cultures and languages have different notions of blue. IIRC, some cultures include green within their notion of blue!
Like any natural language word, you ca |
1,461 | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | The likelihood could, depending on more refined preconditions, be several different values, but 99.995% is the one that makes the most sense to me.
We know, by definition, that the car is blue (that's 100%), but it is not well-specified what this actually means (that would bet somewhat philosophical). I will assume som... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | The likelihood could, depending on more refined preconditions, be several different values, but 99.995% is the one that makes the most sense to me.
We know, by definition, that the car is blue (that's | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
The likelihood could, depending on more refined preconditions, be several different values, but 99.995% is the one that makes the most sense to me.
We know, by definition, that the car is blue (that's 100%), but it is not well-specifi... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
The likelihood could, depending on more refined preconditions, be several different values, but 99.995% is the one that makes the most sense to me.
We know, by definition, that the car is blue (that's |
1,462 | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | You have a blue car (by some objective scientific measure - it is
blue).
...
"What is the probability that the car is blue?"
It is 100% blue.
All they know is that 900 people said it was blue, and 100 did not. You know nothing more about these people (the 1000).
Using these numbers (without any context) is utterl... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | You have a blue car (by some objective scientific measure - it is
blue).
...
"What is the probability that the car is blue?"
It is 100% blue.
All they know is that 900 people said it was blue, an | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
You have a blue car (by some objective scientific measure - it is
blue).
...
"What is the probability that the car is blue?"
It is 100% blue.
All they know is that 900 people said it was blue, and 100 did not. You know nothing mo... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
You have a blue car (by some objective scientific measure - it is
blue).
...
"What is the probability that the car is blue?"
It is 100% blue.
All they know is that 900 people said it was blue, an |
1,463 | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | If we assume the car is blue, then 100 out of 1,000 saying it's not blue implies an extreme sample bias of some kind. Perhaps you were sampling only colour-blind people. If we assume the car is not blue, then the sample bias is even worse. So all we can conclude from the data given is that the sample is very biased, an... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | If we assume the car is blue, then 100 out of 1,000 saying it's not blue implies an extreme sample bias of some kind. Perhaps you were sampling only colour-blind people. If we assume the car is not bl | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
If we assume the car is blue, then 100 out of 1,000 saying it's not blue implies an extreme sample bias of some kind. Perhaps you were sampling only colour-blind people. If we assume the car is not blue, then the sample bias is even w... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
If we assume the car is blue, then 100 out of 1,000 saying it's not blue implies an extreme sample bias of some kind. Perhaps you were sampling only colour-blind people. If we assume the car is not bl |
1,464 | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | There have been some answers. I'm by no means a mathematics guru, but well, here is mine.
There can only be 4 possibilities:
case 1) Persons says car is blue and is correct
case 2) Person says car is blue and is incorrect
case 3) Person says car is not blue and is correct
case 4) Person says car is not blue and is inco... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | There have been some answers. I'm by no means a mathematics guru, but well, here is mine.
There can only be 4 possibilities:
case 1) Persons says car is blue and is correct
case 2) Person says car is | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
There have been some answers. I'm by no means a mathematics guru, but well, here is mine.
There can only be 4 possibilities:
case 1) Persons says car is blue and is correct
case 2) Person says car is blue and is incorrect
case 3) Pers... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
There have been some answers. I'm by no means a mathematics guru, but well, here is mine.
There can only be 4 possibilities:
case 1) Persons says car is blue and is correct
case 2) Person says car is |
1,465 | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | Let $X,Y_1,Y_2,\ldots,Y_{1000} \in \{0,1\}$ denote the true color, and the responses, respectively. "Blue" is coded as a $1$, and vice versa. Assume that $p(x)$ is Bernoulli with parameter $p_x$. Assume that each $Y_i|X=1$ is Bernoull with parameter $p_1$, and assume $Y_i|X=0$ is Bernoulli with parameter $p_0$. Also, p... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | Let $X,Y_1,Y_2,\ldots,Y_{1000} \in \{0,1\}$ denote the true color, and the responses, respectively. "Blue" is coded as a $1$, and vice versa. Assume that $p(x)$ is Bernoulli with parameter $p_x$. Assu | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
Let $X,Y_1,Y_2,\ldots,Y_{1000} \in \{0,1\}$ denote the true color, and the responses, respectively. "Blue" is coded as a $1$, and vice versa. Assume that $p(x)$ is Bernoulli with parameter $p_x$. Assume that each $Y_i|X=1$ is Bernoull... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
Let $X,Y_1,Y_2,\ldots,Y_{1000} \in \{0,1\}$ denote the true color, and the responses, respectively. "Blue" is coded as a $1$, and vice versa. Assume that $p(x)$ is Bernoulli with parameter $p_x$. Assu |
1,466 | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | The person that cannot see the car does not know it is scientifically proven to be blue. The probability to he/she that the car is blue is 50/50 (it is blue, or it isn't). Polling other people may influence this person's opinion but it does not change the probability that an unseen car is either blue, or not.
All of ... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue? | The person that cannot see the car does not know it is scientifically proven to be blue. The probability to he/she that the car is blue is 50/50 (it is blue, or it isn't). Polling other people may i | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
The person that cannot see the car does not know it is scientifically proven to be blue. The probability to he/she that the car is blue is 50/50 (it is blue, or it isn't). Polling other people may influence this person's opinion but... | If 900 out of 1000 people say a car is blue, what is the probability that it is blue?
The person that cannot see the car does not know it is scientifically proven to be blue. The probability to he/she that the car is blue is 50/50 (it is blue, or it isn't). Polling other people may i |
1,467 | ASA discusses limitations of $p$-values - what are the alternatives? | I will focus this answer on the specific question of what are the alternatives to $p$-values.
There are 21 discussion papers published along with the ASA statement (as Supplemental Materials): by Naomi Altman, Douglas Altman,
Daniel J. Benjamin, Yoav Benjamini, Jim Berger, Don Berry, John Carlin, George Cobb, Andrew Ge... | ASA discusses limitations of $p$-values - what are the alternatives? | I will focus this answer on the specific question of what are the alternatives to $p$-values.
There are 21 discussion papers published along with the ASA statement (as Supplemental Materials): by Naom | ASA discusses limitations of $p$-values - what are the alternatives?
I will focus this answer on the specific question of what are the alternatives to $p$-values.
There are 21 discussion papers published along with the ASA statement (as Supplemental Materials): by Naomi Altman, Douglas Altman,
Daniel J. Benjamin, Yoav ... | ASA discusses limitations of $p$-values - what are the alternatives?
I will focus this answer on the specific question of what are the alternatives to $p$-values.
There are 21 discussion papers published along with the ASA statement (as Supplemental Materials): by Naom |
1,468 | ASA discusses limitations of $p$-values - what are the alternatives? | Here is my two cents.
I think that at some point, many applied scientists stated the following "theorem":
Theorem 1: $p\text{-value}<0.05\Leftrightarrow \text{my hypothesis is true}.$
and most of the bad practices come from here.
The $p$-value and scientific induction
I used to work with people using statistics witho... | ASA discusses limitations of $p$-values - what are the alternatives? | Here is my two cents.
I think that at some point, many applied scientists stated the following "theorem":
Theorem 1: $p\text{-value}<0.05\Leftrightarrow \text{my hypothesis is true}.$
and most of th | ASA discusses limitations of $p$-values - what are the alternatives?
Here is my two cents.
I think that at some point, many applied scientists stated the following "theorem":
Theorem 1: $p\text{-value}<0.05\Leftrightarrow \text{my hypothesis is true}.$
and most of the bad practices come from here.
The $p$-value and s... | ASA discusses limitations of $p$-values - what are the alternatives?
Here is my two cents.
I think that at some point, many applied scientists stated the following "theorem":
Theorem 1: $p\text{-value}<0.05\Leftrightarrow \text{my hypothesis is true}.$
and most of th |
1,469 | ASA discusses limitations of $p$-values - what are the alternatives? | The only reasons I continue to use $P$-values are
More software is available for frequentist methods than Bayesian methods.
Currently, some Bayesian analyses take a long time to run.
Bayesian methods require more thinking and more time investment. I don't mind the thinking part but time is often short so we take shor... | ASA discusses limitations of $p$-values - what are the alternatives? | The only reasons I continue to use $P$-values are
More software is available for frequentist methods than Bayesian methods.
Currently, some Bayesian analyses take a long time to run.
Bayesian methods | ASA discusses limitations of $p$-values - what are the alternatives?
The only reasons I continue to use $P$-values are
More software is available for frequentist methods than Bayesian methods.
Currently, some Bayesian analyses take a long time to run.
Bayesian methods require more thinking and more time investment. I... | ASA discusses limitations of $p$-values - what are the alternatives?
The only reasons I continue to use $P$-values are
More software is available for frequentist methods than Bayesian methods.
Currently, some Bayesian analyses take a long time to run.
Bayesian methods |
1,470 | ASA discusses limitations of $p$-values - what are the alternatives? | In this thread, there is already a good amount of illuminating discussion on this subject. But let me ask you: "Alternatives to what exactly?" The damning thing about p-values is that they're forced to live between two worlds: decision theoretic inference and distribution free statistics. If you are looking for an alte... | ASA discusses limitations of $p$-values - what are the alternatives? | In this thread, there is already a good amount of illuminating discussion on this subject. But let me ask you: "Alternatives to what exactly?" The damning thing about p-values is that they're forced t | ASA discusses limitations of $p$-values - what are the alternatives?
In this thread, there is already a good amount of illuminating discussion on this subject. But let me ask you: "Alternatives to what exactly?" The damning thing about p-values is that they're forced to live between two worlds: decision theoretic infer... | ASA discusses limitations of $p$-values - what are the alternatives?
In this thread, there is already a good amount of illuminating discussion on this subject. But let me ask you: "Alternatives to what exactly?" The damning thing about p-values is that they're forced t |
1,471 | ASA discusses limitations of $p$-values - what are the alternatives? | A Brilliant forecaster Scott Armstrong from Wharton published an article a almost 10 years ago titled Significance Tests Harm Progress in Forecasting in the international journal of forecasting a journal that he co-founded. Even though this is in forecasting, it could be generalized to any data analysis or decision mak... | ASA discusses limitations of $p$-values - what are the alternatives? | A Brilliant forecaster Scott Armstrong from Wharton published an article a almost 10 years ago titled Significance Tests Harm Progress in Forecasting in the international journal of forecasting a jour | ASA discusses limitations of $p$-values - what are the alternatives?
A Brilliant forecaster Scott Armstrong from Wharton published an article a almost 10 years ago titled Significance Tests Harm Progress in Forecasting in the international journal of forecasting a journal that he co-founded. Even though this is in fore... | ASA discusses limitations of $p$-values - what are the alternatives?
A Brilliant forecaster Scott Armstrong from Wharton published an article a almost 10 years ago titled Significance Tests Harm Progress in Forecasting in the international journal of forecasting a jour |
1,472 | ASA discusses limitations of $p$-values - what are the alternatives? | What is preferred and why must depend on the field of study. About 30 years ago articles started appearing in medical journals suggesting that $p$-values should be replaced by estimates with confidence intervals. The basic reasoning was that $p$-values just tell you the effect was there whereas the estimate with its co... | ASA discusses limitations of $p$-values - what are the alternatives? | What is preferred and why must depend on the field of study. About 30 years ago articles started appearing in medical journals suggesting that $p$-values should be replaced by estimates with confidenc | ASA discusses limitations of $p$-values - what are the alternatives?
What is preferred and why must depend on the field of study. About 30 years ago articles started appearing in medical journals suggesting that $p$-values should be replaced by estimates with confidence intervals. The basic reasoning was that $p$-value... | ASA discusses limitations of $p$-values - what are the alternatives?
What is preferred and why must depend on the field of study. About 30 years ago articles started appearing in medical journals suggesting that $p$-values should be replaced by estimates with confidenc |
1,473 | ASA discusses limitations of $p$-values - what are the alternatives? | Decision theoretic modeling is superior to $p$-values because it requires the researcher to
develop a more sophisticated model that is capable of simulating outcomes in a target population
identify and measure attributes of a target population in whom a proposed decision, treatment, or policy could be implemented
esti... | ASA discusses limitations of $p$-values - what are the alternatives? | Decision theoretic modeling is superior to $p$-values because it requires the researcher to
develop a more sophisticated model that is capable of simulating outcomes in a target population
identify a | ASA discusses limitations of $p$-values - what are the alternatives?
Decision theoretic modeling is superior to $p$-values because it requires the researcher to
develop a more sophisticated model that is capable of simulating outcomes in a target population
identify and measure attributes of a target population in who... | ASA discusses limitations of $p$-values - what are the alternatives?
Decision theoretic modeling is superior to $p$-values because it requires the researcher to
develop a more sophisticated model that is capable of simulating outcomes in a target population
identify a |
1,474 | ASA discusses limitations of $p$-values - what are the alternatives? | There is a collection of alternatives in the special issue Statistical Inference in the 21st Century: A World Beyond p < 0.05 of The American Statistician that, I think, deserves special mention. I cannot possibly and won't try to list all the ideas about alternatives and/or additions to p-values that are given in the ... | ASA discusses limitations of $p$-values - what are the alternatives? | There is a collection of alternatives in the special issue Statistical Inference in the 21st Century: A World Beyond p < 0.05 of The American Statistician that, I think, deserves special mention. I ca | ASA discusses limitations of $p$-values - what are the alternatives?
There is a collection of alternatives in the special issue Statistical Inference in the 21st Century: A World Beyond p < 0.05 of The American Statistician that, I think, deserves special mention. I cannot possibly and won't try to list all the ideas a... | ASA discusses limitations of $p$-values - what are the alternatives?
There is a collection of alternatives in the special issue Statistical Inference in the 21st Century: A World Beyond p < 0.05 of The American Statistician that, I think, deserves special mention. I ca |
1,475 | ASA discusses limitations of $p$-values - what are the alternatives? | My choice would be to continue using p values, but simply adding confidence/credible intervals, and possibly for the primary outcomes prediction intervals. There is a very nice book by Douglas Altman (Statistics with Confidence, Wiley), and thanks to boostrap and MCMC approaches, you can always build reasonably robust ... | ASA discusses limitations of $p$-values - what are the alternatives? | My choice would be to continue using p values, but simply adding confidence/credible intervals, and possibly for the primary outcomes prediction intervals. There is a very nice book by Douglas Altman | ASA discusses limitations of $p$-values - what are the alternatives?
My choice would be to continue using p values, but simply adding confidence/credible intervals, and possibly for the primary outcomes prediction intervals. There is a very nice book by Douglas Altman (Statistics with Confidence, Wiley), and thanks to ... | ASA discusses limitations of $p$-values - what are the alternatives?
My choice would be to continue using p values, but simply adding confidence/credible intervals, and possibly for the primary outcomes prediction intervals. There is a very nice book by Douglas Altman |
1,476 | ASA discusses limitations of $p$-values - what are the alternatives? | The statistical community's responses to the problem tend to assume that the answer lies in statistics. (The applied research community's preferred response is to ignore the problem entirely.)
In a forthcoming comment, colleagues and I argue that purely statistical standard error underestimates uncertainty, and that b... | ASA discusses limitations of $p$-values - what are the alternatives? | The statistical community's responses to the problem tend to assume that the answer lies in statistics. (The applied research community's preferred response is to ignore the problem entirely.)
In a fo | ASA discusses limitations of $p$-values - what are the alternatives?
The statistical community's responses to the problem tend to assume that the answer lies in statistics. (The applied research community's preferred response is to ignore the problem entirely.)
In a forthcoming comment, colleagues and I argue that pure... | ASA discusses limitations of $p$-values - what are the alternatives?
The statistical community's responses to the problem tend to assume that the answer lies in statistics. (The applied research community's preferred response is to ignore the problem entirely.)
In a fo |
1,477 | What skills are required to perform large scale statistical analyses? | Good answers have already appeared. I will therefore just share some thoughts based on personal experience: adapt the relevant ones to your own situation as needed.
For background and context--so you can account for any personal biases that might creep in to this message--much of my work has been in helping people mak... | What skills are required to perform large scale statistical analyses? | Good answers have already appeared. I will therefore just share some thoughts based on personal experience: adapt the relevant ones to your own situation as needed.
For background and context--so you | What skills are required to perform large scale statistical analyses?
Good answers have already appeared. I will therefore just share some thoughts based on personal experience: adapt the relevant ones to your own situation as needed.
For background and context--so you can account for any personal biases that might cr... | What skills are required to perform large scale statistical analyses?
Good answers have already appeared. I will therefore just share some thoughts based on personal experience: adapt the relevant ones to your own situation as needed.
For background and context--so you |
1,478 | What skills are required to perform large scale statistical analyses? | Your question should yield some good answers. Here are some starting points.
An ability to work with the tradeoffs between precision and the demands placed on computing power.
Facility with data mining techniques that can be used as preliminary screening tools before conducting regression. E.g., chaid, cart, or neur... | What skills are required to perform large scale statistical analyses? | Your question should yield some good answers. Here are some starting points.
An ability to work with the tradeoffs between precision and the demands placed on computing power.
Facility with data min | What skills are required to perform large scale statistical analyses?
Your question should yield some good answers. Here are some starting points.
An ability to work with the tradeoffs between precision and the demands placed on computing power.
Facility with data mining techniques that can be used as preliminary scr... | What skills are required to perform large scale statistical analyses?
Your question should yield some good answers. Here are some starting points.
An ability to work with the tradeoffs between precision and the demands placed on computing power.
Facility with data min |
1,479 | What skills are required to perform large scale statistical analyses? | Good programming skills are a must. You need to be able to write efficient code that can deal with huge amounts of data without choking, and maybe be able to parallelize said code to get it to run in a reasonable amount of time. | What skills are required to perform large scale statistical analyses? | Good programming skills are a must. You need to be able to write efficient code that can deal with huge amounts of data without choking, and maybe be able to parallelize said code to get it to run in | What skills are required to perform large scale statistical analyses?
Good programming skills are a must. You need to be able to write efficient code that can deal with huge amounts of data without choking, and maybe be able to parallelize said code to get it to run in a reasonable amount of time. | What skills are required to perform large scale statistical analyses?
Good programming skills are a must. You need to be able to write efficient code that can deal with huge amounts of data without choking, and maybe be able to parallelize said code to get it to run in |
1,480 | What skills are required to perform large scale statistical analyses? | I would also add that the large scale data also introduces the problem of potential "Bad data". Not only missing data, but data errors and inconsistent definitions introduced by every piece of a system which ever touched the data. So, in additional to statistical skills, you need to become an expert data cleaner, unle... | What skills are required to perform large scale statistical analyses? | I would also add that the large scale data also introduces the problem of potential "Bad data". Not only missing data, but data errors and inconsistent definitions introduced by every piece of a syste | What skills are required to perform large scale statistical analyses?
I would also add that the large scale data also introduces the problem of potential "Bad data". Not only missing data, but data errors and inconsistent definitions introduced by every piece of a system which ever touched the data. So, in additional ... | What skills are required to perform large scale statistical analyses?
I would also add that the large scale data also introduces the problem of potential "Bad data". Not only missing data, but data errors and inconsistent definitions introduced by every piece of a syste |
1,481 | What skills are required to perform large scale statistical analyses? | Framing the problem in the Map-reduce framework.
The Engineering side of the problem, eg., how much does it hurt to use lower precision for the parameters, or model selection based not only on generalization but storage and computation costs as well. | What skills are required to perform large scale statistical analyses? | Framing the problem in the Map-reduce framework.
The Engineering side of the problem, eg., how much does it hurt to use lower precision for the parameters, or model selection based not only on general | What skills are required to perform large scale statistical analyses?
Framing the problem in the Map-reduce framework.
The Engineering side of the problem, eg., how much does it hurt to use lower precision for the parameters, or model selection based not only on generalization but storage and computation costs as well. | What skills are required to perform large scale statistical analyses?
Framing the problem in the Map-reduce framework.
The Engineering side of the problem, eg., how much does it hurt to use lower precision for the parameters, or model selection based not only on general |
1,482 | What is an ablation study? And is there a systematic way to perform it? | The original meaning of “Ablation” is the surgical removal of body tissue. The term “Ablation study” has its roots in the field of experimental neuropsychology of the 1960s and 1970s, where parts of animals’ brains were removed to study the effect that this had on their behaviour.
In the context of machine learning, a... | What is an ablation study? And is there a systematic way to perform it? | The original meaning of “Ablation” is the surgical removal of body tissue. The term “Ablation study” has its roots in the field of experimental neuropsychology of the 1960s and 1970s, where parts of | What is an ablation study? And is there a systematic way to perform it?
The original meaning of “Ablation” is the surgical removal of body tissue. The term “Ablation study” has its roots in the field of experimental neuropsychology of the 1960s and 1970s, where parts of animals’ brains were removed to study the effect... | What is an ablation study? And is there a systematic way to perform it?
The original meaning of “Ablation” is the surgical removal of body tissue. The term “Ablation study” has its roots in the field of experimental neuropsychology of the 1960s and 1970s, where parts of |
1,483 | Why isn't Logistic Regression called Logistic Classification? | Logistic regression is emphatically not a classification algorithm on its own. It is only a classification algorithm in combination with a decision rule that makes dichotomous the predicted probabilities of the outcome. Logistic regression is a regression model because it estimates the probability of class membership a... | Why isn't Logistic Regression called Logistic Classification? | Logistic regression is emphatically not a classification algorithm on its own. It is only a classification algorithm in combination with a decision rule that makes dichotomous the predicted probabilit | Why isn't Logistic Regression called Logistic Classification?
Logistic regression is emphatically not a classification algorithm on its own. It is only a classification algorithm in combination with a decision rule that makes dichotomous the predicted probabilities of the outcome. Logistic regression is a regression mo... | Why isn't Logistic Regression called Logistic Classification?
Logistic regression is emphatically not a classification algorithm on its own. It is only a classification algorithm in combination with a decision rule that makes dichotomous the predicted probabilit |
1,484 | Why isn't Logistic Regression called Logistic Classification? | Abstractly, regression is the problem of calculating a conditional expectation $E[Y|X=x]$. The form taken by this expectation is different depending on the assumptions of how the data were generated:
Assuming (Y|X=x) to be normally distributed yields with classical linear regression.
Assuming a Poisson distribution yi... | Why isn't Logistic Regression called Logistic Classification? | Abstractly, regression is the problem of calculating a conditional expectation $E[Y|X=x]$. The form taken by this expectation is different depending on the assumptions of how the data were generated:
| Why isn't Logistic Regression called Logistic Classification?
Abstractly, regression is the problem of calculating a conditional expectation $E[Y|X=x]$. The form taken by this expectation is different depending on the assumptions of how the data were generated:
Assuming (Y|X=x) to be normally distributed yields with c... | Why isn't Logistic Regression called Logistic Classification?
Abstractly, regression is the problem of calculating a conditional expectation $E[Y|X=x]$. The form taken by this expectation is different depending on the assumptions of how the data were generated:
|
1,485 | Why isn't Logistic Regression called Logistic Classification? | Blockquote
The U.S. Weather Service has always phrased rain forecasts as probabilities. I do not want a classification of “it will rain today.” There is a slight loss/disutility of carrying an umbrella, and I want to be the one to make the tradeoff.
Blockquote
Dr. Frank Harrell, https://www.fharrell.com/post/classific... | Why isn't Logistic Regression called Logistic Classification? | Blockquote
The U.S. Weather Service has always phrased rain forecasts as probabilities. I do not want a classification of “it will rain today.” There is a slight loss/disutility of carrying an umbrell | Why isn't Logistic Regression called Logistic Classification?
Blockquote
The U.S. Weather Service has always phrased rain forecasts as probabilities. I do not want a classification of “it will rain today.” There is a slight loss/disutility of carrying an umbrella, and I want to be the one to make the tradeoff.
Blockquo... | Why isn't Logistic Regression called Logistic Classification?
Blockquote
The U.S. Weather Service has always phrased rain forecasts as probabilities. I do not want a classification of “it will rain today.” There is a slight loss/disutility of carrying an umbrell |
1,486 | Why isn't Logistic Regression called Logistic Classification? | Apart from already provided good answers, another view is that Logistic regression predicts probabilities (which is continuous value) that have got range from 0 to 1. | Why isn't Logistic Regression called Logistic Classification? | Apart from already provided good answers, another view is that Logistic regression predicts probabilities (which is continuous value) that have got range from 0 to 1. | Why isn't Logistic Regression called Logistic Classification?
Apart from already provided good answers, another view is that Logistic regression predicts probabilities (which is continuous value) that have got range from 0 to 1. | Why isn't Logistic Regression called Logistic Classification?
Apart from already provided good answers, another view is that Logistic regression predicts probabilities (which is continuous value) that have got range from 0 to 1. |
1,487 | How do you calculate precision and recall for multiclass classification using confusion matrix? | In a 2-hypothesis case, the confusion matrix is usually:
Declare H1
Declare H0
Is H1
TP
FN
Is H0
FP
TN
where I've used something similar to your notation:
TP = true positive (declare H1 when, in truth, H1),
FN = false negative (declare H0 when, in truth, H1),
FP = false positive
TN = true negative
From... | How do you calculate precision and recall for multiclass classification using confusion matrix? | In a 2-hypothesis case, the confusion matrix is usually:
Declare H1
Declare H0
Is H1
TP
FN
Is H0
FP
TN
where I've used something similar to your notation:
TP = true positive (declare H | How do you calculate precision and recall for multiclass classification using confusion matrix?
In a 2-hypothesis case, the confusion matrix is usually:
Declare H1
Declare H0
Is H1
TP
FN
Is H0
FP
TN
where I've used something similar to your notation:
TP = true positive (declare H1 when, in truth, H1),
F... | How do you calculate precision and recall for multiclass classification using confusion matrix?
In a 2-hypothesis case, the confusion matrix is usually:
Declare H1
Declare H0
Is H1
TP
FN
Is H0
FP
TN
where I've used something similar to your notation:
TP = true positive (declare H |
1,488 | How do you calculate precision and recall for multiclass classification using confusion matrix? | Good summary paper, looking at these metrics for multi-class problems:
Sokolova, M., & Lapalme, G. (2009). A systematic analysis of performance measures for classification tasks. Information Processing and Management, 45, p. 427-437. (pdf)
The abstract reads:
This paper presents a systematic analysis of twen... | How do you calculate precision and recall for multiclass classification using confusion matrix? | Good summary paper, looking at these metrics for multi-class problems:
Sokolova, M., & Lapalme, G. (2009). A systematic analysis of performance measures for classification tasks. Information Proce | How do you calculate precision and recall for multiclass classification using confusion matrix?
Good summary paper, looking at these metrics for multi-class problems:
Sokolova, M., & Lapalme, G. (2009). A systematic analysis of performance measures for classification tasks. Information Processing and Management, 45... | How do you calculate precision and recall for multiclass classification using confusion matrix?
Good summary paper, looking at these metrics for multi-class problems:
Sokolova, M., & Lapalme, G. (2009). A systematic analysis of performance measures for classification tasks. Information Proce |
1,489 | How do you calculate precision and recall for multiclass classification using confusion matrix? | Using sklearn or tensorflow and numpy:
from sklearn.metrics import confusion_matrix
# or:
# from tensorflow.math import confusion_matrix
import numpy as np
labels = ...
predictions = ...
cm = confusion_matrix(labels, predictions)
recall = np.diag(cm) / np.sum(cm, axis = 1)
precision = np.diag(cm) / np.sum(cm, axis =... | How do you calculate precision and recall for multiclass classification using confusion matrix? | Using sklearn or tensorflow and numpy:
from sklearn.metrics import confusion_matrix
# or:
# from tensorflow.math import confusion_matrix
import numpy as np
labels = ...
predictions = ...
cm = confu | How do you calculate precision and recall for multiclass classification using confusion matrix?
Using sklearn or tensorflow and numpy:
from sklearn.metrics import confusion_matrix
# or:
# from tensorflow.math import confusion_matrix
import numpy as np
labels = ...
predictions = ...
cm = confusion_matrix(labels, pred... | How do you calculate precision and recall for multiclass classification using confusion matrix?
Using sklearn or tensorflow and numpy:
from sklearn.metrics import confusion_matrix
# or:
# from tensorflow.math import confusion_matrix
import numpy as np
labels = ...
predictions = ...
cm = confu |
1,490 | How do you calculate precision and recall for multiclass classification using confusion matrix? | @Cristian Garcia code can be reduced by sklearn.
>>> from sklearn.metrics import precision_score
>>> y_true = [0, 1, 2, 0, 1, 2]
>>> y_pred = [0, 2, 1, 0, 0, 1]
>>> precision_score(y_true, y_pred, average='micro') | How do you calculate precision and recall for multiclass classification using confusion matrix? | @Cristian Garcia code can be reduced by sklearn.
>>> from sklearn.metrics import precision_score
>>> y_true = [0, 1, 2, 0, 1, 2]
>>> y_pred = [0, 2, 1, 0, 0, 1]
>>> precision_score(y_true, y_pred, ave | How do you calculate precision and recall for multiclass classification using confusion matrix?
@Cristian Garcia code can be reduced by sklearn.
>>> from sklearn.metrics import precision_score
>>> y_true = [0, 1, 2, 0, 1, 2]
>>> y_pred = [0, 2, 1, 0, 0, 1]
>>> precision_score(y_true, y_pred, average='micro') | How do you calculate precision and recall for multiclass classification using confusion matrix?
@Cristian Garcia code can be reduced by sklearn.
>>> from sklearn.metrics import precision_score
>>> y_true = [0, 1, 2, 0, 1, 2]
>>> y_pred = [0, 2, 1, 0, 0, 1]
>>> precision_score(y_true, y_pred, ave |
1,491 | How do you calculate precision and recall for multiclass classification using confusion matrix? | Here is a different view from the other answers that I think will be helpful to others. The goal here is to allow you to compute these metrics using basic laws of probability.
First, it helps to understand what a confusion matrix is telling us in general. Let $Y$ represent a class label and $\hat Y$ represent a class p... | How do you calculate precision and recall for multiclass classification using confusion matrix? | Here is a different view from the other answers that I think will be helpful to others. The goal here is to allow you to compute these metrics using basic laws of probability.
First, it helps to under | How do you calculate precision and recall for multiclass classification using confusion matrix?
Here is a different view from the other answers that I think will be helpful to others. The goal here is to allow you to compute these metrics using basic laws of probability.
First, it helps to understand what a confusion m... | How do you calculate precision and recall for multiclass classification using confusion matrix?
Here is a different view from the other answers that I think will be helpful to others. The goal here is to allow you to compute these metrics using basic laws of probability.
First, it helps to under |
1,492 | What's a real-world example of "overfitting"? | Here's a nice example of presidential election time series models from xkcd:
There have only been 56 presidential elections and 43 presidents. That is not a lot of data to learn from. When the predictor space expands to include things like having false teeth and the Scrabble point value of names, it's pretty easy for ... | What's a real-world example of "overfitting"? | Here's a nice example of presidential election time series models from xkcd:
There have only been 56 presidential elections and 43 presidents. That is not a lot of data to learn from. When the predic | What's a real-world example of "overfitting"?
Here's a nice example of presidential election time series models from xkcd:
There have only been 56 presidential elections and 43 presidents. That is not a lot of data to learn from. When the predictor space expands to include things like having false teeth and the Scrabb... | What's a real-world example of "overfitting"?
Here's a nice example of presidential election time series models from xkcd:
There have only been 56 presidential elections and 43 presidents. That is not a lot of data to learn from. When the predic |
1,493 | What's a real-world example of "overfitting"? | My favorite was the Matlab example of US census population versus time:
A linear model is pretty good
A quadratic model is closer
A quartic model predicts total annihilation starting next year
(At least I sincerely hope this is an example of overfitting)
http://www.mathworks.com/help/curvefit/examples/polynomial-curv... | What's a real-world example of "overfitting"? | My favorite was the Matlab example of US census population versus time:
A linear model is pretty good
A quadratic model is closer
A quartic model predicts total annihilation starting next year
(At l | What's a real-world example of "overfitting"?
My favorite was the Matlab example of US census population versus time:
A linear model is pretty good
A quadratic model is closer
A quartic model predicts total annihilation starting next year
(At least I sincerely hope this is an example of overfitting)
http://www.mathwo... | What's a real-world example of "overfitting"?
My favorite was the Matlab example of US census population versus time:
A linear model is pretty good
A quadratic model is closer
A quartic model predicts total annihilation starting next year
(At l |
1,494 | What's a real-world example of "overfitting"? | The study of Chen et al. (2013) fits two cubics to a supposed discontinuity in life expectancy as a function of latitude.
Chen Y., Ebenstein, A., Greenstone, M., and Li, H. 2013. Evidence on the impact of sustained
exposure to air pollution on life expectancy from China's Huai River policy. Proceedings of the National... | What's a real-world example of "overfitting"? | The study of Chen et al. (2013) fits two cubics to a supposed discontinuity in life expectancy as a function of latitude.
Chen Y., Ebenstein, A., Greenstone, M., and Li, H. 2013. Evidence on the impa | What's a real-world example of "overfitting"?
The study of Chen et al. (2013) fits two cubics to a supposed discontinuity in life expectancy as a function of latitude.
Chen Y., Ebenstein, A., Greenstone, M., and Li, H. 2013. Evidence on the impact of sustained
exposure to air pollution on life expectancy from China's ... | What's a real-world example of "overfitting"?
The study of Chen et al. (2013) fits two cubics to a supposed discontinuity in life expectancy as a function of latitude.
Chen Y., Ebenstein, A., Greenstone, M., and Li, H. 2013. Evidence on the impa |
1,495 | What's a real-world example of "overfitting"? | In a March 14, 2014 article in Science, David Lazer, Ryan Kennedy, Gary King, and Alessandro Vespignani identified problems in Google Flu Trends that they attribute to overfitting.
Here is how they tell the story, including their explanation of the nature of the overfitting and why it caused the algorithm to fail:
In... | What's a real-world example of "overfitting"? | In a March 14, 2014 article in Science, David Lazer, Ryan Kennedy, Gary King, and Alessandro Vespignani identified problems in Google Flu Trends that they attribute to overfitting.
Here is how they t | What's a real-world example of "overfitting"?
In a March 14, 2014 article in Science, David Lazer, Ryan Kennedy, Gary King, and Alessandro Vespignani identified problems in Google Flu Trends that they attribute to overfitting.
Here is how they tell the story, including their explanation of the nature of the overfittin... | What's a real-world example of "overfitting"?
In a March 14, 2014 article in Science, David Lazer, Ryan Kennedy, Gary King, and Alessandro Vespignani identified problems in Google Flu Trends that they attribute to overfitting.
Here is how they t |
1,496 | What's a real-world example of "overfitting"? | I saw this image a few weeks ago and thought it was rather relevant to the question at hand.
Instead of linearly fitting the sequence, it was fitted with a quartic polynomial, which had perfect fit, but resulted in a clearly ridiculous answer. | What's a real-world example of "overfitting"? | I saw this image a few weeks ago and thought it was rather relevant to the question at hand.
Instead of linearly fitting the sequence, it was fitted with a quartic polynomial, which had perfect fit, | What's a real-world example of "overfitting"?
I saw this image a few weeks ago and thought it was rather relevant to the question at hand.
Instead of linearly fitting the sequence, it was fitted with a quartic polynomial, which had perfect fit, but resulted in a clearly ridiculous answer. | What's a real-world example of "overfitting"?
I saw this image a few weeks ago and thought it was rather relevant to the question at hand.
Instead of linearly fitting the sequence, it was fitted with a quartic polynomial, which had perfect fit, |
1,497 | What's a real-world example of "overfitting"? | To me the best example is Ptolemaic system in astronomy. Ptolemy assumed that Earth is at the center of the universe, and created a sophisticated system of nested circular orbits, which would explain movements of object on the sky pretty well. Astronomers had to keep adding circles to explain deviation, until one day i... | What's a real-world example of "overfitting"? | To me the best example is Ptolemaic system in astronomy. Ptolemy assumed that Earth is at the center of the universe, and created a sophisticated system of nested circular orbits, which would explain | What's a real-world example of "overfitting"?
To me the best example is Ptolemaic system in astronomy. Ptolemy assumed that Earth is at the center of the universe, and created a sophisticated system of nested circular orbits, which would explain movements of object on the sky pretty well. Astronomers had to keep adding... | What's a real-world example of "overfitting"?
To me the best example is Ptolemaic system in astronomy. Ptolemy assumed that Earth is at the center of the universe, and created a sophisticated system of nested circular orbits, which would explain |
1,498 | What's a real-world example of "overfitting"? | Let's say you have 100 dots on a graph.
You could say: hmm, I want to predict the next one.
with a line
with a 2nd order polynomial
with a 3rd order polynomial
...
with a 100th order polynomial
Here you can see a simplified illustration for this example:
The higher the polynomial order, the better it will fit the ex... | What's a real-world example of "overfitting"? | Let's say you have 100 dots on a graph.
You could say: hmm, I want to predict the next one.
with a line
with a 2nd order polynomial
with a 3rd order polynomial
...
with a 100th order polynomial
Here | What's a real-world example of "overfitting"?
Let's say you have 100 dots on a graph.
You could say: hmm, I want to predict the next one.
with a line
with a 2nd order polynomial
with a 3rd order polynomial
...
with a 100th order polynomial
Here you can see a simplified illustration for this example:
The higher the p... | What's a real-world example of "overfitting"?
Let's say you have 100 dots on a graph.
You could say: hmm, I want to predict the next one.
with a line
with a 2nd order polynomial
with a 3rd order polynomial
...
with a 100th order polynomial
Here |
1,499 | What's a real-world example of "overfitting"? | The analysis that may have contributed to the Fukushima disaster is an example of overfitting. There is a well known relationship in Earth Science that describes the probability of earthquakes of a certain size, given the observed frequency of "lesser" earthquakes. This is known as the Gutenberg-Richter relationship, a... | What's a real-world example of "overfitting"? | The analysis that may have contributed to the Fukushima disaster is an example of overfitting. There is a well known relationship in Earth Science that describes the probability of earthquakes of a ce | What's a real-world example of "overfitting"?
The analysis that may have contributed to the Fukushima disaster is an example of overfitting. There is a well known relationship in Earth Science that describes the probability of earthquakes of a certain size, given the observed frequency of "lesser" earthquakes. This is ... | What's a real-world example of "overfitting"?
The analysis that may have contributed to the Fukushima disaster is an example of overfitting. There is a well known relationship in Earth Science that describes the probability of earthquakes of a ce |
1,500 | What's a real-world example of "overfitting"? | "Agh! Pat is leaving the company. How are we ever going to find a replacement?"
Job Posting:
Wanted: Electrical Engineer.
42 year old androgynous person with degrees in Electrical Engineering, mathematics, and animal husbandry. Must be 68 inches tall with brown hair, a mole over the left eye, and prone to long winded... | What's a real-world example of "overfitting"? | "Agh! Pat is leaving the company. How are we ever going to find a replacement?"
Job Posting:
Wanted: Electrical Engineer.
42 year old androgynous person with degrees in Electrical Engineering, mathem | What's a real-world example of "overfitting"?
"Agh! Pat is leaving the company. How are we ever going to find a replacement?"
Job Posting:
Wanted: Electrical Engineer.
42 year old androgynous person with degrees in Electrical Engineering, mathematics, and animal husbandry. Must be 68 inches tall with brown hair, a mo... | What's a real-world example of "overfitting"?
"Agh! Pat is leaving the company. How are we ever going to find a replacement?"
Job Posting:
Wanted: Electrical Engineer.
42 year old androgynous person with degrees in Electrical Engineering, mathem |
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