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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301 | How to understand degrees of freedom? | This is a subtle question. It takes a thoughtful person not to understand those quotations! Although they are suggestive, it turns out that none of them is exactly or generally correct. I haven't the time (and there isn't the space here) to give a full exposition, but I would like to share one approach and an insigh... | How to understand degrees of freedom? | This is a subtle question. It takes a thoughtful person not to understand those quotations! Although they are suggestive, it turns out that none of them is exactly or generally correct. I haven't t | How to understand degrees of freedom?
This is a subtle question. It takes a thoughtful person not to understand those quotations! Although they are suggestive, it turns out that none of them is exactly or generally correct. I haven't the time (and there isn't the space here) to give a full exposition, but I would li... | How to understand degrees of freedom?
This is a subtle question. It takes a thoughtful person not to understand those quotations! Although they are suggestive, it turns out that none of them is exactly or generally correct. I haven't t |
302 | How to understand degrees of freedom? | Or simply: the number of elements in a numerical array that you're allowed to change so that the value of the statistic remains unchanged.
# for instance if:
x + y + z = 10
you can change, for instance, x and y at random, but you cannot change z (you can, but not at random, therefore you're not free to change it - see... | How to understand degrees of freedom? | Or simply: the number of elements in a numerical array that you're allowed to change so that the value of the statistic remains unchanged.
# for instance if:
x + y + z = 10
you can change, for instan | How to understand degrees of freedom?
Or simply: the number of elements in a numerical array that you're allowed to change so that the value of the statistic remains unchanged.
# for instance if:
x + y + z = 10
you can change, for instance, x and y at random, but you cannot change z (you can, but not at random, theref... | How to understand degrees of freedom?
Or simply: the number of elements in a numerical array that you're allowed to change so that the value of the statistic remains unchanged.
# for instance if:
x + y + z = 10
you can change, for instan |
303 | How to understand degrees of freedom? | The concept is not at all difficult to make mathematical precise given a bit of general knowledge of $n$-dimensional Euclidean geometry, subspaces and orthogonal projections.
If $P$ is an orthogonal projection from $\mathbb{R}^n$ to a $p$-dimensional subspace $L$ and $x$ is an arbitrary $n$-vector then $Px$ is in $L$, ... | How to understand degrees of freedom? | The concept is not at all difficult to make mathematical precise given a bit of general knowledge of $n$-dimensional Euclidean geometry, subspaces and orthogonal projections.
If $P$ is an orthogonal p | How to understand degrees of freedom?
The concept is not at all difficult to make mathematical precise given a bit of general knowledge of $n$-dimensional Euclidean geometry, subspaces and orthogonal projections.
If $P$ is an orthogonal projection from $\mathbb{R}^n$ to a $p$-dimensional subspace $L$ and $x$ is an arbi... | How to understand degrees of freedom?
The concept is not at all difficult to make mathematical precise given a bit of general knowledge of $n$-dimensional Euclidean geometry, subspaces and orthogonal projections.
If $P$ is an orthogonal p |
304 | How to understand degrees of freedom? | It's really no different from the way the term "degrees of freedom" works in any other field. For example, suppose you have four variables: the length, the width, the area, and the perimeter of a rectangle. Do you really know four things? No, because there are only two degrees of freedom. If you know the length and the... | How to understand degrees of freedom? | It's really no different from the way the term "degrees of freedom" works in any other field. For example, suppose you have four variables: the length, the width, the area, and the perimeter of a rect | How to understand degrees of freedom?
It's really no different from the way the term "degrees of freedom" works in any other field. For example, suppose you have four variables: the length, the width, the area, and the perimeter of a rectangle. Do you really know four things? No, because there are only two degrees of f... | How to understand degrees of freedom?
It's really no different from the way the term "degrees of freedom" works in any other field. For example, suppose you have four variables: the length, the width, the area, and the perimeter of a rect |
305 | How to understand degrees of freedom? | 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 really like first sentence from
The Little Handbook... | How to understand degrees of freedom? | 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.
| How to understand degrees of freedom?
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 really like fi... | How to understand degrees of freedom?
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.
|
306 | How to understand degrees of freedom? | Wikipedia asserts that degrees of freedom of a random vector can be interpreted as the dimensions of the vector subspace. I want to go step-by-step, very basically through this as a partial answer and elaboration on the Wikipedia entry.
The example proposed is that of a random vector corresponding to the measurements o... | How to understand degrees of freedom? | Wikipedia asserts that degrees of freedom of a random vector can be interpreted as the dimensions of the vector subspace. I want to go step-by-step, very basically through this as a partial answer and | How to understand degrees of freedom?
Wikipedia asserts that degrees of freedom of a random vector can be interpreted as the dimensions of the vector subspace. I want to go step-by-step, very basically through this as a partial answer and elaboration on the Wikipedia entry.
The example proposed is that of a random vect... | How to understand degrees of freedom?
Wikipedia asserts that degrees of freedom of a random vector can be interpreted as the dimensions of the vector subspace. I want to go step-by-step, very basically through this as a partial answer and |
307 | How to understand degrees of freedom? | In my classes, I use one "simple" situation that might help you wonder and perhaps develop a gut feeling for what a degree of freedom may mean.
It is kind of a "Forrest Gump" approach to the subject, but it is worth the try.
Consider you have 10 independent observations $X_1, X_2, \ldots, X_{10}\sim N(\mu,\sigma^2)$ th... | How to understand degrees of freedom? | In my classes, I use one "simple" situation that might help you wonder and perhaps develop a gut feeling for what a degree of freedom may mean.
It is kind of a "Forrest Gump" approach to the subject, | How to understand degrees of freedom?
In my classes, I use one "simple" situation that might help you wonder and perhaps develop a gut feeling for what a degree of freedom may mean.
It is kind of a "Forrest Gump" approach to the subject, but it is worth the try.
Consider you have 10 independent observations $X_1, X_2, ... | How to understand degrees of freedom?
In my classes, I use one "simple" situation that might help you wonder and perhaps develop a gut feeling for what a degree of freedom may mean.
It is kind of a "Forrest Gump" approach to the subject, |
308 | How to understand degrees of freedom? | This particular issue is quite frustrating for students in statistics courses, since they often cannot get a straight answer on exactly what a degree-of-freedom is defined to be. I will try to clear that up here. Suppose we have a random vector $\mathbf{x} \in \mathbb{R}^n$ and we form a new random vector $\mathbf{t}... | How to understand degrees of freedom? | This particular issue is quite frustrating for students in statistics courses, since they often cannot get a straight answer on exactly what a degree-of-freedom is defined to be. I will try to clear | How to understand degrees of freedom?
This particular issue is quite frustrating for students in statistics courses, since they often cannot get a straight answer on exactly what a degree-of-freedom is defined to be. I will try to clear that up here. Suppose we have a random vector $\mathbf{x} \in \mathbb{R}^n$ and w... | How to understand degrees of freedom?
This particular issue is quite frustrating for students in statistics courses, since they often cannot get a straight answer on exactly what a degree-of-freedom is defined to be. I will try to clear |
309 | How to understand degrees of freedom? | You can see the degree of freedom as the number of observations minus the number of necessary relations among these observations. By exemple if you have $n$ sample of independant normal distribution observations $X_1,\dots,X_n$. The random variable $\sum_{i=1}^n (X_i-\overline{X}_n)^2\sim \mathcal{X}^2_{n-1}$, where $\... | How to understand degrees of freedom? | You can see the degree of freedom as the number of observations minus the number of necessary relations among these observations. By exemple if you have $n$ sample of independant normal distribution o | How to understand degrees of freedom?
You can see the degree of freedom as the number of observations minus the number of necessary relations among these observations. By exemple if you have $n$ sample of independant normal distribution observations $X_1,\dots,X_n$. The random variable $\sum_{i=1}^n (X_i-\overline{X}_n... | How to understand degrees of freedom?
You can see the degree of freedom as the number of observations minus the number of necessary relations among these observations. By exemple if you have $n$ sample of independant normal distribution o |
310 | How to understand degrees of freedom? | The clearest "formal" definition of degrees-of-freedom is that it is the dimension of the space of allowable values for a random vector. This generally arises in a context where we have a sample vector $\mathbf{x} \in \mathbb{R}^n$ and we form a new random vector $\mathbf{t} = T(\mathbf{x})$ via the linear function $T... | How to understand degrees of freedom? | The clearest "formal" definition of degrees-of-freedom is that it is the dimension of the space of allowable values for a random vector. This generally arises in a context where we have a sample vect | How to understand degrees of freedom?
The clearest "formal" definition of degrees-of-freedom is that it is the dimension of the space of allowable values for a random vector. This generally arises in a context where we have a sample vector $\mathbf{x} \in \mathbb{R}^n$ and we form a new random vector $\mathbf{t} = T(\... | How to understand degrees of freedom?
The clearest "formal" definition of degrees-of-freedom is that it is the dimension of the space of allowable values for a random vector. This generally arises in a context where we have a sample vect |
311 | How to understand degrees of freedom? | An intuitive explanation of degrees of freedom is that they represent
the number of independent pieces of information available in the data for estimating a parameter (i.e., unknown quantity) of interest.
As an example, in a simple linear regression model of the form:
$$
Y_i=\beta_0 + \beta_1\cdot X_i + \epsilon_i,\q... | How to understand degrees of freedom? | An intuitive explanation of degrees of freedom is that they represent
the number of independent pieces of information available in the data for estimating a parameter (i.e., unknown quantity) of inter | How to understand degrees of freedom?
An intuitive explanation of degrees of freedom is that they represent
the number of independent pieces of information available in the data for estimating a parameter (i.e., unknown quantity) of interest.
As an example, in a simple linear regression model of the form:
$$
Y_i=\bet... | How to understand degrees of freedom?
An intuitive explanation of degrees of freedom is that they represent
the number of independent pieces of information available in the data for estimating a parameter (i.e., unknown quantity) of inter |
312 | How to understand degrees of freedom? | For me the first explanation I understood was:
If you know some statistical value like mean or variation, how many
variables of data you need to know before you can know the value of
every variable?
This is the same as aL3xa said, but without giving any data point a special role and close to the third case given ... | How to understand degrees of freedom? | For me the first explanation I understood was:
If you know some statistical value like mean or variation, how many
variables of data you need to know before you can know the value of
every variab | How to understand degrees of freedom?
For me the first explanation I understood was:
If you know some statistical value like mean or variation, how many
variables of data you need to know before you can know the value of
every variable?
This is the same as aL3xa said, but without giving any data point a special r... | How to understand degrees of freedom?
For me the first explanation I understood was:
If you know some statistical value like mean or variation, how many
variables of data you need to know before you can know the value of
every variab |
313 | How to understand degrees of freedom? | Think of it this way. Variances are additive when independent. For example, suppose we are throwing darts at a board and we measure the standard deviations of the $x$ and $y$ displacements from the exact center of the board. Then $V_{x,y}=V_x+V_y$. But, $V_x=SD_x^2$ if we take the square root of the $V_{x,y}$ formula, ... | How to understand degrees of freedom? | Think of it this way. Variances are additive when independent. For example, suppose we are throwing darts at a board and we measure the standard deviations of the $x$ and $y$ displacements from the ex | How to understand degrees of freedom?
Think of it this way. Variances are additive when independent. For example, suppose we are throwing darts at a board and we measure the standard deviations of the $x$ and $y$ displacements from the exact center of the board. Then $V_{x,y}=V_x+V_y$. But, $V_x=SD_x^2$ if we take the ... | How to understand degrees of freedom?
Think of it this way. Variances are additive when independent. For example, suppose we are throwing darts at a board and we measure the standard deviations of the $x$ and $y$ displacements from the ex |
314 | What's the difference between a confidence interval and a credible interval? | I agree completely with Srikant's explanation. To give a more heuristic spin on it:
Classical approaches generally posit that the world is one way (e.g., a parameter has one particular true value), and try to conduct experiments whose resulting conclusion -- no matter the true value of the parameter -- will be correct ... | What's the difference between a confidence interval and a credible interval? | I agree completely with Srikant's explanation. To give a more heuristic spin on it:
Classical approaches generally posit that the world is one way (e.g., a parameter has one particular true value), an | What's the difference between a confidence interval and a credible interval?
I agree completely with Srikant's explanation. To give a more heuristic spin on it:
Classical approaches generally posit that the world is one way (e.g., a parameter has one particular true value), and try to conduct experiments whose resultin... | What's the difference between a confidence interval and a credible interval?
I agree completely with Srikant's explanation. To give a more heuristic spin on it:
Classical approaches generally posit that the world is one way (e.g., a parameter has one particular true value), an |
315 | What's the difference between a confidence interval and a credible interval? | My understanding is as follows:
Background
Suppose that you have some data $x$ and you are trying to estimate $\theta$. You have a data generating process that describes how $x$ is generated conditional on $\theta$. In other words you know the distribution of $x$ (say, $f(x|\theta)$.
Inference Problem
Your inference pr... | What's the difference between a confidence interval and a credible interval? | My understanding is as follows:
Background
Suppose that you have some data $x$ and you are trying to estimate $\theta$. You have a data generating process that describes how $x$ is generated condition | What's the difference between a confidence interval and a credible interval?
My understanding is as follows:
Background
Suppose that you have some data $x$ and you are trying to estimate $\theta$. You have a data generating process that describes how $x$ is generated conditional on $\theta$. In other words you know the... | What's the difference between a confidence interval and a credible interval?
My understanding is as follows:
Background
Suppose that you have some data $x$ and you are trying to estimate $\theta$. You have a data generating process that describes how $x$ is generated condition |
316 | What's the difference between a confidence interval and a credible interval? | I disagree with Srikant's answer on one fundamental point. Srikant stated this:
"Inference Problem:
Your inference problem is: What values of θ are reasonable given the observed data x?"
In fact this is the BAYESIAN INFERENCE PROBLEM. In Bayesian statistics we seek to calculate P(θ| x) i.e the probability of the param... | What's the difference between a confidence interval and a credible interval? | I disagree with Srikant's answer on one fundamental point. Srikant stated this:
"Inference Problem:
Your inference problem is: What values of θ are reasonable given the observed data x?"
In fact this | What's the difference between a confidence interval and a credible interval?
I disagree with Srikant's answer on one fundamental point. Srikant stated this:
"Inference Problem:
Your inference problem is: What values of θ are reasonable given the observed data x?"
In fact this is the BAYESIAN INFERENCE PROBLEM. In Bayes... | What's the difference between a confidence interval and a credible interval?
I disagree with Srikant's answer on one fundamental point. Srikant stated this:
"Inference Problem:
Your inference problem is: What values of θ are reasonable given the observed data x?"
In fact this |
317 | What's the difference between a confidence interval and a credible interval? | The answers provided before are very helpful and detailed. Here is my $0.25.
Confidence interval (CI) is a concept based on the classical definition of probability (also called the "Frequentist definition") that probability is like proportion and is based on the axiomatic system of Kolmogrov (and others).
Credible int... | What's the difference between a confidence interval and a credible interval? | The answers provided before are very helpful and detailed. Here is my $0.25.
Confidence interval (CI) is a concept based on the classical definition of probability (also called the "Frequentist defini | What's the difference between a confidence interval and a credible interval?
The answers provided before are very helpful and detailed. Here is my $0.25.
Confidence interval (CI) is a concept based on the classical definition of probability (also called the "Frequentist definition") that probability is like proportion ... | What's the difference between a confidence interval and a credible interval?
The answers provided before are very helpful and detailed. Here is my $0.25.
Confidence interval (CI) is a concept based on the classical definition of probability (also called the "Frequentist defini |
318 | What's the difference between a confidence interval and a credible interval? | Always fun to engage in a bit of philosophy. I quite like Keith's response, however I would say that he is taking the position of "Mr forgetful Bayesia". The bad coverage when type B and type C can only come about if (s)he applies the same probability distribution at every trial, and refuses to update his(her) prior.... | What's the difference between a confidence interval and a credible interval? | Always fun to engage in a bit of philosophy. I quite like Keith's response, however I would say that he is taking the position of "Mr forgetful Bayesia". The bad coverage when type B and type C can | What's the difference between a confidence interval and a credible interval?
Always fun to engage in a bit of philosophy. I quite like Keith's response, however I would say that he is taking the position of "Mr forgetful Bayesia". The bad coverage when type B and type C can only come about if (s)he applies the same p... | What's the difference between a confidence interval and a credible interval?
Always fun to engage in a bit of philosophy. I quite like Keith's response, however I would say that he is taking the position of "Mr forgetful Bayesia". The bad coverage when type B and type C can |
319 | What's the difference between a confidence interval and a credible interval? | As I understand it: A credible interval is a statement of the range of values for the statistic of interest that remain plausible given the particular sample of data that we have actually observed. A confidence interval is a statement of the frequency with which the true value lies in the confidence interval when the ... | What's the difference between a confidence interval and a credible interval? | As I understand it: A credible interval is a statement of the range of values for the statistic of interest that remain plausible given the particular sample of data that we have actually observed. A | What's the difference between a confidence interval and a credible interval?
As I understand it: A credible interval is a statement of the range of values for the statistic of interest that remain plausible given the particular sample of data that we have actually observed. A confidence interval is a statement of the ... | What's the difference between a confidence interval and a credible interval?
As I understand it: A credible interval is a statement of the range of values for the statistic of interest that remain plausible given the particular sample of data that we have actually observed. A |
320 | What's the difference between a confidence interval and a credible interval? | I found a lot of interpretations about confidence interval and credible set are wrong. For example, confidence interval cannot be expressed in this format $P(\theta\in CI)$. If you look closely on the 'distributions' in the inference of frequentist and Bayesian, you will see Frequentist works on Sampling Distribution o... | What's the difference between a confidence interval and a credible interval? | I found a lot of interpretations about confidence interval and credible set are wrong. For example, confidence interval cannot be expressed in this format $P(\theta\in CI)$. If you look closely on the | What's the difference between a confidence interval and a credible interval?
I found a lot of interpretations about confidence interval and credible set are wrong. For example, confidence interval cannot be expressed in this format $P(\theta\in CI)$. If you look closely on the 'distributions' in the inference of freque... | What's the difference between a confidence interval and a credible interval?
I found a lot of interpretations about confidence interval and credible set are wrong. For example, confidence interval cannot be expressed in this format $P(\theta\in CI)$. If you look closely on the |
321 | What's the difference between a confidence interval and a credible interval? | Generic and consistent confidence and credible regions.
http://dx.doi.org/10.6084/m9.figshare.1528163
with code at
http://dx.doi.org/10.6084/m9.figshare.1528187
Provides a description of credible intervals and confidence intervals for set selection together with generic R code to calculate both given the likelihood fu... | What's the difference between a confidence interval and a credible interval? | Generic and consistent confidence and credible regions.
http://dx.doi.org/10.6084/m9.figshare.1528163
with code at
http://dx.doi.org/10.6084/m9.figshare.1528187
Provides a description of credible int | What's the difference between a confidence interval and a credible interval?
Generic and consistent confidence and credible regions.
http://dx.doi.org/10.6084/m9.figshare.1528163
with code at
http://dx.doi.org/10.6084/m9.figshare.1528187
Provides a description of credible intervals and confidence intervals for set sel... | What's the difference between a confidence interval and a credible interval?
Generic and consistent confidence and credible regions.
http://dx.doi.org/10.6084/m9.figshare.1528163
with code at
http://dx.doi.org/10.6084/m9.figshare.1528187
Provides a description of credible int |
322 | What's the difference between a confidence interval and a credible interval? | This is more of a comment but too long. In the following paper: The Dawning of the Age of Stochasticity
(David Mumford) Mumford have the following interesting comment:
While all these really exciting uses were being made of statistics,
the majority of statisticians themselves, led by Sir R.A. Fisher, were
tying th... | What's the difference between a confidence interval and a credible interval? | This is more of a comment but too long. In the following paper: The Dawning of the Age of Stochasticity
(David Mumford) Mumford have the following interesting comment:
While all these really exci | What's the difference between a confidence interval and a credible interval?
This is more of a comment but too long. In the following paper: The Dawning of the Age of Stochasticity
(David Mumford) Mumford have the following interesting comment:
While all these really exciting uses were being made of statistics,
th... | What's the difference between a confidence interval and a credible interval?
This is more of a comment but too long. In the following paper: The Dawning of the Age of Stochasticity
(David Mumford) Mumford have the following interesting comment:
While all these really exci |
323 | What's the difference between a confidence interval and a credible interval? | Both the confidence interval and the credible interval address the question, "what values of the parameter are consistent with the observed data." The confidence interval does so by identifying those hypotheses for which the observed result is within a $100(1-\alpha)\%$ margin of error, while the credible interval doe... | What's the difference between a confidence interval and a credible interval? | Both the confidence interval and the credible interval address the question, "what values of the parameter are consistent with the observed data." The confidence interval does so by identifying those | What's the difference between a confidence interval and a credible interval?
Both the confidence interval and the credible interval address the question, "what values of the parameter are consistent with the observed data." The confidence interval does so by identifying those hypotheses for which the observed result i... | What's the difference between a confidence interval and a credible interval?
Both the confidence interval and the credible interval address the question, "what values of the parameter are consistent with the observed data." The confidence interval does so by identifying those |
324 | Bagging, boosting and stacking in machine learning | All three are so-called "meta-algorithms": approaches to combine several machine learning techniques into one predictive model in order to decrease the variance (bagging), bias (boosting) or improving the predictive force (stacking alias ensemble).
Every algorithm consists of two steps:
Producing a distribution of sim... | Bagging, boosting and stacking in machine learning | All three are so-called "meta-algorithms": approaches to combine several machine learning techniques into one predictive model in order to decrease the variance (bagging), bias (boosting) or improving | Bagging, boosting and stacking in machine learning
All three are so-called "meta-algorithms": approaches to combine several machine learning techniques into one predictive model in order to decrease the variance (bagging), bias (boosting) or improving the predictive force (stacking alias ensemble).
Every algorithm cons... | Bagging, boosting and stacking in machine learning
All three are so-called "meta-algorithms": approaches to combine several machine learning techniques into one predictive model in order to decrease the variance (bagging), bias (boosting) or improving |
325 | Bagging, boosting and stacking in machine learning | Bagging:
parallel ensemble: each model is built independently
aim to decrease variance, not bias
suitable for high variance low bias models (complex models)
an example of a tree based method is random forest, which develop fully grown trees (note that RF modifies the grown procedure to reduce the correlation between... | Bagging, boosting and stacking in machine learning | Bagging:
parallel ensemble: each model is built independently
aim to decrease variance, not bias
suitable for high variance low bias models (complex models)
an example of a tree based method is ran | Bagging, boosting and stacking in machine learning
Bagging:
parallel ensemble: each model is built independently
aim to decrease variance, not bias
suitable for high variance low bias models (complex models)
an example of a tree based method is random forest, which develop fully grown trees (note that RF modifies th... | Bagging, boosting and stacking in machine learning
Bagging:
parallel ensemble: each model is built independently
aim to decrease variance, not bias
suitable for high variance low bias models (complex models)
an example of a tree based method is ran |
326 | Bagging, boosting and stacking in machine learning | Just to elaborate on Yuqian's answer a bit. The idea behind bagging is that when you OVERFIT with a nonparametric regression method (usually regression or classification trees, but can be just about any nonparametric method), you tend to go to the high variance, no (or low) bias part of the bias/variance tradeoff. Th... | Bagging, boosting and stacking in machine learning | Just to elaborate on Yuqian's answer a bit. The idea behind bagging is that when you OVERFIT with a nonparametric regression method (usually regression or classification trees, but can be just about | Bagging, boosting and stacking in machine learning
Just to elaborate on Yuqian's answer a bit. The idea behind bagging is that when you OVERFIT with a nonparametric regression method (usually regression or classification trees, but can be just about any nonparametric method), you tend to go to the high variance, no (o... | Bagging, boosting and stacking in machine learning
Just to elaborate on Yuqian's answer a bit. The idea behind bagging is that when you OVERFIT with a nonparametric regression method (usually regression or classification trees, but can be just about |
327 | Bagging, boosting and stacking in machine learning | See my ensemble learning blog post
Sources for this image:
Wikipedia
sklearn | Bagging, boosting and stacking in machine learning | See my ensemble learning blog post
Sources for this image:
Wikipedia
sklearn | Bagging, boosting and stacking in machine learning
See my ensemble learning blog post
Sources for this image:
Wikipedia
sklearn | Bagging, boosting and stacking in machine learning
See my ensemble learning blog post
Sources for this image:
Wikipedia
sklearn |
328 | Bagging, boosting and stacking in machine learning | To recap in short, Bagging and Boosting are normally used inside one algorithm, while Stacking is usually used to summarize several results from different algorithms.
Bagging: Bootstrap subsets of features and samples to get several predictions and average(or other ways) the results, for example, Random Forest, which ... | Bagging, boosting and stacking in machine learning | To recap in short, Bagging and Boosting are normally used inside one algorithm, while Stacking is usually used to summarize several results from different algorithms.
Bagging: Bootstrap subsets of fe | Bagging, boosting and stacking in machine learning
To recap in short, Bagging and Boosting are normally used inside one algorithm, while Stacking is usually used to summarize several results from different algorithms.
Bagging: Bootstrap subsets of features and samples to get several predictions and average(or other wa... | Bagging, boosting and stacking in machine learning
To recap in short, Bagging and Boosting are normally used inside one algorithm, while Stacking is usually used to summarize several results from different algorithms.
Bagging: Bootstrap subsets of fe |
329 | Bagging, boosting and stacking in machine learning | Bagging
Bootstrap AGGregatING (Bagging) is an ensemble generation method that uses variations of samples used to train base classifiers. For each classifier to be generated, Bagging selects (with repetition) N samples from the training set with size N and train a base classifier. This is repeated until the desired size... | Bagging, boosting and stacking in machine learning | Bagging
Bootstrap AGGregatING (Bagging) is an ensemble generation method that uses variations of samples used to train base classifiers. For each classifier to be generated, Bagging selects (with repe | Bagging, boosting and stacking in machine learning
Bagging
Bootstrap AGGregatING (Bagging) is an ensemble generation method that uses variations of samples used to train base classifiers. For each classifier to be generated, Bagging selects (with repetition) N samples from the training set with size N and train a base ... | Bagging, boosting and stacking in machine learning
Bagging
Bootstrap AGGregatING (Bagging) is an ensemble generation method that uses variations of samples used to train base classifiers. For each classifier to be generated, Bagging selects (with repe |
330 | Bagging, boosting and stacking in machine learning | both bagging and boosting use a single learning algorithm for all steps; but they use different methods on handling training samples. both are ensemble learning method that combines decisions from multiple models
Bagging:
1. resamples training data to get M subsets (bootstrapping);
2. trains M classifiers(same algori... | Bagging, boosting and stacking in machine learning | both bagging and boosting use a single learning algorithm for all steps; but they use different methods on handling training samples. both are ensemble learning method that combines decisions from mul | Bagging, boosting and stacking in machine learning
both bagging and boosting use a single learning algorithm for all steps; but they use different methods on handling training samples. both are ensemble learning method that combines decisions from multiple models
Bagging:
1. resamples training data to get M subsets (b... | Bagging, boosting and stacking in machine learning
both bagging and boosting use a single learning algorithm for all steps; but they use different methods on handling training samples. both are ensemble learning method that combines decisions from mul |
331 | Bagging, boosting and stacking in machine learning | Bagging and boosting tend to use many homogeneous models.
Stacking combines results from heterogenous model types.
As no single model type tends to be the best fit across any entire distribution you can see why this may increase predictive power. | Bagging, boosting and stacking in machine learning | Bagging and boosting tend to use many homogeneous models.
Stacking combines results from heterogenous model types.
As no single model type tends to be the best fit across any entire distribution you | Bagging, boosting and stacking in machine learning
Bagging and boosting tend to use many homogeneous models.
Stacking combines results from heterogenous model types.
As no single model type tends to be the best fit across any entire distribution you can see why this may increase predictive power. | Bagging, boosting and stacking in machine learning
Bagging and boosting tend to use many homogeneous models.
Stacking combines results from heterogenous model types.
As no single model type tends to be the best fit across any entire distribution you |
332 | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | Part of the issue is that the frequentist definition of a probability doesn't allow a nontrivial probability to be applied to the outcome of a particular experiment, but only to some fictitious population of experiments from which this particular experiment can be considered a sample. The definition of a CI is confusi... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | Part of the issue is that the frequentist definition of a probability doesn't allow a nontrivial probability to be applied to the outcome of a particular experiment, but only to some fictitious popula | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
Part of the issue is that the frequentist definition of a probability doesn't allow a nontrivial probability to be applied to the outcome of a particular experiment, but only to some fictitious population of experiments from which th... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
Part of the issue is that the frequentist definition of a probability doesn't allow a nontrivial probability to be applied to the outcome of a particular experiment, but only to some fictitious popula |
333 | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | In frequentist statistics probabilities are about events in the long run. They just don't apply to a single event after it's done. And the running of an experiment and calculation of the CI is just such an event.
You wanted to compare it to the probability of a hidden coin being heads but you can't. You can relate it t... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | In frequentist statistics probabilities are about events in the long run. They just don't apply to a single event after it's done. And the running of an experiment and calculation of the CI is just su | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
In frequentist statistics probabilities are about events in the long run. They just don't apply to a single event after it's done. And the running of an experiment and calculation of the CI is just such an event.
You wanted to compar... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
In frequentist statistics probabilities are about events in the long run. They just don't apply to a single event after it's done. And the running of an experiment and calculation of the CI is just su |
334 | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | Formal, explicit ideas about arguments, inference and logic originated, within the Western tradition, with Aristotle. Aristotle wrote about these topics in several different works (including one called the Topics ;-) ). However, the most basic single principle is The Law of Non-contradiction, which can be found in va... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | Formal, explicit ideas about arguments, inference and logic originated, within the Western tradition, with Aristotle. Aristotle wrote about these topics in several different works (including one call | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
Formal, explicit ideas about arguments, inference and logic originated, within the Western tradition, with Aristotle. Aristotle wrote about these topics in several different works (including one called the Topics ;-) ). However, th... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
Formal, explicit ideas about arguments, inference and logic originated, within the Western tradition, with Aristotle. Aristotle wrote about these topics in several different works (including one call |
335 | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | Why does a 95% CI not imply a 95% chance of containing the mean?
There are many issues to be clarified in this question and in the majority of the given responses. I shall confine myself only to two of them.
a. What is a population mean? Does exist a true population mean?
The concept of population mean is model-depende... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | Why does a 95% CI not imply a 95% chance of containing the mean?
There are many issues to be clarified in this question and in the majority of the given responses. I shall confine myself only to two o | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
Why does a 95% CI not imply a 95% chance of containing the mean?
There are many issues to be clarified in this question and in the majority of the given responses. I shall confine myself only to two of them.
a. What is a population m... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
Why does a 95% CI not imply a 95% chance of containing the mean?
There are many issues to be clarified in this question and in the majority of the given responses. I shall confine myself only to two o |
336 | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | I'm surprised that no one has brought up Berger's example of an essentially useless 75% confidence interval described in the second chapter of "The Likelihood Principle". The details can be found in the original text (which is available for free on Project Euclid): what is essential about the example is that it describ... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | I'm surprised that no one has brought up Berger's example of an essentially useless 75% confidence interval described in the second chapter of "The Likelihood Principle". The details can be found in t | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
I'm surprised that no one has brought up Berger's example of an essentially useless 75% confidence interval described in the second chapter of "The Likelihood Principle". The details can be found in the original text (which is availa... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
I'm surprised that no one has brought up Berger's example of an essentially useless 75% confidence interval described in the second chapter of "The Likelihood Principle". The details can be found in t |
337 | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | I don't know whether this should be asked as a new question but it is addressing the very same question asked above by proposing a thought experiment.
Firstly, I'm going to assume that if I select a playing card at random from a standard deck, the probability that I've selected a club (without looking at it) is 13 / 52... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | I don't know whether this should be asked as a new question but it is addressing the very same question asked above by proposing a thought experiment.
Firstly, I'm going to assume that if I select a p | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
I don't know whether this should be asked as a new question but it is addressing the very same question asked above by proposing a thought experiment.
Firstly, I'm going to assume that if I select a playing card at random from a stan... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
I don't know whether this should be asked as a new question but it is addressing the very same question asked above by proposing a thought experiment.
Firstly, I'm going to assume that if I select a p |
338 | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | For practical purposes, you're no more wrong to bet that your 95% CI included the true mean at 95:5 odds, than you are to bet on your friend's coin flip at 50:50 odds.
If your friend already flipped the coin, and you think there's a 50% probability of it being heads, then you're just using a different definition of the... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | For practical purposes, you're no more wrong to bet that your 95% CI included the true mean at 95:5 odds, than you are to bet on your friend's coin flip at 50:50 odds.
If your friend already flipped t | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
For practical purposes, you're no more wrong to bet that your 95% CI included the true mean at 95:5 odds, than you are to bet on your friend's coin flip at 50:50 odds.
If your friend already flipped the coin, and you think there's a ... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
For practical purposes, you're no more wrong to bet that your 95% CI included the true mean at 95:5 odds, than you are to bet on your friend's coin flip at 50:50 odds.
If your friend already flipped t |
339 | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | While there has been extensive discussion in the numerous great answers, I want to add a more simple perspective. (although it has been alluded in other answers - but not explicitly.) For some parameter $\theta$, and given a sample $(X_1,X_2,\cdots,X_n)$, a $100p\%$ confidence interval is a probability statement of the... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | While there has been extensive discussion in the numerous great answers, I want to add a more simple perspective. (although it has been alluded in other answers - but not explicitly.) For some paramet | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
While there has been extensive discussion in the numerous great answers, I want to add a more simple perspective. (although it has been alluded in other answers - but not explicitly.) For some parameter $\theta$, and given a sample $... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
While there has been extensive discussion in the numerous great answers, I want to add a more simple perspective. (although it has been alluded in other answers - but not explicitly.) For some paramet |
340 | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | It all depends on whether you are looking at the probability conditional or unconditional on the data. Suppose you have an unknown parameter $\theta \in \Theta$ and you make a confidence interval for this parameter using sample data $\mathbf{x}$. Let $\text{CI}_\theta(\mathbf{X},1-\alpha)$ denote the (random) confide... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | It all depends on whether you are looking at the probability conditional or unconditional on the data. Suppose you have an unknown parameter $\theta \in \Theta$ and you make a confidence interval for | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
It all depends on whether you are looking at the probability conditional or unconditional on the data. Suppose you have an unknown parameter $\theta \in \Theta$ and you make a confidence interval for this parameter using sample data... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
It all depends on whether you are looking at the probability conditional or unconditional on the data. Suppose you have an unknown parameter $\theta \in \Theta$ and you make a confidence interval for |
341 | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | In this answer to a different question, Are there any examples where Bayesian credible intervals are obviously inferior to frequentist confidence intervals, I explained a difference between confidence intervals and credible intervals. Both intervals can be constructed such that they will contain a certain fraction of t... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | In this answer to a different question, Are there any examples where Bayesian credible intervals are obviously inferior to frequentist confidence intervals, I explained a difference between confidence | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
In this answer to a different question, Are there any examples where Bayesian credible intervals are obviously inferior to frequentist confidence intervals, I explained a difference between confidence intervals and credible intervals... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
In this answer to a different question, Are there any examples where Bayesian credible intervals are obviously inferior to frequentist confidence intervals, I explained a difference between confidence |
342 | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | Say that the CI you calculated from the particular set of data you have is one of the 5% of possible CIs that does not contain the mean. How close is it to being the 95% credible interval that you would like to imagine it to be? (That is, how close is it to containing the mean with 95% probability?) You have no assuran... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | Say that the CI you calculated from the particular set of data you have is one of the 5% of possible CIs that does not contain the mean. How close is it to being the 95% credible interval that you wou | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
Say that the CI you calculated from the particular set of data you have is one of the 5% of possible CIs that does not contain the mean. How close is it to being the 95% credible interval that you would like to imagine it to be? (Tha... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
Say that the CI you calculated from the particular set of data you have is one of the 5% of possible CIs that does not contain the mean. How close is it to being the 95% credible interval that you wou |
343 | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | First, let's give a definition of the confidence interval, or, in spaces of dimension greater than one, the confidence region. The definition is a concise version of that given by Jerzy Neyman in his 1937 paper to the Royal Society.
Let the parameter be $\mathfrak{p}$ and the statistic be $\mathfrak{s}$. Each possible ... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | First, let's give a definition of the confidence interval, or, in spaces of dimension greater than one, the confidence region. The definition is a concise version of that given by Jerzy Neyman in his | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
First, let's give a definition of the confidence interval, or, in spaces of dimension greater than one, the confidence region. The definition is a concise version of that given by Jerzy Neyman in his 1937 paper to the Royal Society.
... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
First, let's give a definition of the confidence interval, or, in spaces of dimension greater than one, the confidence region. The definition is a concise version of that given by Jerzy Neyman in his |
344 | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | What one should not say when using frequentist inference is, "There is 95% probability that the unknown fixed true theta is within the computed confidence interval." To the frequentist probability describes the emergent pattern over many (observable!) samples and is not a statement about a single event. However, unders... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | What one should not say when using frequentist inference is, "There is 95% probability that the unknown fixed true theta is within the computed confidence interval." To the frequentist probability des | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
What one should not say when using frequentist inference is, "There is 95% probability that the unknown fixed true theta is within the computed confidence interval." To the frequentist probability describes the emergent pattern over ... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
What one should not say when using frequentist inference is, "There is 95% probability that the unknown fixed true theta is within the computed confidence interval." To the frequentist probability des |
345 | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | In his answer, Dikran Marsupial provides the following example as evidence that no confidence interval is admissible as a set of plausible parameter values consistent with the observed data:
Let the parameter of interest be $\theta$ and the data $D$, a pair of
points $x_1$ and $x_2$ drawn independently from the follow... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | In his answer, Dikran Marsupial provides the following example as evidence that no confidence interval is admissible as a set of plausible parameter values consistent with the observed data:
Let the | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
In his answer, Dikran Marsupial provides the following example as evidence that no confidence interval is admissible as a set of plausible parameter values consistent with the observed data:
Let the parameter of interest be $\theta$... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
In his answer, Dikran Marsupial provides the following example as evidence that no confidence interval is admissible as a set of plausible parameter values consistent with the observed data:
Let the |
346 | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | There are some interesting answers here, but I thought I'd add a little hands-on demonstration using R. We recently used this code in a stats course to highlight how confidence intervals work. Here's what the code does:
1 - It samples from a known distribution (n=1000)
2 - It calculates the 95% CI for the mean of eac... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | There are some interesting answers here, but I thought I'd add a little hands-on demonstration using R. We recently used this code in a stats course to highlight how confidence intervals work. Here' | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
There are some interesting answers here, but I thought I'd add a little hands-on demonstration using R. We recently used this code in a stats course to highlight how confidence intervals work. Here's what the code does:
1 - It samp... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
There are some interesting answers here, but I thought I'd add a little hands-on demonstration using R. We recently used this code in a stats course to highlight how confidence intervals work. Here' |
347 | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | I've always wondered this myself. My statistics background is limited, but here are the two different thoughts that made the difference clear to me.
If you flip a fair coin 20 times and get 18 heads. Does your confidence interval have a 95% chance of containing 10? Obviously not. The probability only works the other wa... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean? | I've always wondered this myself. My statistics background is limited, but here are the two different thoughts that made the difference clear to me.
If you flip a fair coin 20 times and get 18 heads. | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
I've always wondered this myself. My statistics background is limited, but here are the two different thoughts that made the difference clear to me.
If you flip a fair coin 20 times and get 18 heads. Does your confidence interval hav... | Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
I've always wondered this myself. My statistics background is limited, but here are the two different thoughts that made the difference clear to me.
If you flip a fair coin 20 times and get 18 heads. |
348 | What is batch size in neural network? | The batch size defines the number of samples that will be propagated through the network.
For instance, let's say you have 1050 training samples and you want to set up a batch_size equal to 100. The algorithm takes the first 100 samples (from 1st to 100th) from the training dataset and trains the network. Next, it take... | What is batch size in neural network? | The batch size defines the number of samples that will be propagated through the network.
For instance, let's say you have 1050 training samples and you want to set up a batch_size equal to 100. The a | What is batch size in neural network?
The batch size defines the number of samples that will be propagated through the network.
For instance, let's say you have 1050 training samples and you want to set up a batch_size equal to 100. The algorithm takes the first 100 samples (from 1st to 100th) from the training dataset... | What is batch size in neural network?
The batch size defines the number of samples that will be propagated through the network.
For instance, let's say you have 1050 training samples and you want to set up a batch_size equal to 100. The a |
349 | What is batch size in neural network? | In the neural network terminology:
one epoch = one forward pass and one backward pass of all the training examples
batch size = the number of training examples in one forward/backward pass. The higher the batch size, the more memory space you'll need.
number of iterations = number of passes, each pass using [batch si... | What is batch size in neural network? | In the neural network terminology:
one epoch = one forward pass and one backward pass of all the training examples
batch size = the number of training examples in one forward/backward pass. The highe | What is batch size in neural network?
In the neural network terminology:
one epoch = one forward pass and one backward pass of all the training examples
batch size = the number of training examples in one forward/backward pass. The higher the batch size, the more memory space you'll need.
number of iterations = numbe... | What is batch size in neural network?
In the neural network terminology:
one epoch = one forward pass and one backward pass of all the training examples
batch size = the number of training examples in one forward/backward pass. The highe |
350 | What is batch size in neural network? | The question has been asked a while ago but I think people are still tumbling across it. For me it helped to know about the mathematical background to understand batching and where the advantages/disadvantages mentioned in itdxer's answer come from. So please take this as a complementary explanation to the accepted ans... | What is batch size in neural network? | The question has been asked a while ago but I think people are still tumbling across it. For me it helped to know about the mathematical background to understand batching and where the advantages/disa | What is batch size in neural network?
The question has been asked a while ago but I think people are still tumbling across it. For me it helped to know about the mathematical background to understand batching and where the advantages/disadvantages mentioned in itdxer's answer come from. So please take this as a complem... | What is batch size in neural network?
The question has been asked a while ago but I think people are still tumbling across it. For me it helped to know about the mathematical background to understand batching and where the advantages/disa |
351 | What is batch size in neural network? | When solving with a CPU or a GPU an Optimization Problem, you iteratively apply an Algorithm over some Input Data. In each of these iterations you usually update a Metric of your problem doing some Calculations on the Data. Now when the size of your data is large it might need a considerable amount of time to complete ... | What is batch size in neural network? | When solving with a CPU or a GPU an Optimization Problem, you iteratively apply an Algorithm over some Input Data. In each of these iterations you usually update a Metric of your problem doing some Ca | What is batch size in neural network?
When solving with a CPU or a GPU an Optimization Problem, you iteratively apply an Algorithm over some Input Data. In each of these iterations you usually update a Metric of your problem doing some Calculations on the Data. Now when the size of your data is large it might need a co... | What is batch size in neural network?
When solving with a CPU or a GPU an Optimization Problem, you iteratively apply an Algorithm over some Input Data. In each of these iterations you usually update a Metric of your problem doing some Ca |
352 | What is batch size in neural network? | The documentation for Keras about batch size can be found under the fit function in the Models (functional API) page
batch_size: Integer or None. Number of samples per gradient update.
If unspecified, batch_size will default to 32.
If you have a small dataset, it would be best to make the batch size equal to the si... | What is batch size in neural network? | The documentation for Keras about batch size can be found under the fit function in the Models (functional API) page
batch_size: Integer or None. Number of samples per gradient update.
If unspecifi | What is batch size in neural network?
The documentation for Keras about batch size can be found under the fit function in the Models (functional API) page
batch_size: Integer or None. Number of samples per gradient update.
If unspecified, batch_size will default to 32.
If you have a small dataset, it would be best ... | What is batch size in neural network?
The documentation for Keras about batch size can be found under the fit function in the Models (functional API) page
batch_size: Integer or None. Number of samples per gradient update.
If unspecifi |
353 | What is batch size in neural network? | Batch size is a hyperparameter that define number of sample to work through before updating internal model parameters. | What is batch size in neural network? | Batch size is a hyperparameter that define number of sample to work through before updating internal model parameters. | What is batch size in neural network?
Batch size is a hyperparameter that define number of sample to work through before updating internal model parameters. | What is batch size in neural network?
Batch size is a hyperparameter that define number of sample to work through before updating internal model parameters. |
354 | What is the meaning of p values and t values in statistical tests? | Understanding $p$-value
Suppose, that you want to test the hypothesis that the average height of male students at your University is $5$ ft $7$ inches. You collect heights of $100$ students selected at random and compute the sample mean (say it turns out to be $5$ ft $9$ inches). Using an appropriate formula/statistica... | What is the meaning of p values and t values in statistical tests? | Understanding $p$-value
Suppose, that you want to test the hypothesis that the average height of male students at your University is $5$ ft $7$ inches. You collect heights of $100$ students selected a | What is the meaning of p values and t values in statistical tests?
Understanding $p$-value
Suppose, that you want to test the hypothesis that the average height of male students at your University is $5$ ft $7$ inches. You collect heights of $100$ students selected at random and compute the sample mean (say it turns ou... | What is the meaning of p values and t values in statistical tests?
Understanding $p$-value
Suppose, that you want to test the hypothesis that the average height of male students at your University is $5$ ft $7$ inches. You collect heights of $100$ students selected a |
355 | What is the meaning of p values and t values in statistical tests? | A Dialog Between a Teacher and a Thoughtful Student
Humbly submitted in the belief that not enough crayons have been used so far in this thread. A brief illustrated synopsis appears at the end.
Student: What does a p-value mean? A lot of people seem to agree it's the chance we will "see a sample mean greater than or... | What is the meaning of p values and t values in statistical tests? | A Dialog Between a Teacher and a Thoughtful Student
Humbly submitted in the belief that not enough crayons have been used so far in this thread. A brief illustrated synopsis appears at the end.
Stud | What is the meaning of p values and t values in statistical tests?
A Dialog Between a Teacher and a Thoughtful Student
Humbly submitted in the belief that not enough crayons have been used so far in this thread. A brief illustrated synopsis appears at the end.
Student: What does a p-value mean? A lot of people seem ... | What is the meaning of p values and t values in statistical tests?
A Dialog Between a Teacher and a Thoughtful Student
Humbly submitted in the belief that not enough crayons have been used so far in this thread. A brief illustrated synopsis appears at the end.
Stud |
356 | What is the meaning of p values and t values in statistical tests? | Before touching this topic, I always make sure that students are happy moving between percentages, decimals, odds and fractions. If they are not completely happy with this then they can get confused very quickly.
I like to explain hypothesis testing for the first time (and therefore p-values and test statistics) throug... | What is the meaning of p values and t values in statistical tests? | Before touching this topic, I always make sure that students are happy moving between percentages, decimals, odds and fractions. If they are not completely happy with this then they can get confused v | What is the meaning of p values and t values in statistical tests?
Before touching this topic, I always make sure that students are happy moving between percentages, decimals, odds and fractions. If they are not completely happy with this then they can get confused very quickly.
I like to explain hypothesis testing for... | What is the meaning of p values and t values in statistical tests?
Before touching this topic, I always make sure that students are happy moving between percentages, decimals, odds and fractions. If they are not completely happy with this then they can get confused v |
357 | What is the meaning of p values and t values in statistical tests? | No amount of verbal explanation or calculations really helped me to understand at a gut level what p-values were, but it really snapped into focus for me once I took a course that involved simulation. That gave me the ability to actually see data generated by the null hypothesis and to plot the means/etc. of simulated... | What is the meaning of p values and t values in statistical tests? | No amount of verbal explanation or calculations really helped me to understand at a gut level what p-values were, but it really snapped into focus for me once I took a course that involved simulation. | What is the meaning of p values and t values in statistical tests?
No amount of verbal explanation or calculations really helped me to understand at a gut level what p-values were, but it really snapped into focus for me once I took a course that involved simulation. That gave me the ability to actually see data gener... | What is the meaning of p values and t values in statistical tests?
No amount of verbal explanation or calculations really helped me to understand at a gut level what p-values were, but it really snapped into focus for me once I took a course that involved simulation. |
358 | What is the meaning of p values and t values in statistical tests? | A nice definition of p-value is "the probability of observing a test statistic at least as large as the one calculated assuming the null hypothesis is true".
The problem with that is that it requires an understanding of "test statistic" and "null hypothesis". But, that's easy to get across. If the null hypothesis is t... | What is the meaning of p values and t values in statistical tests? | A nice definition of p-value is "the probability of observing a test statistic at least as large as the one calculated assuming the null hypothesis is true".
The problem with that is that it requires | What is the meaning of p values and t values in statistical tests?
A nice definition of p-value is "the probability of observing a test statistic at least as large as the one calculated assuming the null hypothesis is true".
The problem with that is that it requires an understanding of "test statistic" and "null hypot... | What is the meaning of p values and t values in statistical tests?
A nice definition of p-value is "the probability of observing a test statistic at least as large as the one calculated assuming the null hypothesis is true".
The problem with that is that it requires |
359 | What is the meaning of p values and t values in statistical tests? | Imagine you have a bag containing 900 black marbles and 100 white, i.e. 10% of the marbles are white. Now imagine you take 1 marble out, look at it and record its colour, take out another, record its colour etc.. and do this 100 times. At the end of this process you will have a number for white marbles which, ideally, ... | What is the meaning of p values and t values in statistical tests? | Imagine you have a bag containing 900 black marbles and 100 white, i.e. 10% of the marbles are white. Now imagine you take 1 marble out, look at it and record its colour, take out another, record its | What is the meaning of p values and t values in statistical tests?
Imagine you have a bag containing 900 black marbles and 100 white, i.e. 10% of the marbles are white. Now imagine you take 1 marble out, look at it and record its colour, take out another, record its colour etc.. and do this 100 times. At the end of thi... | What is the meaning of p values and t values in statistical tests?
Imagine you have a bag containing 900 black marbles and 100 white, i.e. 10% of the marbles are white. Now imagine you take 1 marble out, look at it and record its colour, take out another, record its |
360 | What is the meaning of p values and t values in statistical tests? | What the p-value doesn't tell you is how likely it is that the null hypothesis is true. Under the conventional (Fisher) significance testing framework we first compute the likelihood of observing the data assuming the null hypothesis is true, this is the p-value. It seems intuitively reasonable then to assume the nul... | What is the meaning of p values and t values in statistical tests? | What the p-value doesn't tell you is how likely it is that the null hypothesis is true. Under the conventional (Fisher) significance testing framework we first compute the likelihood of observing the | What is the meaning of p values and t values in statistical tests?
What the p-value doesn't tell you is how likely it is that the null hypothesis is true. Under the conventional (Fisher) significance testing framework we first compute the likelihood of observing the data assuming the null hypothesis is true, this is t... | What is the meaning of p values and t values in statistical tests?
What the p-value doesn't tell you is how likely it is that the null hypothesis is true. Under the conventional (Fisher) significance testing framework we first compute the likelihood of observing the |
361 | What is the meaning of p values and t values in statistical tests? | In statistics you can never say something is absolutely certain, so statisticians use another approach to gauge whether a hypothesis is true or not. They try to reject all the other hypotheses that are not supported by the data.
To do this, statistical tests have a null hypothesis and an alternate hypothesis. The p-va... | What is the meaning of p values and t values in statistical tests? | In statistics you can never say something is absolutely certain, so statisticians use another approach to gauge whether a hypothesis is true or not. They try to reject all the other hypotheses that ar | What is the meaning of p values and t values in statistical tests?
In statistics you can never say something is absolutely certain, so statisticians use another approach to gauge whether a hypothesis is true or not. They try to reject all the other hypotheses that are not supported by the data.
To do this, statistical... | What is the meaning of p values and t values in statistical tests?
In statistics you can never say something is absolutely certain, so statisticians use another approach to gauge whether a hypothesis is true or not. They try to reject all the other hypotheses that ar |
362 | What is the meaning of p values and t values in statistical tests? | I am bit diffident to revive the old topic, but I jumped from here, so I post this as a response to the question in the link.
The p-value is a concrete term, there should be no room for misunderstanding. But, it is somehow mystical that colloquial translations of the definition of p-value leads to many different misint... | What is the meaning of p values and t values in statistical tests? | I am bit diffident to revive the old topic, but I jumped from here, so I post this as a response to the question in the link.
The p-value is a concrete term, there should be no room for misunderstandi | What is the meaning of p values and t values in statistical tests?
I am bit diffident to revive the old topic, but I jumped from here, so I post this as a response to the question in the link.
The p-value is a concrete term, there should be no room for misunderstanding. But, it is somehow mystical that colloquial trans... | What is the meaning of p values and t values in statistical tests?
I am bit diffident to revive the old topic, but I jumped from here, so I post this as a response to the question in the link.
The p-value is a concrete term, there should be no room for misunderstandi |
363 | What is the meaning of p values and t values in statistical tests? | I have also found simulations to be a useful in teaching.
Here is a simulation for the arguably most basic case in which we sample $n$ times from $N(\mu,1)$ (hence, $\sigma^2=1$ is known for simplicity) and test $H_0:\mu=\mu_0$ against a left-sided alternative.
Then, the $t$-statistic $\text{tstat}:=\sqrt{n}(\bar{X}-... | What is the meaning of p values and t values in statistical tests? | I have also found simulations to be a useful in teaching.
Here is a simulation for the arguably most basic case in which we sample $n$ times from $N(\mu,1)$ (hence, $\sigma^2=1$ is known for simplici | What is the meaning of p values and t values in statistical tests?
I have also found simulations to be a useful in teaching.
Here is a simulation for the arguably most basic case in which we sample $n$ times from $N(\mu,1)$ (hence, $\sigma^2=1$ is known for simplicity) and test $H_0:\mu=\mu_0$ against a left-sided alt... | What is the meaning of p values and t values in statistical tests?
I have also found simulations to be a useful in teaching.
Here is a simulation for the arguably most basic case in which we sample $n$ times from $N(\mu,1)$ (hence, $\sigma^2=1$ is known for simplici |
364 | What is the meaning of p values and t values in statistical tests? | I find it helpful to follow a sequence in which you explain concepts in the following order:
(1) The z score and proportions above and below the z score assuming a normal curve.
(2) The notion of a sampling distribution, and the z score for a given sample mean when the population standard deviation is known (and thence... | What is the meaning of p values and t values in statistical tests? | I find it helpful to follow a sequence in which you explain concepts in the following order:
(1) The z score and proportions above and below the z score assuming a normal curve.
(2) The notion of a sa | What is the meaning of p values and t values in statistical tests?
I find it helpful to follow a sequence in which you explain concepts in the following order:
(1) The z score and proportions above and below the z score assuming a normal curve.
(2) The notion of a sampling distribution, and the z score for a given samp... | What is the meaning of p values and t values in statistical tests?
I find it helpful to follow a sequence in which you explain concepts in the following order:
(1) The z score and proportions above and below the z score assuming a normal curve.
(2) The notion of a sa |
365 | What is the meaning of p values and t values in statistical tests? | I have yet to prove the following argument so it might contain errors, but I really want to throw in my two cents (Hopefully, I'll update it with a rigorous proof soon). Another way of looking at the $p$-value is
$p$-value - A statistic $X$ such that $$\forall 0 \le c \le 1, F_{X|H_0}(\inf\{x: F_{X|H_0}(x) \ge c\}) = ... | What is the meaning of p values and t values in statistical tests? | I have yet to prove the following argument so it might contain errors, but I really want to throw in my two cents (Hopefully, I'll update it with a rigorous proof soon). Another way of looking at the | What is the meaning of p values and t values in statistical tests?
I have yet to prove the following argument so it might contain errors, but I really want to throw in my two cents (Hopefully, I'll update it with a rigorous proof soon). Another way of looking at the $p$-value is
$p$-value - A statistic $X$ such that $... | What is the meaning of p values and t values in statistical tests?
I have yet to prove the following argument so it might contain errors, but I really want to throw in my two cents (Hopefully, I'll update it with a rigorous proof soon). Another way of looking at the |
366 | What is the meaning of p values and t values in statistical tests? | What does a "p-value" mean in relation to the hypothesis being tested?
In an ontological sense (what is truth?), it means nothing. Any hypothesis testing is based on untested assumptions. This are normally part of the test itself, but are also part of whatever model you are using (e.g. in a regression model). Since we... | What is the meaning of p values and t values in statistical tests? | What does a "p-value" mean in relation to the hypothesis being tested?
In an ontological sense (what is truth?), it means nothing. Any hypothesis testing is based on untested assumptions. This are no | What is the meaning of p values and t values in statistical tests?
What does a "p-value" mean in relation to the hypothesis being tested?
In an ontological sense (what is truth?), it means nothing. Any hypothesis testing is based on untested assumptions. This are normally part of the test itself, but are also part of ... | What is the meaning of p values and t values in statistical tests?
What does a "p-value" mean in relation to the hypothesis being tested?
In an ontological sense (what is truth?), it means nothing. Any hypothesis testing is based on untested assumptions. This are no |
367 | What is the meaning of p values and t values in statistical tests? | I think that examples involving marbles or coins or height-measuring can be fine for practicing the math, but they aren't good for building intuition. College students like to question society, right? How about using a political example?
Say a political candidate ran a campaign promising that some policy will help the ... | What is the meaning of p values and t values in statistical tests? | I think that examples involving marbles or coins or height-measuring can be fine for practicing the math, but they aren't good for building intuition. College students like to question society, right? | What is the meaning of p values and t values in statistical tests?
I think that examples involving marbles or coins or height-measuring can be fine for practicing the math, but they aren't good for building intuition. College students like to question society, right? How about using a political example?
Say a political... | What is the meaning of p values and t values in statistical tests?
I think that examples involving marbles or coins or height-measuring can be fine for practicing the math, but they aren't good for building intuition. College students like to question society, right? |
368 | What is the meaning of p values and t values in statistical tests? | The p-value isnt as mysterious as most analysts make it out to be. It is a way of not having to calculate the confidence interval for a t-test but simply determining the confidence level with which null hypothesis can be rejected.
ILLUSTRATION.
You run a test. The p-value comes up as 0.1866 for Q-variable, 0.0023 for R... | What is the meaning of p values and t values in statistical tests? | The p-value isnt as mysterious as most analysts make it out to be. It is a way of not having to calculate the confidence interval for a t-test but simply determining the confidence level with which nu | What is the meaning of p values and t values in statistical tests?
The p-value isnt as mysterious as most analysts make it out to be. It is a way of not having to calculate the confidence interval for a t-test but simply determining the confidence level with which null hypothesis can be rejected.
ILLUSTRATION.
You run ... | What is the meaning of p values and t values in statistical tests?
The p-value isnt as mysterious as most analysts make it out to be. It is a way of not having to calculate the confidence interval for a t-test but simply determining the confidence level with which nu |
369 | What does AUC stand for and what is it? | Abbreviations
AUC = Area Under the Curve.
AUROC = Area Under the Receiver Operating Characteristic curve.
AUC is used most of the time to mean AUROC, which is a bad practice since as Marc Claesen pointed out AUC is ambiguous (could be any curve) while AUROC is not.
Interpreting the AUROC
The AUROC has several equiv... | What does AUC stand for and what is it? | Abbreviations
AUC = Area Under the Curve.
AUROC = Area Under the Receiver Operating Characteristic curve.
AUC is used most of the time to mean AUROC, which is a bad practice since as Marc Claesen po | What does AUC stand for and what is it?
Abbreviations
AUC = Area Under the Curve.
AUROC = Area Under the Receiver Operating Characteristic curve.
AUC is used most of the time to mean AUROC, which is a bad practice since as Marc Claesen pointed out AUC is ambiguous (could be any curve) while AUROC is not.
Interpreti... | What does AUC stand for and what is it?
Abbreviations
AUC = Area Under the Curve.
AUROC = Area Under the Receiver Operating Characteristic curve.
AUC is used most of the time to mean AUROC, which is a bad practice since as Marc Claesen po |
370 | What does AUC stand for and what is it? | Although I'm a bit late to the party, but here's my 5 cents. @FranckDernoncourt (+1) already mentioned possible interpretations of AUC ROC, and my favorite one is the first on his list (I use different wording, but it's the same):
the AUC of a classifier is equal to the probability that the classifier will rank a ran... | What does AUC stand for and what is it? | Although I'm a bit late to the party, but here's my 5 cents. @FranckDernoncourt (+1) already mentioned possible interpretations of AUC ROC, and my favorite one is the first on his list (I use differen | What does AUC stand for and what is it?
Although I'm a bit late to the party, but here's my 5 cents. @FranckDernoncourt (+1) already mentioned possible interpretations of AUC ROC, and my favorite one is the first on his list (I use different wording, but it's the same):
the AUC of a classifier is equal to the probabi... | What does AUC stand for and what is it?
Although I'm a bit late to the party, but here's my 5 cents. @FranckDernoncourt (+1) already mentioned possible interpretations of AUC ROC, and my favorite one is the first on his list (I use differen |
371 | What does AUC stand for and what is it? | Important considerations are not included in any of these discussions. The procedures discussed above invite inappropriate thresholding and utilize improper accuracy scoring rules (proportions) that are optimized by choosing the wrong features and giving them the wrong weights.
Dichotomization of continuous prediction... | What does AUC stand for and what is it? | Important considerations are not included in any of these discussions. The procedures discussed above invite inappropriate thresholding and utilize improper accuracy scoring rules (proportions) that | What does AUC stand for and what is it?
Important considerations are not included in any of these discussions. The procedures discussed above invite inappropriate thresholding and utilize improper accuracy scoring rules (proportions) that are optimized by choosing the wrong features and giving them the wrong weights.
... | What does AUC stand for and what is it?
Important considerations are not included in any of these discussions. The procedures discussed above invite inappropriate thresholding and utilize improper accuracy scoring rules (proportions) that |
372 | What does AUC stand for and what is it? | The answers in this forum are great and I come back here often for reference. However, one thing was always missing. From @Frank's answer, we see the interpretation of AUC as the probability that a positive sample will have a higher score than the negative sample. At the same time, the way to calculate it is to plot ou... | What does AUC stand for and what is it? | The answers in this forum are great and I come back here often for reference. However, one thing was always missing. From @Frank's answer, we see the interpretation of AUC as the probability that a po | What does AUC stand for and what is it?
The answers in this forum are great and I come back here often for reference. However, one thing was always missing. From @Frank's answer, we see the interpretation of AUC as the probability that a positive sample will have a higher score than the negative sample. At the same tim... | What does AUC stand for and what is it?
The answers in this forum are great and I come back here often for reference. However, one thing was always missing. From @Frank's answer, we see the interpretation of AUC as the probability that a po |
373 | What does AUC stand for and what is it? | AUC is an abbrevation for area under the curve. It is used in classification analysis in order to determine which of the used models predicts the classes best.
An example of its application are ROC curves. Here, the true positive rates are plotted against false positive rates. An example is below. The closer AUC for a... | What does AUC stand for and what is it? | AUC is an abbrevation for area under the curve. It is used in classification analysis in order to determine which of the used models predicts the classes best.
An example of its application are ROC c | What does AUC stand for and what is it?
AUC is an abbrevation for area under the curve. It is used in classification analysis in order to determine which of the used models predicts the classes best.
An example of its application are ROC curves. Here, the true positive rates are plotted against false positive rates. A... | What does AUC stand for and what is it?
AUC is an abbrevation for area under the curve. It is used in classification analysis in order to determine which of the used models predicts the classes best.
An example of its application are ROC c |
374 | What does AUC stand for and what is it? | Very late to respond but after learning from multiple sources I've been able to form my own understanding of the AUC. This response is mainly heuristic in nature and not meant to be rigorous
Let's say we have M positive samples and N negative samples and some "score funcion $s(x)$" that assigns a value to sample $x$. F... | What does AUC stand for and what is it? | Very late to respond but after learning from multiple sources I've been able to form my own understanding of the AUC. This response is mainly heuristic in nature and not meant to be rigorous
Let's say | What does AUC stand for and what is it?
Very late to respond but after learning from multiple sources I've been able to form my own understanding of the AUC. This response is mainly heuristic in nature and not meant to be rigorous
Let's say we have M positive samples and N negative samples and some "score funcion $s(x)... | What does AUC stand for and what is it?
Very late to respond but after learning from multiple sources I've been able to form my own understanding of the AUC. This response is mainly heuristic in nature and not meant to be rigorous
Let's say |
375 | What does AUC stand for and what is it? | I just wanted to share an animation about the construction of the ROC Curve and so the AUC. One sees clearly that each point of the ROC Curve comes from a different threshold used to classify the output of a binary classifier. The threshold defines which samples are predicted as 1 and which ones as 0. True Positive and... | What does AUC stand for and what is it? | I just wanted to share an animation about the construction of the ROC Curve and so the AUC. One sees clearly that each point of the ROC Curve comes from a different threshold used to classify the outp | What does AUC stand for and what is it?
I just wanted to share an animation about the construction of the ROC Curve and so the AUC. One sees clearly that each point of the ROC Curve comes from a different threshold used to classify the output of a binary classifier. The threshold defines which samples are predicted as ... | What does AUC stand for and what is it?
I just wanted to share an animation about the construction of the ROC Curve and so the AUC. One sees clearly that each point of the ROC Curve comes from a different threshold used to classify the outp |
376 | Is there any reason to prefer the AIC or BIC over the other? | Your question implies that AIC and BIC try to answer the same question, which is not true. The AIC tries to select the model that most adequately describes an unknown, high dimensional reality. This means that reality is never in the set of candidate models that are being considered. On the contrary, BIC tries to find... | Is there any reason to prefer the AIC or BIC over the other? | Your question implies that AIC and BIC try to answer the same question, which is not true. The AIC tries to select the model that most adequately describes an unknown, high dimensional reality. This m | Is there any reason to prefer the AIC or BIC over the other?
Your question implies that AIC and BIC try to answer the same question, which is not true. The AIC tries to select the model that most adequately describes an unknown, high dimensional reality. This means that reality is never in the set of candidate models t... | Is there any reason to prefer the AIC or BIC over the other?
Your question implies that AIC and BIC try to answer the same question, which is not true. The AIC tries to select the model that most adequately describes an unknown, high dimensional reality. This m |
377 | Is there any reason to prefer the AIC or BIC over the other? | Though AIC and BIC are both Maximum Likelihood estimate driven and penalize free parameters in an effort to combat overfitting, they do so in ways that result in significantly different behavior. Lets look at one commonly presented version of the methods (which results form stipulating normally distributed errors and ... | Is there any reason to prefer the AIC or BIC over the other? | Though AIC and BIC are both Maximum Likelihood estimate driven and penalize free parameters in an effort to combat overfitting, they do so in ways that result in significantly different behavior. Let | Is there any reason to prefer the AIC or BIC over the other?
Though AIC and BIC are both Maximum Likelihood estimate driven and penalize free parameters in an effort to combat overfitting, they do so in ways that result in significantly different behavior. Lets look at one commonly presented version of the methods (wh... | Is there any reason to prefer the AIC or BIC over the other?
Though AIC and BIC are both Maximum Likelihood estimate driven and penalize free parameters in an effort to combat overfitting, they do so in ways that result in significantly different behavior. Let |
378 | Is there any reason to prefer the AIC or BIC over the other? | My quick explanation is
AIC is best for prediction as it is asymptotically equivalent to cross-validation.
BIC is best for explanation as it is allows consistent estimation of the underlying data generating process. | Is there any reason to prefer the AIC or BIC over the other? | My quick explanation is
AIC is best for prediction as it is asymptotically equivalent to cross-validation.
BIC is best for explanation as it is allows consistent estimation of the underlying data gen | Is there any reason to prefer the AIC or BIC over the other?
My quick explanation is
AIC is best for prediction as it is asymptotically equivalent to cross-validation.
BIC is best for explanation as it is allows consistent estimation of the underlying data generating process. | Is there any reason to prefer the AIC or BIC over the other?
My quick explanation is
AIC is best for prediction as it is asymptotically equivalent to cross-validation.
BIC is best for explanation as it is allows consistent estimation of the underlying data gen |
379 | Is there any reason to prefer the AIC or BIC over the other? | In my experience, BIC results in serious underfitting and AIC typically performs well, when the goal is to maximize predictive discrimination. | Is there any reason to prefer the AIC or BIC over the other? | In my experience, BIC results in serious underfitting and AIC typically performs well, when the goal is to maximize predictive discrimination. | Is there any reason to prefer the AIC or BIC over the other?
In my experience, BIC results in serious underfitting and AIC typically performs well, when the goal is to maximize predictive discrimination. | Is there any reason to prefer the AIC or BIC over the other?
In my experience, BIC results in serious underfitting and AIC typically performs well, when the goal is to maximize predictive discrimination. |
380 | Is there any reason to prefer the AIC or BIC over the other? | An informative and accessible "derivation" of AIC and BIC by Brian Ripley can be found here:
http://www.stats.ox.ac.uk/~ripley/Nelder80.pdf
Ripley provides some remarks on the assumptions behind the mathematical results. Contrary to what some of the other answers indicate, Ripley emphasizes that AIC is based on assumin... | Is there any reason to prefer the AIC or BIC over the other? | An informative and accessible "derivation" of AIC and BIC by Brian Ripley can be found here:
http://www.stats.ox.ac.uk/~ripley/Nelder80.pdf
Ripley provides some remarks on the assumptions behind the m | Is there any reason to prefer the AIC or BIC over the other?
An informative and accessible "derivation" of AIC and BIC by Brian Ripley can be found here:
http://www.stats.ox.ac.uk/~ripley/Nelder80.pdf
Ripley provides some remarks on the assumptions behind the mathematical results. Contrary to what some of the other ans... | Is there any reason to prefer the AIC or BIC over the other?
An informative and accessible "derivation" of AIC and BIC by Brian Ripley can be found here:
http://www.stats.ox.ac.uk/~ripley/Nelder80.pdf
Ripley provides some remarks on the assumptions behind the m |
381 | Is there any reason to prefer the AIC or BIC over the other? | Indeed the only difference is that BIC is AIC extended to take number of objects (samples) into account. I would say that while both are quite weak (in comparison to for instance cross-validation) it is better to use AIC, than more people will be familiar with the abbreviation -- indeed I have never seen a paper or a p... | Is there any reason to prefer the AIC or BIC over the other? | Indeed the only difference is that BIC is AIC extended to take number of objects (samples) into account. I would say that while both are quite weak (in comparison to for instance cross-validation) it | Is there any reason to prefer the AIC or BIC over the other?
Indeed the only difference is that BIC is AIC extended to take number of objects (samples) into account. I would say that while both are quite weak (in comparison to for instance cross-validation) it is better to use AIC, than more people will be familiar wit... | Is there any reason to prefer the AIC or BIC over the other?
Indeed the only difference is that BIC is AIC extended to take number of objects (samples) into account. I would say that while both are quite weak (in comparison to for instance cross-validation) it |
382 | Is there any reason to prefer the AIC or BIC over the other? | From what I can tell, there isn't much difference between AIC and BIC. They are both mathematically convenient approximations one can make in order to efficiently compare models. If they give you different "best" models, it probably means you have high model uncertainty, which is more important to worry about than wh... | Is there any reason to prefer the AIC or BIC over the other? | From what I can tell, there isn't much difference between AIC and BIC. They are both mathematically convenient approximations one can make in order to efficiently compare models. If they give you di | Is there any reason to prefer the AIC or BIC over the other?
From what I can tell, there isn't much difference between AIC and BIC. They are both mathematically convenient approximations one can make in order to efficiently compare models. If they give you different "best" models, it probably means you have high mode... | Is there any reason to prefer the AIC or BIC over the other?
From what I can tell, there isn't much difference between AIC and BIC. They are both mathematically convenient approximations one can make in order to efficiently compare models. If they give you di |
383 | Is there any reason to prefer the AIC or BIC over the other? | As you mentioned, AIC and BIC are methods to penalize models for having more regressor variables. A penalty function is used in these methods, which is a function of the number of parameters in the model.
When applying AIC, the penalty function is z(p) = 2 p.
When applying BIC, the penalty function is z(p) = p ln(n),... | Is there any reason to prefer the AIC or BIC over the other? | As you mentioned, AIC and BIC are methods to penalize models for having more regressor variables. A penalty function is used in these methods, which is a function of the number of parameters in the mo | Is there any reason to prefer the AIC or BIC over the other?
As you mentioned, AIC and BIC are methods to penalize models for having more regressor variables. A penalty function is used in these methods, which is a function of the number of parameters in the model.
When applying AIC, the penalty function is z(p) = 2 ... | Is there any reason to prefer the AIC or BIC over the other?
As you mentioned, AIC and BIC are methods to penalize models for having more regressor variables. A penalty function is used in these methods, which is a function of the number of parameters in the mo |
384 | Is there any reason to prefer the AIC or BIC over the other? | AIC should rarely be used, as it is really only valid asymptotically. It is almost always better to use AICc (AIC with a correction for finite sample size). AIC tends to overparameterize: that problem is greatly lessened with AICc. The main exception to using AICc is when the underlying distributions are heavily lep... | Is there any reason to prefer the AIC or BIC over the other? | AIC should rarely be used, as it is really only valid asymptotically. It is almost always better to use AICc (AIC with a correction for finite sample size). AIC tends to overparameterize: that probl | Is there any reason to prefer the AIC or BIC over the other?
AIC should rarely be used, as it is really only valid asymptotically. It is almost always better to use AICc (AIC with a correction for finite sample size). AIC tends to overparameterize: that problem is greatly lessened with AICc. The main exception to us... | Is there any reason to prefer the AIC or BIC over the other?
AIC should rarely be used, as it is really only valid asymptotically. It is almost always better to use AICc (AIC with a correction for finite sample size). AIC tends to overparameterize: that probl |
385 | Is there any reason to prefer the AIC or BIC over the other? | AIC and BIC are information criteria for comparing models. Each tries to balance model fit and parsimony and each penalizes differently for number of parameters.
AIC is Akaike Information Criterion the formula is
$$\text{AIC}= 2k - 2\ln(L)$$ where $k$ is number of parameters and $L$ is maximum likelihood; with this fo... | Is there any reason to prefer the AIC or BIC over the other? | AIC and BIC are information criteria for comparing models. Each tries to balance model fit and parsimony and each penalizes differently for number of parameters.
AIC is Akaike Information Criterion th | Is there any reason to prefer the AIC or BIC over the other?
AIC and BIC are information criteria for comparing models. Each tries to balance model fit and parsimony and each penalizes differently for number of parameters.
AIC is Akaike Information Criterion the formula is
$$\text{AIC}= 2k - 2\ln(L)$$ where $k$ is num... | Is there any reason to prefer the AIC or BIC over the other?
AIC and BIC are information criteria for comparing models. Each tries to balance model fit and parsimony and each penalizes differently for number of parameters.
AIC is Akaike Information Criterion th |
386 | Is there any reason to prefer the AIC or BIC over the other? | Very briefly:
AIC approximately minimizes the prediction error and is asymptotically equivalent to leave-1-out cross-validation (LOOCV) (Stone 1977). It is not consistent though, which means that even with a very large amount of data ($n$ going to infinity) and if the true model is among the candidate models, the prob... | Is there any reason to prefer the AIC or BIC over the other? | Very briefly:
AIC approximately minimizes the prediction error and is asymptotically equivalent to leave-1-out cross-validation (LOOCV) (Stone 1977). It is not consistent though, which means that eve | Is there any reason to prefer the AIC or BIC over the other?
Very briefly:
AIC approximately minimizes the prediction error and is asymptotically equivalent to leave-1-out cross-validation (LOOCV) (Stone 1977). It is not consistent though, which means that even with a very large amount of data ($n$ going to infinity) ... | Is there any reason to prefer the AIC or BIC over the other?
Very briefly:
AIC approximately minimizes the prediction error and is asymptotically equivalent to leave-1-out cross-validation (LOOCV) (Stone 1977). It is not consistent though, which means that eve |
387 | Is there any reason to prefer the AIC or BIC over the other? | AIC and BIC are both penalized-likelihood criteria. They are usually written in the form [-2logL + kp], where L is the likelihood function, p is the number of parameters in the model, and k is 2 for AIC and log(n) for BIC.
AIC is an estimate of a constant plus the relative distance between the unknown true likelihood f... | Is there any reason to prefer the AIC or BIC over the other? | AIC and BIC are both penalized-likelihood criteria. They are usually written in the form [-2logL + kp], where L is the likelihood function, p is the number of parameters in the model, and k is 2 for A | Is there any reason to prefer the AIC or BIC over the other?
AIC and BIC are both penalized-likelihood criteria. They are usually written in the form [-2logL + kp], where L is the likelihood function, p is the number of parameters in the model, and k is 2 for AIC and log(n) for BIC.
AIC is an estimate of a constant plu... | Is there any reason to prefer the AIC or BIC over the other?
AIC and BIC are both penalized-likelihood criteria. They are usually written in the form [-2logL + kp], where L is the likelihood function, p is the number of parameters in the model, and k is 2 for A |
388 | Is there any reason to prefer the AIC or BIC over the other? | From Shmueli (2010, Statistical Science), on the difference between explanatory and predictive modelling:
A popular predictive metric is the in-sample Akaike Information Criterion (AIC).
Akaike derived the AIC from a predictive viewpoint, where the model is not
intended to accurately infer the “true distribution”, but... | Is there any reason to prefer the AIC or BIC over the other? | From Shmueli (2010, Statistical Science), on the difference between explanatory and predictive modelling:
A popular predictive metric is the in-sample Akaike Information Criterion (AIC).
Akaike deriv | Is there any reason to prefer the AIC or BIC over the other?
From Shmueli (2010, Statistical Science), on the difference between explanatory and predictive modelling:
A popular predictive metric is the in-sample Akaike Information Criterion (AIC).
Akaike derived the AIC from a predictive viewpoint, where the model is ... | Is there any reason to prefer the AIC or BIC over the other?
From Shmueli (2010, Statistical Science), on the difference between explanatory and predictive modelling:
A popular predictive metric is the in-sample Akaike Information Criterion (AIC).
Akaike deriv |
389 | Famous statistical quotations | All models are wrong, but some are useful. (George E. P. Box)
Reference: Box & Draper (1987), Empirical model-building and response surfaces, Wiley, p. 424.
Also: G.E.P. Box (1979), "Robustness in the Strategy of Scientific Model Building" in Robustness in Statistics (Launer & Wilkinson eds.), p. 202. | Famous statistical quotations | All models are wrong, but some are useful. (George E. P. Box)
Reference: Box & Draper (1987), Empirical model-building and response surfaces, Wiley, p. 424.
Also: G.E.P. Box (1979), "Robustness in th | Famous statistical quotations
All models are wrong, but some are useful. (George E. P. Box)
Reference: Box & Draper (1987), Empirical model-building and response surfaces, Wiley, p. 424.
Also: G.E.P. Box (1979), "Robustness in the Strategy of Scientific Model Building" in Robustness in Statistics (Launer & Wilkinson e... | Famous statistical quotations
All models are wrong, but some are useful. (George E. P. Box)
Reference: Box & Draper (1987), Empirical model-building and response surfaces, Wiley, p. 424.
Also: G.E.P. Box (1979), "Robustness in th |
390 | Famous statistical quotations | "An approximate answer to the right problem is worth a good deal more than an exact answer to an approximate problem." -- John Tukey | Famous statistical quotations | "An approximate answer to the right problem is worth a good deal more than an exact answer to an approximate problem." -- John Tukey | Famous statistical quotations
"An approximate answer to the right problem is worth a good deal more than an exact answer to an approximate problem." -- John Tukey | Famous statistical quotations
"An approximate answer to the right problem is worth a good deal more than an exact answer to an approximate problem." -- John Tukey |
391 | Famous statistical quotations | "To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of."
-- Ronald Fisher (1938)
The quotation can be read on page 17 of the article.
R. A. Fisher. Presidential Address by Professor R. A. Fisher, S... | Famous statistical quotations | "To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of."
-- Ronald Fisher (19 | Famous statistical quotations
"To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of."
-- Ronald Fisher (1938)
The quotation can be read on page 17 of the article.
R. A. Fisher. Presidential Addres... | Famous statistical quotations
"To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of."
-- Ronald Fisher (19 |
392 | Famous statistical quotations | 87% of statistics are made up on the spot
-Unknown
Dilbert.com | Famous statistical quotations | 87% of statistics are made up on the spot
-Unknown
Dilbert.com | Famous statistical quotations
87% of statistics are made up on the spot
-Unknown
Dilbert.com | Famous statistical quotations
87% of statistics are made up on the spot
-Unknown
Dilbert.com |
393 | Famous statistical quotations | In God we trust. All others must bring
data.
(W. Edwards Deming) | Famous statistical quotations | In God we trust. All others must bring
data.
(W. Edwards Deming) | Famous statistical quotations
In God we trust. All others must bring
data.
(W. Edwards Deming) | Famous statistical quotations
In God we trust. All others must bring
data.
(W. Edwards Deming) |
394 | Famous statistical quotations | Statisticians, like artists, have the bad habit of falling in love with their models.
-- George Box | Famous statistical quotations | Statisticians, like artists, have the bad habit of falling in love with their models.
-- George Box | Famous statistical quotations
Statisticians, like artists, have the bad habit of falling in love with their models.
-- George Box | Famous statistical quotations
Statisticians, like artists, have the bad habit of falling in love with their models.
-- George Box |
395 | Famous statistical quotations | Statistics are like bikinis. What
they reveal is suggestive, but what
they conceal is vital.
-Aaron Levenstein | Famous statistical quotations | Statistics are like bikinis. What
they reveal is suggestive, but what
they conceal is vital.
-Aaron Levenstein | Famous statistical quotations
Statistics are like bikinis. What
they reveal is suggestive, but what
they conceal is vital.
-Aaron Levenstein | Famous statistical quotations
Statistics are like bikinis. What
they reveal is suggestive, but what
they conceal is vital.
-Aaron Levenstein |
396 | Famous statistical quotations | Prediction is very difficult, especially about the future.
-- Niels Bohr | Famous statistical quotations | Prediction is very difficult, especially about the future.
-- Niels Bohr | Famous statistical quotations
Prediction is very difficult, especially about the future.
-- Niels Bohr | Famous statistical quotations
Prediction is very difficult, especially about the future.
-- Niels Bohr |
397 | Famous statistical quotations | If you torture the data enough, nature will always confess.
--Ronald Coase (quoted from Coase, R. H. 1982. How should economists chose? American Enterprise Institute, Washington, D. C.). I think most who hear this quote misunderstand its profound message against data dredging. | Famous statistical quotations | If you torture the data enough, nature will always confess.
--Ronald Coase (quoted from Coase, R. H. 1982. How should economists chose? American Enterprise Institute, Washington, D. C.). I think m | Famous statistical quotations
If you torture the data enough, nature will always confess.
--Ronald Coase (quoted from Coase, R. H. 1982. How should economists chose? American Enterprise Institute, Washington, D. C.). I think most who hear this quote misunderstand its profound message against data dredging. | Famous statistical quotations
If you torture the data enough, nature will always confess.
--Ronald Coase (quoted from Coase, R. H. 1982. How should economists chose? American Enterprise Institute, Washington, D. C.). I think m |
398 | Famous statistical quotations | All generalizations are false,
including this one.
Mark Twain | Famous statistical quotations | All generalizations are false,
including this one.
Mark Twain | Famous statistical quotations
All generalizations are false,
including this one.
Mark Twain | Famous statistical quotations
All generalizations are false,
including this one.
Mark Twain |
399 | Famous statistical quotations | A big computer, a complex algorithm and a long time does not equal science.
-- Robert Gentleman | Famous statistical quotations | A big computer, a complex algorithm and a long time does not equal science.
-- Robert Gentleman | Famous statistical quotations
A big computer, a complex algorithm and a long time does not equal science.
-- Robert Gentleman | Famous statistical quotations
A big computer, a complex algorithm and a long time does not equal science.
-- Robert Gentleman |
400 | Famous statistical quotations | Statistical thinking will one day be
as necessary a qualification for
efficient citizenship as the ability
to read and write.
--H.G. Wells | Famous statistical quotations | Statistical thinking will one day be
as necessary a qualification for
efficient citizenship as the ability
to read and write.
--H.G. Wells | Famous statistical quotations
Statistical thinking will one day be
as necessary a qualification for
efficient citizenship as the ability
to read and write.
--H.G. Wells | Famous statistical quotations
Statistical thinking will one day be
as necessary a qualification for
efficient citizenship as the ability
to read and write.
--H.G. Wells |
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