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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3,301 | What is a good, convincing example in which p-values are useful? | I will consider both Matloff's points:
With large samples, significance tests pounce on tiny, unimportant departures from the null hypothesis.
The logic here is that if somebody reports highly significant $p=0.0001$, then from this number alone we cannot say if the effect is large and important or irrelevantly tiny ... | What is a good, convincing example in which p-values are useful? | I will consider both Matloff's points:
With large samples, significance tests pounce on tiny, unimportant departures from the null hypothesis.
The logic here is that if somebody reports highly sign | What is a good, convincing example in which p-values are useful?
I will consider both Matloff's points:
With large samples, significance tests pounce on tiny, unimportant departures from the null hypothesis.
The logic here is that if somebody reports highly significant $p=0.0001$, then from this number alone we cann... | What is a good, convincing example in which p-values are useful?
I will consider both Matloff's points:
With large samples, significance tests pounce on tiny, unimportant departures from the null hypothesis.
The logic here is that if somebody reports highly sign |
3,302 | What is a good, convincing example in which p-values are useful? | I take great offense at the following two ideas:
With large samples, significance tests pounce on tiny, unimportant departures from the null hypothesis.
Almost no null hypotheses are true in the real world, so performing a significance test on them is absurd and bizarre.
It is such a strawman argument about p-val... | What is a good, convincing example in which p-values are useful? | I take great offense at the following two ideas:
With large samples, significance tests pounce on tiny, unimportant departures from the null hypothesis.
Almost no null hypotheses are true in the re | What is a good, convincing example in which p-values are useful?
I take great offense at the following two ideas:
With large samples, significance tests pounce on tiny, unimportant departures from the null hypothesis.
Almost no null hypotheses are true in the real world, so performing a significance test on them is ... | What is a good, convincing example in which p-values are useful?
I take great offense at the following two ideas:
With large samples, significance tests pounce on tiny, unimportant departures from the null hypothesis.
Almost no null hypotheses are true in the re |
3,303 | What is a good, convincing example in which p-values are useful? | Forgive my sarcasm, but one obvious good example of the utility of p-values is in getting published. I had one experimenter approach me for producing a p-value... he had introduced a transgene in a single plant to improve growth. From that single plant he produced multiple clones and chose the largest clone, an example... | What is a good, convincing example in which p-values are useful? | Forgive my sarcasm, but one obvious good example of the utility of p-values is in getting published. I had one experimenter approach me for producing a p-value... he had introduced a transgene in a si | What is a good, convincing example in which p-values are useful?
Forgive my sarcasm, but one obvious good example of the utility of p-values is in getting published. I had one experimenter approach me for producing a p-value... he had introduced a transgene in a single plant to improve growth. From that single plant he... | What is a good, convincing example in which p-values are useful?
Forgive my sarcasm, but one obvious good example of the utility of p-values is in getting published. I had one experimenter approach me for producing a p-value... he had introduced a transgene in a si |
3,304 | What is a good, convincing example in which p-values are useful? | I'll give you the exemplary case of how p-values should be used and reported. It's a very recent report on the search of a mysterious particle on Large Hadron Collider(LHC) in CERN.
A few months ago there was a lot of excited chatter in high energy physics circles about a possibility that a large particle was detected ... | What is a good, convincing example in which p-values are useful? | I'll give you the exemplary case of how p-values should be used and reported. It's a very recent report on the search of a mysterious particle on Large Hadron Collider(LHC) in CERN.
A few months ago t | What is a good, convincing example in which p-values are useful?
I'll give you the exemplary case of how p-values should be used and reported. It's a very recent report on the search of a mysterious particle on Large Hadron Collider(LHC) in CERN.
A few months ago there was a lot of excited chatter in high energy physic... | What is a good, convincing example in which p-values are useful?
I'll give you the exemplary case of how p-values should be used and reported. It's a very recent report on the search of a mysterious particle on Large Hadron Collider(LHC) in CERN.
A few months ago t |
3,305 | What is a good, convincing example in which p-values are useful? | The other explanations are all fine, I just wanted to try and give a brief and direct answer to the question that popped into my head.
Checking Covariate Imbalance in Randomized Experiments
Your second claim (about unrealistic null hypotheses) is not true when we are checking covariate balance in randomized experiments... | What is a good, convincing example in which p-values are useful? | The other explanations are all fine, I just wanted to try and give a brief and direct answer to the question that popped into my head.
Checking Covariate Imbalance in Randomized Experiments
Your secon | What is a good, convincing example in which p-values are useful?
The other explanations are all fine, I just wanted to try and give a brief and direct answer to the question that popped into my head.
Checking Covariate Imbalance in Randomized Experiments
Your second claim (about unrealistic null hypotheses) is not true... | What is a good, convincing example in which p-values are useful?
The other explanations are all fine, I just wanted to try and give a brief and direct answer to the question that popped into my head.
Checking Covariate Imbalance in Randomized Experiments
Your secon |
3,306 | What is a good, convincing example in which p-values are useful? | Error rates control is similar to quality control in production. A robot in a production line has a rule for deciding that a part is defective which guarantees not to exceed a specified rate of defective parts that go through undetected. Similarly, an agency that makes decisions for drug approval based on "honest" P-va... | What is a good, convincing example in which p-values are useful? | Error rates control is similar to quality control in production. A robot in a production line has a rule for deciding that a part is defective which guarantees not to exceed a specified rate of defect | What is a good, convincing example in which p-values are useful?
Error rates control is similar to quality control in production. A robot in a production line has a rule for deciding that a part is defective which guarantees not to exceed a specified rate of defective parts that go through undetected. Similarly, an age... | What is a good, convincing example in which p-values are useful?
Error rates control is similar to quality control in production. A robot in a production line has a rule for deciding that a part is defective which guarantees not to exceed a specified rate of defect |
3,307 | What is a good, convincing example in which p-values are useful? | I agree with Matt that p-values are useful when the null hypothesis is true.
The simplest example I can think of is testing a random number generator. If the generator is working correctly, you can use any appropriate sample size of realizations and when testing the fit over many samples, the p-values should have a un... | What is a good, convincing example in which p-values are useful? | I agree with Matt that p-values are useful when the null hypothesis is true.
The simplest example I can think of is testing a random number generator. If the generator is working correctly, you can u | What is a good, convincing example in which p-values are useful?
I agree with Matt that p-values are useful when the null hypothesis is true.
The simplest example I can think of is testing a random number generator. If the generator is working correctly, you can use any appropriate sample size of realizations and when... | What is a good, convincing example in which p-values are useful?
I agree with Matt that p-values are useful when the null hypothesis is true.
The simplest example I can think of is testing a random number generator. If the generator is working correctly, you can u |
3,308 | What is a good, convincing example in which p-values are useful? | I can think of example in which p-values are useful, in Experimental High Energy Physics. See Fig.1 This plot is taken from this paper:
Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
In this Fig, the p-value is shown versus the mass of an hypothetical ... | What is a good, convincing example in which p-values are useful? | I can think of example in which p-values are useful, in Experimental High Energy Physics. See Fig.1 This plot is taken from this paper:
Observation of a new particle in the search for the Standard Mo | What is a good, convincing example in which p-values are useful?
I can think of example in which p-values are useful, in Experimental High Energy Physics. See Fig.1 This plot is taken from this paper:
Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
In t... | What is a good, convincing example in which p-values are useful?
I can think of example in which p-values are useful, in Experimental High Energy Physics. See Fig.1 This plot is taken from this paper:
Observation of a new particle in the search for the Standard Mo |
3,309 | Test if two binomial distributions are statistically different from each other | The solution is a simple google away: http://en.wikipedia.org/wiki/Statistical_hypothesis_testing
So you would like to test the following null hypothesis against the given alternative
$H_0:p_1=p_2$ versus $H_A:p_1\neq p_2$
So you just need to calculate the test statistic which is
$$z=\frac{\hat p_1-\hat p_2}{\sqrt{\hat... | Test if two binomial distributions are statistically different from each other | The solution is a simple google away: http://en.wikipedia.org/wiki/Statistical_hypothesis_testing
So you would like to test the following null hypothesis against the given alternative
$H_0:p_1=p_2$ ve | Test if two binomial distributions are statistically different from each other
The solution is a simple google away: http://en.wikipedia.org/wiki/Statistical_hypothesis_testing
So you would like to test the following null hypothesis against the given alternative
$H_0:p_1=p_2$ versus $H_A:p_1\neq p_2$
So you just need t... | Test if two binomial distributions are statistically different from each other
The solution is a simple google away: http://en.wikipedia.org/wiki/Statistical_hypothesis_testing
So you would like to test the following null hypothesis against the given alternative
$H_0:p_1=p_2$ ve |
3,310 | Test if two binomial distributions are statistically different from each other | 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.
In R the answer is calculated as:
fisher.test(rbind(... | Test if two binomial distributions are statistically different from each other | 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.
| Test if two binomial distributions are statistically different from each other
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.
... | Test if two binomial distributions are statistically different from each other
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.
|
3,311 | Test if two binomial distributions are statistically different from each other | Just a summary:
Dan and Abaumann's answers suggest testing under a binomial model where the null hypothesis is a unified single binomial model with its mean estimated from the empirical data. Their answers are correct in theory but they need approximation using normal distribution since the distribution of test statist... | Test if two binomial distributions are statistically different from each other | Just a summary:
Dan and Abaumann's answers suggest testing under a binomial model where the null hypothesis is a unified single binomial model with its mean estimated from the empirical data. Their an | Test if two binomial distributions are statistically different from each other
Just a summary:
Dan and Abaumann's answers suggest testing under a binomial model where the null hypothesis is a unified single binomial model with its mean estimated from the empirical data. Their answers are correct in theory but they need... | Test if two binomial distributions are statistically different from each other
Just a summary:
Dan and Abaumann's answers suggest testing under a binomial model where the null hypothesis is a unified single binomial model with its mean estimated from the empirical data. Their an |
3,312 | Test if two binomial distributions are statistically different from each other | Your test statistic is
$Z = \frac{\hat{p_1}-\hat{p_2}}{\sqrt{\hat{p}(1-\hat{p})(1/n_1+1/n_2)}}$, where $\hat{p}=\frac{n_1\hat{p_1}+n_2\hat{p_2}}{n_1+n_2}$.
The critical regions are $Z > \Phi^{-1}(1-\alpha/2)$ and $Z<\Phi^{-1}(\alpha/2)$ for the two-tailed test with the usual adjustments for a one-tailed test. | Test if two binomial distributions are statistically different from each other | Your test statistic is
$Z = \frac{\hat{p_1}-\hat{p_2}}{\sqrt{\hat{p}(1-\hat{p})(1/n_1+1/n_2)}}$, where $\hat{p}=\frac{n_1\hat{p_1}+n_2\hat{p_2}}{n_1+n_2}$.
The critical regions are $Z > \Phi^{-1}(1-\ | Test if two binomial distributions are statistically different from each other
Your test statistic is
$Z = \frac{\hat{p_1}-\hat{p_2}}{\sqrt{\hat{p}(1-\hat{p})(1/n_1+1/n_2)}}$, where $\hat{p}=\frac{n_1\hat{p_1}+n_2\hat{p_2}}{n_1+n_2}$.
The critical regions are $Z > \Phi^{-1}(1-\alpha/2)$ and $Z<\Phi^{-1}(\alpha/2)$ for... | Test if two binomial distributions are statistically different from each other
Your test statistic is
$Z = \frac{\hat{p_1}-\hat{p_2}}{\sqrt{\hat{p}(1-\hat{p})(1/n_1+1/n_2)}}$, where $\hat{p}=\frac{n_1\hat{p_1}+n_2\hat{p_2}}{n_1+n_2}$.
The critical regions are $Z > \Phi^{-1}(1-\ |
3,313 | Test if two binomial distributions are statistically different from each other | Original post: Dan's answer is actually incorrect, not to offend anyone. A z-test is used only if your data follows a standard normal distribution. In this case, your data follows a binomial distribution, therefore a use a chi-squared test if your sample is large or fisher's test if your sample is small.
Edit: My mist... | Test if two binomial distributions are statistically different from each other | Original post: Dan's answer is actually incorrect, not to offend anyone. A z-test is used only if your data follows a standard normal distribution. In this case, your data follows a binomial distribut | Test if two binomial distributions are statistically different from each other
Original post: Dan's answer is actually incorrect, not to offend anyone. A z-test is used only if your data follows a standard normal distribution. In this case, your data follows a binomial distribution, therefore a use a chi-squared test i... | Test if two binomial distributions are statistically different from each other
Original post: Dan's answer is actually incorrect, not to offend anyone. A z-test is used only if your data follows a standard normal distribution. In this case, your data follows a binomial distribut |
3,314 | Test if two binomial distributions are statistically different from each other | As suggested in other answers and comments, you can use an exact test that takes into account the origin of the data. Under the null hypothesis that the probability of success $\theta$ is the same in both experiments,
$P \bigl(\begin{smallmatrix}k_1 & k_2 \\ n_1-k_1 & n_2-k_2\end{smallmatrix}\bigr) = \binom{n_1}{k_1}\b... | Test if two binomial distributions are statistically different from each other | As suggested in other answers and comments, you can use an exact test that takes into account the origin of the data. Under the null hypothesis that the probability of success $\theta$ is the same in | Test if two binomial distributions are statistically different from each other
As suggested in other answers and comments, you can use an exact test that takes into account the origin of the data. Under the null hypothesis that the probability of success $\theta$ is the same in both experiments,
$P \bigl(\begin{smallma... | Test if two binomial distributions are statistically different from each other
As suggested in other answers and comments, you can use an exact test that takes into account the origin of the data. Under the null hypothesis that the probability of success $\theta$ is the same in |
3,315 | Why is tanh almost always better than sigmoid as an activation function? | Yan LeCun and others argue in Efficient BackProp that
Convergence is usually faster if the average of each input variable over the training set is close to zero. To see this, consider the extreme case where all the inputs are positive. Weights to a particular node in the first weight layer are updated by an amount pro... | Why is tanh almost always better than sigmoid as an activation function? | Yan LeCun and others argue in Efficient BackProp that
Convergence is usually faster if the average of each input variable over the training set is close to zero. To see this, consider the extreme cas | Why is tanh almost always better than sigmoid as an activation function?
Yan LeCun and others argue in Efficient BackProp that
Convergence is usually faster if the average of each input variable over the training set is close to zero. To see this, consider the extreme case where all the inputs are positive. Weights to... | Why is tanh almost always better than sigmoid as an activation function?
Yan LeCun and others argue in Efficient BackProp that
Convergence is usually faster if the average of each input variable over the training set is close to zero. To see this, consider the extreme cas |
3,316 | Why is tanh almost always better than sigmoid as an activation function? | It's not that it is necessarily better than $\text{sigmoid}$. In other words, it's not the center of an activation fuction that makes it better. And the idea behind both functions is the same, and they also share a similar "trend". Needless to say that the $\tanh$ function is called a shifted version of the $\text{sigm... | Why is tanh almost always better than sigmoid as an activation function? | It's not that it is necessarily better than $\text{sigmoid}$. In other words, it's not the center of an activation fuction that makes it better. And the idea behind both functions is the same, and the | Why is tanh almost always better than sigmoid as an activation function?
It's not that it is necessarily better than $\text{sigmoid}$. In other words, it's not the center of an activation fuction that makes it better. And the idea behind both functions is the same, and they also share a similar "trend". Needless to say... | Why is tanh almost always better than sigmoid as an activation function?
It's not that it is necessarily better than $\text{sigmoid}$. In other words, it's not the center of an activation fuction that makes it better. And the idea behind both functions is the same, and the |
3,317 | Why is tanh almost always better than sigmoid as an activation function? | It all essentially depends on the derivatives of the activation function, the main problem with the sigmoid function is that the max value of its derivative is 0.25, this means that the update of the values of W and b will be small.
The tanh function on the other hand, has a derivativ of up to 1.0, making the updates o... | Why is tanh almost always better than sigmoid as an activation function? | It all essentially depends on the derivatives of the activation function, the main problem with the sigmoid function is that the max value of its derivative is 0.25, this means that the update of the | Why is tanh almost always better than sigmoid as an activation function?
It all essentially depends on the derivatives of the activation function, the main problem with the sigmoid function is that the max value of its derivative is 0.25, this means that the update of the values of W and b will be small.
The tanh funct... | Why is tanh almost always better than sigmoid as an activation function?
It all essentially depends on the derivatives of the activation function, the main problem with the sigmoid function is that the max value of its derivative is 0.25, this means that the update of the |
3,318 | Why is tanh almost always better than sigmoid as an activation function? | Answering the part of the question so far unaddressed:
Andrew Ng says that using the logistic function (commonly know as sigmoid) really only makes sense in the final layer of a binary classification network.
As the output of the network is expected to be between $0$ and $1$, the logistic is a perfect choice as it's ra... | Why is tanh almost always better than sigmoid as an activation function? | Answering the part of the question so far unaddressed:
Andrew Ng says that using the logistic function (commonly know as sigmoid) really only makes sense in the final layer of a binary classification | Why is tanh almost always better than sigmoid as an activation function?
Answering the part of the question so far unaddressed:
Andrew Ng says that using the logistic function (commonly know as sigmoid) really only makes sense in the final layer of a binary classification network.
As the output of the network is expect... | Why is tanh almost always better than sigmoid as an activation function?
Answering the part of the question so far unaddressed:
Andrew Ng says that using the logistic function (commonly know as sigmoid) really only makes sense in the final layer of a binary classification |
3,319 | Why is tanh almost always better than sigmoid as an activation function? | Generally, the non-zero centered activation function restricts the movement of parameters over the surface area in some specific directions. Which makes the training slower because it needs mush steps to move from the initial point to the minimum point with these restricted movements.
For more details watch only 7 min ... | Why is tanh almost always better than sigmoid as an activation function? | Generally, the non-zero centered activation function restricts the movement of parameters over the surface area in some specific directions. Which makes the training slower because it needs mush steps | Why is tanh almost always better than sigmoid as an activation function?
Generally, the non-zero centered activation function restricts the movement of parameters over the surface area in some specific directions. Which makes the training slower because it needs mush steps to move from the initial point to the minimum ... | Why is tanh almost always better than sigmoid as an activation function?
Generally, the non-zero centered activation function restricts the movement of parameters over the surface area in some specific directions. Which makes the training slower because it needs mush steps |
3,320 | Testing equality of coefficients from two different regressions | Although this isn't a common analysis, it really is one of interest. The accepted answer fits the way you asked your question, but I'm going to provide another reasonably well accepted technique that may or may not be equivalent (I'll leave it to better minds to comment on that).
This approach is to use the following ... | Testing equality of coefficients from two different regressions | Although this isn't a common analysis, it really is one of interest. The accepted answer fits the way you asked your question, but I'm going to provide another reasonably well accepted technique that | Testing equality of coefficients from two different regressions
Although this isn't a common analysis, it really is one of interest. The accepted answer fits the way you asked your question, but I'm going to provide another reasonably well accepted technique that may or may not be equivalent (I'll leave it to better m... | Testing equality of coefficients from two different regressions
Although this isn't a common analysis, it really is one of interest. The accepted answer fits the way you asked your question, but I'm going to provide another reasonably well accepted technique that |
3,321 | Testing equality of coefficients from two different regressions | For people with a similar question, let me provide a simple outline of the answer.
The trick is to set up the two equations as a system of seemingly unrelated equations and to estimate them jointly. That is, we stack $y_1$ and $y_2$ on top of each other, and doing more or less the same with the design matrix. That is, ... | Testing equality of coefficients from two different regressions | For people with a similar question, let me provide a simple outline of the answer.
The trick is to set up the two equations as a system of seemingly unrelated equations and to estimate them jointly. T | Testing equality of coefficients from two different regressions
For people with a similar question, let me provide a simple outline of the answer.
The trick is to set up the two equations as a system of seemingly unrelated equations and to estimate them jointly. That is, we stack $y_1$ and $y_2$ on top of each other, a... | Testing equality of coefficients from two different regressions
For people with a similar question, let me provide a simple outline of the answer.
The trick is to set up the two equations as a system of seemingly unrelated equations and to estimate them jointly. T |
3,322 | Testing equality of coefficients from two different regressions | When the regressions come from two different samples, you can assume:
$Var(\beta_1-\beta_2)=Var(\beta_1)+Var(\beta_2)$ which leads to the formula provided in another answer.
But your question was precisely related to the case when $covar(\beta_1,\beta_2) \neq 0$. In this case, seemingly unrelated equations seems the mo... | Testing equality of coefficients from two different regressions | When the regressions come from two different samples, you can assume:
$Var(\beta_1-\beta_2)=Var(\beta_1)+Var(\beta_2)$ which leads to the formula provided in another answer.
But your question was prec | Testing equality of coefficients from two different regressions
When the regressions come from two different samples, you can assume:
$Var(\beta_1-\beta_2)=Var(\beta_1)+Var(\beta_2)$ which leads to the formula provided in another answer.
But your question was precisely related to the case when $covar(\beta_1,\beta_2) \... | Testing equality of coefficients from two different regressions
When the regressions come from two different samples, you can assume:
$Var(\beta_1-\beta_2)=Var(\beta_1)+Var(\beta_2)$ which leads to the formula provided in another answer.
But your question was prec |
3,323 | Testing equality of coefficients from two different regressions | Using some data, here is how you could use the Clifford Clogg et al. (1995) paper cited by Ray Paternoster et al. (1998). I have a small script, which can be improved to do that.
This assumes that you are using the R language and that you have two sets of regression coefficients that you have extracted from your model ... | Testing equality of coefficients from two different regressions | Using some data, here is how you could use the Clifford Clogg et al. (1995) paper cited by Ray Paternoster et al. (1998). I have a small script, which can be improved to do that.
This assumes that you | Testing equality of coefficients from two different regressions
Using some data, here is how you could use the Clifford Clogg et al. (1995) paper cited by Ray Paternoster et al. (1998). I have a small script, which can be improved to do that.
This assumes that you are using the R language and that you have two sets of ... | Testing equality of coefficients from two different regressions
Using some data, here is how you could use the Clifford Clogg et al. (1995) paper cited by Ray Paternoster et al. (1998). I have a small script, which can be improved to do that.
This assumes that you |
3,324 | Taleb and the Black Swan | I read the Black Swan a couple of years ago. The Black Swan idea is good and the attack on the ludic fallacy (seeing things as though they are dice games, with knowable probabilities) is good but statistics is outrageously misrepresented, with the central problem being the wrong claim that all statistics falls apart i... | Taleb and the Black Swan | I read the Black Swan a couple of years ago. The Black Swan idea is good and the attack on the ludic fallacy (seeing things as though they are dice games, with knowable probabilities) is good but sta | Taleb and the Black Swan
I read the Black Swan a couple of years ago. The Black Swan idea is good and the attack on the ludic fallacy (seeing things as though they are dice games, with knowable probabilities) is good but statistics is outrageously misrepresented, with the central problem being the wrong claim that all... | Taleb and the Black Swan
I read the Black Swan a couple of years ago. The Black Swan idea is good and the attack on the ludic fallacy (seeing things as though they are dice games, with knowable probabilities) is good but sta |
3,325 | Taleb and the Black Swan | I did read "The Black Swan", I did enjoy it, and I am a statistician. I didn't find its "criticism of statistics" unbearable, at all. Point by point:
Taleb did not invent the concept of the black swan. It had been a favored example in philosophical thought for quite a while!
Taleb is not so much criticizing "statist... | Taleb and the Black Swan | I did read "The Black Swan", I did enjoy it, and I am a statistician. I didn't find its "criticism of statistics" unbearable, at all. Point by point:
Taleb did not invent the concept of the black sw | Taleb and the Black Swan
I did read "The Black Swan", I did enjoy it, and I am a statistician. I didn't find its "criticism of statistics" unbearable, at all. Point by point:
Taleb did not invent the concept of the black swan. It had been a favored example in philosophical thought for quite a while!
Taleb is not so ... | Taleb and the Black Swan
I did read "The Black Swan", I did enjoy it, and I am a statistician. I didn't find its "criticism of statistics" unbearable, at all. Point by point:
Taleb did not invent the concept of the black sw |
3,326 | Taleb and the Black Swan | I've not read the book, but as stated the criticism seems pretty unreasonable to me. If extreme events are important, then statistics has appropriate tools in the toolbox, such as extreme value theory, and a good statistician will know how to use them (or at least find out how to use them and will be sufficiently enga... | Taleb and the Black Swan | I've not read the book, but as stated the criticism seems pretty unreasonable to me. If extreme events are important, then statistics has appropriate tools in the toolbox, such as extreme value theor | Taleb and the Black Swan
I've not read the book, but as stated the criticism seems pretty unreasonable to me. If extreme events are important, then statistics has appropriate tools in the toolbox, such as extreme value theory, and a good statistician will know how to use them (or at least find out how to use them and ... | Taleb and the Black Swan
I've not read the book, but as stated the criticism seems pretty unreasonable to me. If extreme events are important, then statistics has appropriate tools in the toolbox, such as extreme value theor |
3,327 | Taleb and the Black Swan | Saying that " the thrust of the book is that statistics is not very useful " is inaccurate, I think. Having read the book, what he appears to be saying is that things like quantitative finance or any sort of securities trading that assumes a normal distribution is fundamentally flawed (actually, in the book, he calls p... | Taleb and the Black Swan | Saying that " the thrust of the book is that statistics is not very useful " is inaccurate, I think. Having read the book, what he appears to be saying is that things like quantitative finance or any | Taleb and the Black Swan
Saying that " the thrust of the book is that statistics is not very useful " is inaccurate, I think. Having read the book, what he appears to be saying is that things like quantitative finance or any sort of securities trading that assumes a normal distribution is fundamentally flawed (actually... | Taleb and the Black Swan
Saying that " the thrust of the book is that statistics is not very useful " is inaccurate, I think. Having read the book, what he appears to be saying is that things like quantitative finance or any |
3,328 | Taleb and the Black Swan | I strongly recommend Dennis Lindley's review of this book. It contains a number of devastating arguments against the poor and arrogant exposition of ideas in the book:
http://onlinelibrary.wiley.com/doi/10.1111/j.1740-9713.2008.00281.x/abstract
The Black Swan is another example where being a "Best-seller" does not guar... | Taleb and the Black Swan | I strongly recommend Dennis Lindley's review of this book. It contains a number of devastating arguments against the poor and arrogant exposition of ideas in the book:
http://onlinelibrary.wiley.com/d | Taleb and the Black Swan
I strongly recommend Dennis Lindley's review of this book. It contains a number of devastating arguments against the poor and arrogant exposition of ideas in the book:
http://onlinelibrary.wiley.com/doi/10.1111/j.1740-9713.2008.00281.x/abstract
The Black Swan is another example where being a "B... | Taleb and the Black Swan
I strongly recommend Dennis Lindley's review of this book. It contains a number of devastating arguments against the poor and arrogant exposition of ideas in the book:
http://onlinelibrary.wiley.com/d |
3,329 | Taleb and the Black Swan | I haven't read the Black Swan, but if his criticism of statistics is really as simple as you say, then it's ridiculous. Obviously some statistics relies on the Normal distribution, but much does not.
Can rare events be modeled? Of course they can. The real question is how well they can be modeled. And that question wi... | Taleb and the Black Swan | I haven't read the Black Swan, but if his criticism of statistics is really as simple as you say, then it's ridiculous. Obviously some statistics relies on the Normal distribution, but much does not. | Taleb and the Black Swan
I haven't read the Black Swan, but if his criticism of statistics is really as simple as you say, then it's ridiculous. Obviously some statistics relies on the Normal distribution, but much does not.
Can rare events be modeled? Of course they can. The real question is how well they can be mode... | Taleb and the Black Swan
I haven't read the Black Swan, but if his criticism of statistics is really as simple as you say, then it's ridiculous. Obviously some statistics relies on the Normal distribution, but much does not. |
3,330 | Taleb and the Black Swan | I also have not read the book, but there is no way that his point can be as simplistic as saying that there are distributions with fatter tails than the normal distribution. This would be a comment to the other answers, but I have not accumulated enough accolades on this website.
From Wikipedia:
"He states that statis... | Taleb and the Black Swan | I also have not read the book, but there is no way that his point can be as simplistic as saying that there are distributions with fatter tails than the normal distribution. This would be a comment t | Taleb and the Black Swan
I also have not read the book, but there is no way that his point can be as simplistic as saying that there are distributions with fatter tails than the normal distribution. This would be a comment to the other answers, but I have not accumulated enough accolades on this website.
From Wikipedi... | Taleb and the Black Swan
I also have not read the book, but there is no way that his point can be as simplistic as saying that there are distributions with fatter tails than the normal distribution. This would be a comment t |
3,331 | Taleb and the Black Swan | I don't think Taleb would actually say that statistical techniques relying on the Gaussian distribution are not useful. His point in the book was that they are highly useful for many (but not all) physical or biological processes and modeling. He makes some good points and some bad (The Black Swan and Linked were the b... | Taleb and the Black Swan | I don't think Taleb would actually say that statistical techniques relying on the Gaussian distribution are not useful. His point in the book was that they are highly useful for many (but not all) phy | Taleb and the Black Swan
I don't think Taleb would actually say that statistical techniques relying on the Gaussian distribution are not useful. His point in the book was that they are highly useful for many (but not all) physical or biological processes and modeling. He makes some good points and some bad (The Black S... | Taleb and the Black Swan
I don't think Taleb would actually say that statistical techniques relying on the Gaussian distribution are not useful. His point in the book was that they are highly useful for many (but not all) phy |
3,332 | Taleb and the Black Swan | Those of you who have not read the book are way off base. He makes a LARGE distinction between the scalable and unscalable. For unscalable matters traditional stats will serve one well enough. He is not critiquing that whatsoever. Black Swans originate in the scalable and are hard to predict given past empirical data. ... | Taleb and the Black Swan | Those of you who have not read the book are way off base. He makes a LARGE distinction between the scalable and unscalable. For unscalable matters traditional stats will serve one well enough. He is n | Taleb and the Black Swan
Those of you who have not read the book are way off base. He makes a LARGE distinction between the scalable and unscalable. For unscalable matters traditional stats will serve one well enough. He is not critiquing that whatsoever. Black Swans originate in the scalable and are hard to predict gi... | Taleb and the Black Swan
Those of you who have not read the book are way off base. He makes a LARGE distinction between the scalable and unscalable. For unscalable matters traditional stats will serve one well enough. He is n |
3,333 | Standard errors for lasso prediction using R | Kyung et al. (2010), "Penalized regression, standard errors, & Bayesian lassos", Bayesian Analysis , 5, 2, suggest that there might not be a consensus on a statistically valid method of calculating standard errors for the lasso predictions. Tibshirani seems to agree (slide 43) that standard errors are still an unresolv... | Standard errors for lasso prediction using R | Kyung et al. (2010), "Penalized regression, standard errors, & Bayesian lassos", Bayesian Analysis , 5, 2, suggest that there might not be a consensus on a statistically valid method of calculating st | Standard errors for lasso prediction using R
Kyung et al. (2010), "Penalized regression, standard errors, & Bayesian lassos", Bayesian Analysis , 5, 2, suggest that there might not be a consensus on a statistically valid method of calculating standard errors for the lasso predictions. Tibshirani seems to agree (slide 4... | Standard errors for lasso prediction using R
Kyung et al. (2010), "Penalized regression, standard errors, & Bayesian lassos", Bayesian Analysis , 5, 2, suggest that there might not be a consensus on a statistically valid method of calculating st |
3,334 | Standard errors for lasso prediction using R | On a related note, which may be helpful, Tibshirani and colleagues have proposed a significance test for the lasso. The paper is available, and titled "A significance test for the lasso". A free version of the paper can be found here | Standard errors for lasso prediction using R | On a related note, which may be helpful, Tibshirani and colleagues have proposed a significance test for the lasso. The paper is available, and titled "A significance test for the lasso". A free versi | Standard errors for lasso prediction using R
On a related note, which may be helpful, Tibshirani and colleagues have proposed a significance test for the lasso. The paper is available, and titled "A significance test for the lasso". A free version of the paper can be found here | Standard errors for lasso prediction using R
On a related note, which may be helpful, Tibshirani and colleagues have proposed a significance test for the lasso. The paper is available, and titled "A significance test for the lasso". A free versi |
3,335 | Standard errors for lasso prediction using R | Sandipan Karmakar answer tells you what to do, this should help you on the "how":
> library(monomvn)
>
> ## following the lars diabetes example
> data(diabetes)
> str(diabetes)
'data.frame': 442 obs. of 3 variables:
$ x : AsIs [1:442, 1:10] 0.038075.... -0.00188.... 0.085298.... -0.08906.... 0.005383.... ...
... | Standard errors for lasso prediction using R | Sandipan Karmakar answer tells you what to do, this should help you on the "how":
> library(monomvn)
>
> ## following the lars diabetes example
> data(diabetes)
> str(diabetes)
'data.frame': 442 obs | Standard errors for lasso prediction using R
Sandipan Karmakar answer tells you what to do, this should help you on the "how":
> library(monomvn)
>
> ## following the lars diabetes example
> data(diabetes)
> str(diabetes)
'data.frame': 442 obs. of 3 variables:
$ x : AsIs [1:442, 1:10] 0.038075.... -0.00188.... 0.08... | Standard errors for lasso prediction using R
Sandipan Karmakar answer tells you what to do, this should help you on the "how":
> library(monomvn)
>
> ## following the lars diabetes example
> data(diabetes)
> str(diabetes)
'data.frame': 442 obs |
3,336 | Standard errors for lasso prediction using R | Bayesian LASSO is the only alternative to the problem of calculating standard errors. Standard errors are automatically calculated in Bayesian LASSO...You can implement Bayesian LASSO very easily using Gibbs Sampling scheme...
Bayesian LASSO needs prior distributions to be assigned to the parameters of the model. In LA... | Standard errors for lasso prediction using R | Bayesian LASSO is the only alternative to the problem of calculating standard errors. Standard errors are automatically calculated in Bayesian LASSO...You can implement Bayesian LASSO very easily usin | Standard errors for lasso prediction using R
Bayesian LASSO is the only alternative to the problem of calculating standard errors. Standard errors are automatically calculated in Bayesian LASSO...You can implement Bayesian LASSO very easily using Gibbs Sampling scheme...
Bayesian LASSO needs prior distributions to be a... | Standard errors for lasso prediction using R
Bayesian LASSO is the only alternative to the problem of calculating standard errors. Standard errors are automatically calculated in Bayesian LASSO...You can implement Bayesian LASSO very easily usin |
3,337 | Standard errors for lasso prediction using R | To add to the answers above, the issue appears to be that even a bootstrap is likely insufficient as the estimate from the penalized model is biased and bootstrapping will only speak to the variance - ignoring the bias of the estimate. This is nicely summarized in the vignette for the penalized package on Page 18.
If b... | Standard errors for lasso prediction using R | To add to the answers above, the issue appears to be that even a bootstrap is likely insufficient as the estimate from the penalized model is biased and bootstrapping will only speak to the variance - | Standard errors for lasso prediction using R
To add to the answers above, the issue appears to be that even a bootstrap is likely insufficient as the estimate from the penalized model is biased and bootstrapping will only speak to the variance - ignoring the bias of the estimate. This is nicely summarized in the vignet... | Standard errors for lasso prediction using R
To add to the answers above, the issue appears to be that even a bootstrap is likely insufficient as the estimate from the penalized model is biased and bootstrapping will only speak to the variance - |
3,338 | Standard errors for lasso prediction using R | There is the selectiveInference package in R, https://cran.r-project.org/web/packages/selectiveInference/index.html, that provides confidence intervals and p values for your coefficients fitted by the LASSO, based on the following paper:
Stephen Reid, Jerome Friedman, and Rob Tibshirani (2014). A study of error varianc... | Standard errors for lasso prediction using R | There is the selectiveInference package in R, https://cran.r-project.org/web/packages/selectiveInference/index.html, that provides confidence intervals and p values for your coefficients fitted by the | Standard errors for lasso prediction using R
There is the selectiveInference package in R, https://cran.r-project.org/web/packages/selectiveInference/index.html, that provides confidence intervals and p values for your coefficients fitted by the LASSO, based on the following paper:
Stephen Reid, Jerome Friedman, and Ro... | Standard errors for lasso prediction using R
There is the selectiveInference package in R, https://cran.r-project.org/web/packages/selectiveInference/index.html, that provides confidence intervals and p values for your coefficients fitted by the |
3,339 | How do you calculate the probability density function of the maximum of a sample of IID uniform random variables? | It is possible that this question is homework but I felt this classical elementary probability question was still lacking a complete answer after several months, so I'll give one here.
From the problem statement, we want the distribution of
$$Y = \max \{ X_1, ..., X_n \}$$
where $X_1, ..., X_n$ are iid ${\rm Uniform}(a... | How do you calculate the probability density function of the maximum of a sample of IID uniform rand | It is possible that this question is homework but I felt this classical elementary probability question was still lacking a complete answer after several months, so I'll give one here.
From the proble | How do you calculate the probability density function of the maximum of a sample of IID uniform random variables?
It is possible that this question is homework but I felt this classical elementary probability question was still lacking a complete answer after several months, so I'll give one here.
From the problem stat... | How do you calculate the probability density function of the maximum of a sample of IID uniform rand
It is possible that this question is homework but I felt this classical elementary probability question was still lacking a complete answer after several months, so I'll give one here.
From the proble |
3,340 | How do you calculate the probability density function of the maximum of a sample of IID uniform random variables? | The maximum of a sample is one of the order statistics, in particular the $n$th order statistic of the sample $X_1,\dots,X_n$. In general, computing the distribution of order statistics is difficult, as described by the Wikipedia article; for some special distributions, the order statistics are well-known (e.g. for the... | How do you calculate the probability density function of the maximum of a sample of IID uniform rand | The maximum of a sample is one of the order statistics, in particular the $n$th order statistic of the sample $X_1,\dots,X_n$. In general, computing the distribution of order statistics is difficult, | How do you calculate the probability density function of the maximum of a sample of IID uniform random variables?
The maximum of a sample is one of the order statistics, in particular the $n$th order statistic of the sample $X_1,\dots,X_n$. In general, computing the distribution of order statistics is difficult, as des... | How do you calculate the probability density function of the maximum of a sample of IID uniform rand
The maximum of a sample is one of the order statistics, in particular the $n$th order statistic of the sample $X_1,\dots,X_n$. In general, computing the distribution of order statistics is difficult, |
3,341 | How do you calculate the probability density function of the maximum of a sample of IID uniform random variables? | If $F_{Y}(y)$ is the CDF of $Y$, then
$$F_Y(y)=\text{Prob}(y>X_1,y>X_2,...,y>X_n)$$
You can then use the iid property and the cdf of a uniform variate to compute $F_Y(y)$. | How do you calculate the probability density function of the maximum of a sample of IID uniform rand | If $F_{Y}(y)$ is the CDF of $Y$, then
$$F_Y(y)=\text{Prob}(y>X_1,y>X_2,...,y>X_n)$$
You can then use the iid property and the cdf of a uniform variate to compute $F_Y(y)$. | How do you calculate the probability density function of the maximum of a sample of IID uniform random variables?
If $F_{Y}(y)$ is the CDF of $Y$, then
$$F_Y(y)=\text{Prob}(y>X_1,y>X_2,...,y>X_n)$$
You can then use the iid property and the cdf of a uniform variate to compute $F_Y(y)$. | How do you calculate the probability density function of the maximum of a sample of IID uniform rand
If $F_{Y}(y)$ is the CDF of $Y$, then
$$F_Y(y)=\text{Prob}(y>X_1,y>X_2,...,y>X_n)$$
You can then use the iid property and the cdf of a uniform variate to compute $F_Y(y)$. |
3,342 | How do you calculate the probability density function of the maximum of a sample of IID uniform random variables? | The maximum of a set of IID random variables when appropriately normalized will generally converge to one of the three extreme value types. This is Gnedenko's theorem,the equivalence of the central limit theorem for extremes. The particular type depends on the tail behavior of the population distribution. Knowing th... | How do you calculate the probability density function of the maximum of a sample of IID uniform rand | The maximum of a set of IID random variables when appropriately normalized will generally converge to one of the three extreme value types. This is Gnedenko's theorem,the equivalence of the central l | How do you calculate the probability density function of the maximum of a sample of IID uniform random variables?
The maximum of a set of IID random variables when appropriately normalized will generally converge to one of the three extreme value types. This is Gnedenko's theorem,the equivalence of the central limit t... | How do you calculate the probability density function of the maximum of a sample of IID uniform rand
The maximum of a set of IID random variables when appropriately normalized will generally converge to one of the three extreme value types. This is Gnedenko's theorem,the equivalence of the central l |
3,343 | Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regression? | Controlling for something and ignoring something are not the same thing. Let's consider a universe in which only 3 variables exist: $Y$, $X_1$, and $X_2$. We want to build a regression model that predicts $Y$, and we are especially interested in its relationship with $X_1$. There are two basic possibilities.
We c... | Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regressio | Controlling for something and ignoring something are not the same thing. Let's consider a universe in which only 3 variables exist: $Y$, $X_1$, and $X_2$. We want to build a regression model that pr | Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regression?
Controlling for something and ignoring something are not the same thing. Let's consider a universe in which only 3 variables exist: $Y$, $X_1$, and $X_2$. We want to build a regression model that predicts $Y$, and w... | Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regressio
Controlling for something and ignoring something are not the same thing. Let's consider a universe in which only 3 variables exist: $Y$, $X_1$, and $X_2$. We want to build a regression model that pr |
3,344 | Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regression? | They are not ignored. If they were 'ignored' they would not be in the model. The estimate of the explanatory variable of interest is conditional on the other variables. The estimate is formed "in the context of" or "allowing for the impact of" the other variables in the model. | Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regressio | They are not ignored. If they were 'ignored' they would not be in the model. The estimate of the explanatory variable of interest is conditional on the other variables. The estimate is formed "in the | Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regression?
They are not ignored. If they were 'ignored' they would not be in the model. The estimate of the explanatory variable of interest is conditional on the other variables. The estimate is formed "in the context of" or "a... | Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regressio
They are not ignored. If they were 'ignored' they would not be in the model. The estimate of the explanatory variable of interest is conditional on the other variables. The estimate is formed "in the |
3,345 | Why is expectation the same as the arithmetic mean? | Informally, a probability distribution defines the relative frequency of outcomes of a random variable - the expected value can be thought of as a weighted average of those outcomes (weighted by the relative frequency). Similarly, the expected value can be thought of as the arithmetic mean of a set of numbers generated... | Why is expectation the same as the arithmetic mean? | Informally, a probability distribution defines the relative frequency of outcomes of a random variable - the expected value can be thought of as a weighted average of those outcomes (weighted by the r | Why is expectation the same as the arithmetic mean?
Informally, a probability distribution defines the relative frequency of outcomes of a random variable - the expected value can be thought of as a weighted average of those outcomes (weighted by the relative frequency). Similarly, the expected value can be thought of ... | Why is expectation the same as the arithmetic mean?
Informally, a probability distribution defines the relative frequency of outcomes of a random variable - the expected value can be thought of as a weighted average of those outcomes (weighted by the r |
3,346 | Why is expectation the same as the arithmetic mean? | The expectation is the average value or mean of a random variable not a probability distribution. As such it is for discrete random variables the weighted average of the values the random variable takes on where the weighting is according to the relative frequency of occurrence of those individual values. For an absol... | Why is expectation the same as the arithmetic mean? | The expectation is the average value or mean of a random variable not a probability distribution. As such it is for discrete random variables the weighted average of the values the random variable tak | Why is expectation the same as the arithmetic mean?
The expectation is the average value or mean of a random variable not a probability distribution. As such it is for discrete random variables the weighted average of the values the random variable takes on where the weighting is according to the relative frequency of ... | Why is expectation the same as the arithmetic mean?
The expectation is the average value or mean of a random variable not a probability distribution. As such it is for discrete random variables the weighted average of the values the random variable tak |
3,347 | Why is expectation the same as the arithmetic mean? | Let's pay close attention to the definitions:
Mean is defined as the sum of a collection of numbers divided by the number of numbers in the collection. The calculation would be "for i in 1 to n, (sum of x sub i) divided by n."
Expected value (EV) is the long-run average value of repetitions of the experiment it repres... | Why is expectation the same as the arithmetic mean? | Let's pay close attention to the definitions:
Mean is defined as the sum of a collection of numbers divided by the number of numbers in the collection. The calculation would be "for i in 1 to n, (sum | Why is expectation the same as the arithmetic mean?
Let's pay close attention to the definitions:
Mean is defined as the sum of a collection of numbers divided by the number of numbers in the collection. The calculation would be "for i in 1 to n, (sum of x sub i) divided by n."
Expected value (EV) is the long-run aver... | Why is expectation the same as the arithmetic mean?
Let's pay close attention to the definitions:
Mean is defined as the sum of a collection of numbers divided by the number of numbers in the collection. The calculation would be "for i in 1 to n, (sum |
3,348 | Why is expectation the same as the arithmetic mean? | The only difference between "mean" and "expected value" is that mean is mainly used for frequency distribution and expectation is used for probability distribution. In frequency distribution, sample space consists of variables and their frequencies of occurrence. In probability distribution, sample space consists of ra... | Why is expectation the same as the arithmetic mean? | The only difference between "mean" and "expected value" is that mean is mainly used for frequency distribution and expectation is used for probability distribution. In frequency distribution, sample s | Why is expectation the same as the arithmetic mean?
The only difference between "mean" and "expected value" is that mean is mainly used for frequency distribution and expectation is used for probability distribution. In frequency distribution, sample space consists of variables and their frequencies of occurrence. In p... | Why is expectation the same as the arithmetic mean?
The only difference between "mean" and "expected value" is that mean is mainly used for frequency distribution and expectation is used for probability distribution. In frequency distribution, sample s |
3,349 | Derivation of closed form lasso solution | This can be attacked in a number of ways, including fairly economical approaches via the Karush–Kuhn–Tucker conditions.
Below is a quite elementary alternative argument.
The least squares solution for an orthogonal design
Suppose $X$ is composed of orthogonal columns. Then, the least-squares solution is
$$
\newcomman... | Derivation of closed form lasso solution | This can be attacked in a number of ways, including fairly economical approaches via the Karush–Kuhn–Tucker conditions.
Below is a quite elementary alternative argument.
The least squares solution for | Derivation of closed form lasso solution
This can be attacked in a number of ways, including fairly economical approaches via the Karush–Kuhn–Tucker conditions.
Below is a quite elementary alternative argument.
The least squares solution for an orthogonal design
Suppose $X$ is composed of orthogonal columns. Then, the ... | Derivation of closed form lasso solution
This can be attacked in a number of ways, including fairly economical approaches via the Karush–Kuhn–Tucker conditions.
Below is a quite elementary alternative argument.
The least squares solution for |
3,350 | Derivation of closed form lasso solution | Assume that the covariates $x_j$, the columns of $X \in \mathbb{R}^{n \times p}$, are also standardized so that $X^T X = I$. This is just for convenience later: without it, the notation just gets heavier since $X^T X$ is only diagonal. Further assume that $n \geq p$. This is a necessary assumption for the result to ho... | Derivation of closed form lasso solution | Assume that the covariates $x_j$, the columns of $X \in \mathbb{R}^{n \times p}$, are also standardized so that $X^T X = I$. This is just for convenience later: without it, the notation just gets heav | Derivation of closed form lasso solution
Assume that the covariates $x_j$, the columns of $X \in \mathbb{R}^{n \times p}$, are also standardized so that $X^T X = I$. This is just for convenience later: without it, the notation just gets heavier since $X^T X$ is only diagonal. Further assume that $n \geq p$. This is a ... | Derivation of closed form lasso solution
Assume that the covariates $x_j$, the columns of $X \in \mathbb{R}^{n \times p}$, are also standardized so that $X^T X = I$. This is just for convenience later: without it, the notation just gets heav |
3,351 | Advanced statistics books recommendation | Maximum likelihood: In all Likelihood (Pawitan). Moderately clear book and the most clear (IMO) with respect to books dealing with likelihood only. Also has R code.
GLMs: Categorical Data Analysis (Agresti, 2002) is one of the best written stat books I have read (also has R code available). This text will also help wit... | Advanced statistics books recommendation | Maximum likelihood: In all Likelihood (Pawitan). Moderately clear book and the most clear (IMO) with respect to books dealing with likelihood only. Also has R code.
GLMs: Categorical Data Analysis (Ag | Advanced statistics books recommendation
Maximum likelihood: In all Likelihood (Pawitan). Moderately clear book and the most clear (IMO) with respect to books dealing with likelihood only. Also has R code.
GLMs: Categorical Data Analysis (Agresti, 2002) is one of the best written stat books I have read (also has R code... | Advanced statistics books recommendation
Maximum likelihood: In all Likelihood (Pawitan). Moderately clear book and the most clear (IMO) with respect to books dealing with likelihood only. Also has R code.
GLMs: Categorical Data Analysis (Ag |
3,352 | Advanced statistics books recommendation | Some books on Likelihood Estimation
* Amari, Barndorff-Nielsen, Kass, Lauritzen and Rao, Differential geometry in statistical inference.
$-\small{\text{Geometrical approach for proving existence, uniqueness and other properties of MLE.}}$
* Butler, Saddlepoint Approximations with Applications.
$-\small{\text{Saddlepo... | Advanced statistics books recommendation | Some books on Likelihood Estimation
* Amari, Barndorff-Nielsen, Kass, Lauritzen and Rao, Differential geometry in statistical inference.
$-\small{\text{Geometrical approach for proving existence, uni | Advanced statistics books recommendation
Some books on Likelihood Estimation
* Amari, Barndorff-Nielsen, Kass, Lauritzen and Rao, Differential geometry in statistical inference.
$-\small{\text{Geometrical approach for proving existence, uniqueness and other properties of MLE.}}$
* Butler, Saddlepoint Approximations w... | Advanced statistics books recommendation
Some books on Likelihood Estimation
* Amari, Barndorff-Nielsen, Kass, Lauritzen and Rao, Differential geometry in statistical inference.
$-\small{\text{Geometrical approach for proving existence, uni |
3,353 | Advanced statistics books recommendation | My guess is that, for your requirements, the best book on generalized linear models is probably:
Agresti's Introduction to Categorical Data Analysis
There are other books that might be considered better, but I suspect would be less appealing to a practitioner who would prefer to avoid dense mathematics:
Agresti... | Advanced statistics books recommendation | My guess is that, for your requirements, the best book on generalized linear models is probably:
Agresti's Introduction to Categorical Data Analysis
There are other books that might be considered | Advanced statistics books recommendation
My guess is that, for your requirements, the best book on generalized linear models is probably:
Agresti's Introduction to Categorical Data Analysis
There are other books that might be considered better, but I suspect would be less appealing to a practitioner who would pref... | Advanced statistics books recommendation
My guess is that, for your requirements, the best book on generalized linear models is probably:
Agresti's Introduction to Categorical Data Analysis
There are other books that might be considered |
3,354 | Advanced statistics books recommendation | Not sure if these are at the level you're looking for, but some books I've found useful-
GLMs - McCullagh and Nelder is the canonical book
PCA - A User's Guide to Principal Components - despite the title it does go into some degree of depth on the topic | Advanced statistics books recommendation | Not sure if these are at the level you're looking for, but some books I've found useful-
GLMs - McCullagh and Nelder is the canonical book
PCA - A User's Guide to Principal Components - despite the ti | Advanced statistics books recommendation
Not sure if these are at the level you're looking for, but some books I've found useful-
GLMs - McCullagh and Nelder is the canonical book
PCA - A User's Guide to Principal Components - despite the title it does go into some degree of depth on the topic | Advanced statistics books recommendation
Not sure if these are at the level you're looking for, but some books I've found useful-
GLMs - McCullagh and Nelder is the canonical book
PCA - A User's Guide to Principal Components - despite the ti |
3,355 | Advanced statistics books recommendation | I really like Larry Wasserman's books "All of Statistics" and "All of Nonparametric Statistics". They are very readable, and cover a lot of ground quickly. | Advanced statistics books recommendation | I really like Larry Wasserman's books "All of Statistics" and "All of Nonparametric Statistics". They are very readable, and cover a lot of ground quickly. | Advanced statistics books recommendation
I really like Larry Wasserman's books "All of Statistics" and "All of Nonparametric Statistics". They are very readable, and cover a lot of ground quickly. | Advanced statistics books recommendation
I really like Larry Wasserman's books "All of Statistics" and "All of Nonparametric Statistics". They are very readable, and cover a lot of ground quickly. |
3,356 | Advanced statistics books recommendation | 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.
The Nonlinear Models books that I like and rely on are... | Advanced statistics books recommendation | 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.
| Advanced statistics books recommendation
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.
The Nonlinear... | Advanced statistics books recommendation
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.
|
3,357 | Advanced statistics books recommendation | For Bayesian analysis (including imprecise analysis), I'm going to put in big plugs for:
Bernardo, J.M. and Smith, A.F.M. (2000) Bayesian Theory. Wiley: Chichester.
Gelman, A. et al (2013) Bayesian Data Analysis (Third Edition). CRC Press: Boca Raton.
Walley, P. (1990) Statistical Reasoning with Imprecise Probabiliti... | Advanced statistics books recommendation | For Bayesian analysis (including imprecise analysis), I'm going to put in big plugs for:
Bernardo, J.M. and Smith, A.F.M. (2000) Bayesian Theory. Wiley: Chichester.
Gelman, A. et al (2013) Bayesian D | Advanced statistics books recommendation
For Bayesian analysis (including imprecise analysis), I'm going to put in big plugs for:
Bernardo, J.M. and Smith, A.F.M. (2000) Bayesian Theory. Wiley: Chichester.
Gelman, A. et al (2013) Bayesian Data Analysis (Third Edition). CRC Press: Boca Raton.
Walley, P. (1990) Statist... | Advanced statistics books recommendation
For Bayesian analysis (including imprecise analysis), I'm going to put in big plugs for:
Bernardo, J.M. and Smith, A.F.M. (2000) Bayesian Theory. Wiley: Chichester.
Gelman, A. et al (2013) Bayesian D |
3,358 | Advanced statistics books recommendation | Mehta (2014) Statistical Topics (ISBN: 978-1499273533) is good intermediate level statistics story telling. Doesn't cover much of you topics you noted above though. | Advanced statistics books recommendation | Mehta (2014) Statistical Topics (ISBN: 978-1499273533) is good intermediate level statistics story telling. Doesn't cover much of you topics you noted above though. | Advanced statistics books recommendation
Mehta (2014) Statistical Topics (ISBN: 978-1499273533) is good intermediate level statistics story telling. Doesn't cover much of you topics you noted above though. | Advanced statistics books recommendation
Mehta (2014) Statistical Topics (ISBN: 978-1499273533) is good intermediate level statistics story telling. Doesn't cover much of you topics you noted above though. |
3,359 | Advanced statistics books recommendation | One really simple introductory statistics book is Andy Field's "Discovering Statistics using R" - also available for SPSS.
It contains a lot of nice examples and is even fun to read. Less precise, though compared to other books, but with very little mathematical formulations and lots of text. I found it easy for a basi... | Advanced statistics books recommendation | One really simple introductory statistics book is Andy Field's "Discovering Statistics using R" - also available for SPSS.
It contains a lot of nice examples and is even fun to read. Less precise, tho | Advanced statistics books recommendation
One really simple introductory statistics book is Andy Field's "Discovering Statistics using R" - also available for SPSS.
It contains a lot of nice examples and is even fun to read. Less precise, though compared to other books, but with very little mathematical formulations and... | Advanced statistics books recommendation
One really simple introductory statistics book is Andy Field's "Discovering Statistics using R" - also available for SPSS.
It contains a lot of nice examples and is even fun to read. Less precise, tho |
3,360 | What is the proper usage of scale_pos_weight in xgboost for imbalanced datasets? | Generally, scale_pos_weight is the ratio of number of negative class to the positive class.
Suppose, the dataset has 90 observations of negative class and 10 observations of positive class, then ideal value of scale_pos_weight should be 9.
See the doc:
http://xgboost.readthedocs.io/en/latest/parameter.html | What is the proper usage of scale_pos_weight in xgboost for imbalanced datasets? | Generally, scale_pos_weight is the ratio of number of negative class to the positive class.
Suppose, the dataset has 90 observations of negative class and 10 observations of positive class, then ideal | What is the proper usage of scale_pos_weight in xgboost for imbalanced datasets?
Generally, scale_pos_weight is the ratio of number of negative class to the positive class.
Suppose, the dataset has 90 observations of negative class and 10 observations of positive class, then ideal value of scale_pos_weight should be 9.... | What is the proper usage of scale_pos_weight in xgboost for imbalanced datasets?
Generally, scale_pos_weight is the ratio of number of negative class to the positive class.
Suppose, the dataset has 90 observations of negative class and 10 observations of positive class, then ideal |
3,361 | What is the proper usage of scale_pos_weight in xgboost for imbalanced datasets? | All the documentation says that is should be:
scale_pos_weight = count(negative examples)/count(Positive examples)
In practice, that works pretty well, but if your dataset is extremely unbalanced I'd recommend using something more conservative like:
scale_pos_weight = sqrt(count(negative examples)/count(Positive exam... | What is the proper usage of scale_pos_weight in xgboost for imbalanced datasets? | All the documentation says that is should be:
scale_pos_weight = count(negative examples)/count(Positive examples)
In practice, that works pretty well, but if your dataset is extremely unbalanced I'd | What is the proper usage of scale_pos_weight in xgboost for imbalanced datasets?
All the documentation says that is should be:
scale_pos_weight = count(negative examples)/count(Positive examples)
In practice, that works pretty well, but if your dataset is extremely unbalanced I'd recommend using something more conserv... | What is the proper usage of scale_pos_weight in xgboost for imbalanced datasets?
All the documentation says that is should be:
scale_pos_weight = count(negative examples)/count(Positive examples)
In practice, that works pretty well, but if your dataset is extremely unbalanced I'd |
3,362 | What is the proper usage of scale_pos_weight in xgboost for imbalanced datasets? | I understand your question and frustration, but I am not sure this is something that could be computed analytically, rather you'd have to determine a good setting empirically for your data, as you do for most hyper parameters, using cross validation as @user2149631 suggested. I've had some success using SelectFPR with ... | What is the proper usage of scale_pos_weight in xgboost for imbalanced datasets? | I understand your question and frustration, but I am not sure this is something that could be computed analytically, rather you'd have to determine a good setting empirically for your data, as you do | What is the proper usage of scale_pos_weight in xgboost for imbalanced datasets?
I understand your question and frustration, but I am not sure this is something that could be computed analytically, rather you'd have to determine a good setting empirically for your data, as you do for most hyper parameters, using cross ... | What is the proper usage of scale_pos_weight in xgboost for imbalanced datasets?
I understand your question and frustration, but I am not sure this is something that could be computed analytically, rather you'd have to determine a good setting empirically for your data, as you do |
3,363 | What is the proper usage of scale_pos_weight in xgboost for imbalanced datasets? | I also stumbled upon this dilemma and still looking for the best solution. However, I would suggest you using methods such as Grid Search (GridSearchCV in sklearn) for best parameter tuning for your classifier. However, if your dataset is highly imbalanced, its worthwhile to consider sampling methods (especially random... | What is the proper usage of scale_pos_weight in xgboost for imbalanced datasets? | I also stumbled upon this dilemma and still looking for the best solution. However, I would suggest you using methods such as Grid Search (GridSearchCV in sklearn) for best parameter tuning for your c | What is the proper usage of scale_pos_weight in xgboost for imbalanced datasets?
I also stumbled upon this dilemma and still looking for the best solution. However, I would suggest you using methods such as Grid Search (GridSearchCV in sklearn) for best parameter tuning for your classifier. However, if your dataset is ... | What is the proper usage of scale_pos_weight in xgboost for imbalanced datasets?
I also stumbled upon this dilemma and still looking for the best solution. However, I would suggest you using methods such as Grid Search (GridSearchCV in sklearn) for best parameter tuning for your c |
3,364 | Variables are often adjusted (e.g. standardised) before making a model - when is this a good idea, and when is it a bad one? | Standardization is all about the weights of different variables for the model.
If you do the standardisation "only" for the sake of numerical stability, there may be transformations that yield very similar numerical properties but different physical meaning that could be much more appropriate for the interpretation. T... | Variables are often adjusted (e.g. standardised) before making a model - when is this a good idea, a | Standardization is all about the weights of different variables for the model.
If you do the standardisation "only" for the sake of numerical stability, there may be transformations that yield very s | Variables are often adjusted (e.g. standardised) before making a model - when is this a good idea, and when is it a bad one?
Standardization is all about the weights of different variables for the model.
If you do the standardisation "only" for the sake of numerical stability, there may be transformations that yield v... | Variables are often adjusted (e.g. standardised) before making a model - when is this a good idea, a
Standardization is all about the weights of different variables for the model.
If you do the standardisation "only" for the sake of numerical stability, there may be transformations that yield very s |
3,365 | Variables are often adjusted (e.g. standardised) before making a model - when is this a good idea, and when is it a bad one? | One thing I always ask myself before standardizing is, "How will I interpret the output?" If there is a way to analyze data without transformation, this may well be preferable purely from an interpretation standpoint. | Variables are often adjusted (e.g. standardised) before making a model - when is this a good idea, a | One thing I always ask myself before standardizing is, "How will I interpret the output?" If there is a way to analyze data without transformation, this may well be preferable purely from an interpre | Variables are often adjusted (e.g. standardised) before making a model - when is this a good idea, and when is it a bad one?
One thing I always ask myself before standardizing is, "How will I interpret the output?" If there is a way to analyze data without transformation, this may well be preferable purely from an int... | Variables are often adjusted (e.g. standardised) before making a model - when is this a good idea, a
One thing I always ask myself before standardizing is, "How will I interpret the output?" If there is a way to analyze data without transformation, this may well be preferable purely from an interpre |
3,366 | Variables are often adjusted (e.g. standardised) before making a model - when is this a good idea, and when is it a bad one? | In general I don't recommend scaling or standardization unless it's absolutely necessary. The advantage or appeal of such a process is that, when an explanatory variable has a totally different physical dimension and magnitude from the response variable, scaling through division by standard deviation may help in terms ... | Variables are often adjusted (e.g. standardised) before making a model - when is this a good idea, a | In general I don't recommend scaling or standardization unless it's absolutely necessary. The advantage or appeal of such a process is that, when an explanatory variable has a totally different physic | Variables are often adjusted (e.g. standardised) before making a model - when is this a good idea, and when is it a bad one?
In general I don't recommend scaling or standardization unless it's absolutely necessary. The advantage or appeal of such a process is that, when an explanatory variable has a totally different p... | Variables are often adjusted (e.g. standardised) before making a model - when is this a good idea, a
In general I don't recommend scaling or standardization unless it's absolutely necessary. The advantage or appeal of such a process is that, when an explanatory variable has a totally different physic |
3,367 | What is the relationship between a chi squared test and test of equal proportions? | Very short answer:
The chi-Squared test (chisq.test() in R) compares the observed frequencies in each category of a contingency table with the expected frequencies (computed as the product of the marginal frequencies). It is used to determine whether the deviations between the observed and the expected counts are too ... | What is the relationship between a chi squared test and test of equal proportions? | Very short answer:
The chi-Squared test (chisq.test() in R) compares the observed frequencies in each category of a contingency table with the expected frequencies (computed as the product of the mar | What is the relationship between a chi squared test and test of equal proportions?
Very short answer:
The chi-Squared test (chisq.test() in R) compares the observed frequencies in each category of a contingency table with the expected frequencies (computed as the product of the marginal frequencies). It is used to det... | What is the relationship between a chi squared test and test of equal proportions?
Very short answer:
The chi-Squared test (chisq.test() in R) compares the observed frequencies in each category of a contingency table with the expected frequencies (computed as the product of the mar |
3,368 | What is the relationship between a chi squared test and test of equal proportions? | A chi-square test for equality of two proportions is exactly the same thing as a $z$-test. The chi-squared distribution with one degree of freedom is just that of a normal deviate, squared. You're basically just repeating the chi-squared test on a subset of the contingency table. (This is why @chl gets the exact same $... | What is the relationship between a chi squared test and test of equal proportions? | A chi-square test for equality of two proportions is exactly the same thing as a $z$-test. The chi-squared distribution with one degree of freedom is just that of a normal deviate, squared. You're bas | What is the relationship between a chi squared test and test of equal proportions?
A chi-square test for equality of two proportions is exactly the same thing as a $z$-test. The chi-squared distribution with one degree of freedom is just that of a normal deviate, squared. You're basically just repeating the chi-squared... | What is the relationship between a chi squared test and test of equal proportions?
A chi-square test for equality of two proportions is exactly the same thing as a $z$-test. The chi-squared distribution with one degree of freedom is just that of a normal deviate, squared. You're bas |
3,369 | What is the difference between a "nested" and a "non-nested" model? | Nested versus non-nested can mean a whole lot of things. You have nested designs versus crossed designs (see eg this explanation). You have nested models in model comparison. Nested means here that all terms of a smaller model occur in a larger model. This is a necessary condition for using most model comparison tests ... | What is the difference between a "nested" and a "non-nested" model? | Nested versus non-nested can mean a whole lot of things. You have nested designs versus crossed designs (see eg this explanation). You have nested models in model comparison. Nested means here that al | What is the difference between a "nested" and a "non-nested" model?
Nested versus non-nested can mean a whole lot of things. You have nested designs versus crossed designs (see eg this explanation). You have nested models in model comparison. Nested means here that all terms of a smaller model occur in a larger model. ... | What is the difference between a "nested" and a "non-nested" model?
Nested versus non-nested can mean a whole lot of things. You have nested designs versus crossed designs (see eg this explanation). You have nested models in model comparison. Nested means here that al |
3,370 | What is the difference between a "nested" and a "non-nested" model? | Nested vs non-nested models come up in conjoint analysis and IIA. Consider the "red bus blue bus problem". You have a population where 50% of people take a car to work and the other 50% take the red bus. What happens if you add a blue bus which has the same specifications as the red bus to the equation? A multinomial ... | What is the difference between a "nested" and a "non-nested" model? | Nested vs non-nested models come up in conjoint analysis and IIA. Consider the "red bus blue bus problem". You have a population where 50% of people take a car to work and the other 50% take the red b | What is the difference between a "nested" and a "non-nested" model?
Nested vs non-nested models come up in conjoint analysis and IIA. Consider the "red bus blue bus problem". You have a population where 50% of people take a car to work and the other 50% take the red bus. What happens if you add a blue bus which has the... | What is the difference between a "nested" and a "non-nested" model?
Nested vs non-nested models come up in conjoint analysis and IIA. Consider the "red bus blue bus problem". You have a population where 50% of people take a car to work and the other 50% take the red b |
3,371 | What is the difference between a "nested" and a "non-nested" model? | One model is nested in another if you can always obtain the first model by constraining some of the parameters of the second model. For example, the linear model $ y = a x + c $ is nested within the 2-degree polynomial $ y = ax + bx^2 + c $, because by setting b = 0, the 2-deg. polynomial becomes identical to the linea... | What is the difference between a "nested" and a "non-nested" model? | One model is nested in another if you can always obtain the first model by constraining some of the parameters of the second model. For example, the linear model $ y = a x + c $ is nested within the 2 | What is the difference between a "nested" and a "non-nested" model?
One model is nested in another if you can always obtain the first model by constraining some of the parameters of the second model. For example, the linear model $ y = a x + c $ is nested within the 2-degree polynomial $ y = ax + bx^2 + c $, because by... | What is the difference between a "nested" and a "non-nested" model?
One model is nested in another if you can always obtain the first model by constraining some of the parameters of the second model. For example, the linear model $ y = a x + c $ is nested within the 2 |
3,372 | What is the difference between a "nested" and a "non-nested" model? | Two models are nonested or separate if one model cannot be obtained as limit of the other (or one model is not a particular case of the other) | What is the difference between a "nested" and a "non-nested" model? | Two models are nonested or separate if one model cannot be obtained as limit of the other (or one model is not a particular case of the other) | What is the difference between a "nested" and a "non-nested" model?
Two models are nonested or separate if one model cannot be obtained as limit of the other (or one model is not a particular case of the other) | What is the difference between a "nested" and a "non-nested" model?
Two models are nonested or separate if one model cannot be obtained as limit of the other (or one model is not a particular case of the other) |
3,373 | What is the difference between a "nested" and a "non-nested" model? | See a simpler answer in this pdf. Essentially, a nested model is a model with less variables than a full model. One intention is to look for more parsimonious answers. | What is the difference between a "nested" and a "non-nested" model? | See a simpler answer in this pdf. Essentially, a nested model is a model with less variables than a full model. One intention is to look for more parsimonious answers. | What is the difference between a "nested" and a "non-nested" model?
See a simpler answer in this pdf. Essentially, a nested model is a model with less variables than a full model. One intention is to look for more parsimonious answers. | What is the difference between a "nested" and a "non-nested" model?
See a simpler answer in this pdf. Essentially, a nested model is a model with less variables than a full model. One intention is to look for more parsimonious answers. |
3,374 | Neural Network: For Binary Classification use 1 or 2 output neurons? | In the second case you are probably writing about softmax activation function. If that's true, than the sigmoid is just a special case of softmax function. That's easy to show.
$$
y = \frac{1}{1 + e ^ {-x}} = \frac{1}{1 + \frac{1}{e ^ x}} = \frac{1}{\frac{e ^ x + 1}{e ^ x}} = \frac{e ^ x}{1 + e ^ x} = \frac{e ^ x}{e ^ ... | Neural Network: For Binary Classification use 1 or 2 output neurons? | In the second case you are probably writing about softmax activation function. If that's true, than the sigmoid is just a special case of softmax function. That's easy to show.
$$
y = \frac{1}{1 + e ^ | Neural Network: For Binary Classification use 1 or 2 output neurons?
In the second case you are probably writing about softmax activation function. If that's true, than the sigmoid is just a special case of softmax function. That's easy to show.
$$
y = \frac{1}{1 + e ^ {-x}} = \frac{1}{1 + \frac{1}{e ^ x}} = \frac{1}{\... | Neural Network: For Binary Classification use 1 or 2 output neurons?
In the second case you are probably writing about softmax activation function. If that's true, than the sigmoid is just a special case of softmax function. That's easy to show.
$$
y = \frac{1}{1 + e ^ |
3,375 | Neural Network: For Binary Classification use 1 or 2 output neurons? | Machine learning algorithms such as classifiers statistically model the input data, here, by determining the probabilities of the input belonging to different categories. For an arbitrary number of classes, normally a softmax layer is appended to the model so the outputs would have probabilistic properties by design:
$... | Neural Network: For Binary Classification use 1 or 2 output neurons? | Machine learning algorithms such as classifiers statistically model the input data, here, by determining the probabilities of the input belonging to different categories. For an arbitrary number of cl | Neural Network: For Binary Classification use 1 or 2 output neurons?
Machine learning algorithms such as classifiers statistically model the input data, here, by determining the probabilities of the input belonging to different categories. For an arbitrary number of classes, normally a softmax layer is appended to the ... | Neural Network: For Binary Classification use 1 or 2 output neurons?
Machine learning algorithms such as classifiers statistically model the input data, here, by determining the probabilities of the input belonging to different categories. For an arbitrary number of cl |
3,376 | Neural Network: For Binary Classification use 1 or 2 output neurons? | For binary classification, there are 2 outputs p0 and p1 which represent probabilities and 2 targets y0 and y1.
where p0, p1 = [0 1] and p0 + p1 = 1; y0,y1 = {0, 1} and y0 + y1 = 1.
e.g. p0 = 0.8, p1 = 0.2; y0 = 1, y1 = 0.
To satisfy the above conditions, the output layer must have sigmoid activations, and the loss fun... | Neural Network: For Binary Classification use 1 or 2 output neurons? | For binary classification, there are 2 outputs p0 and p1 which represent probabilities and 2 targets y0 and y1.
where p0, p1 = [0 1] and p0 + p1 = 1; y0,y1 = {0, 1} and y0 + y1 = 1.
e.g. p0 = 0.8, p1 | Neural Network: For Binary Classification use 1 or 2 output neurons?
For binary classification, there are 2 outputs p0 and p1 which represent probabilities and 2 targets y0 and y1.
where p0, p1 = [0 1] and p0 + p1 = 1; y0,y1 = {0, 1} and y0 + y1 = 1.
e.g. p0 = 0.8, p1 = 0.2; y0 = 1, y1 = 0.
To satisfy the above conditi... | Neural Network: For Binary Classification use 1 or 2 output neurons?
For binary classification, there are 2 outputs p0 and p1 which represent probabilities and 2 targets y0 and y1.
where p0, p1 = [0 1] and p0 + p1 = 1; y0,y1 = {0, 1} and y0 + y1 = 1.
e.g. p0 = 0.8, p1 |
3,377 | What does standard deviation tell us in non-normal distribution | It's the square root of the second central moment, the variance. The moments are related to characteristic functions(CF), which are called characteristic for a reason that they define the probability distribution. So, if you know all moments, you know CF, hence you know the entire probability distribution.
Normal distr... | What does standard deviation tell us in non-normal distribution | It's the square root of the second central moment, the variance. The moments are related to characteristic functions(CF), which are called characteristic for a reason that they define the probability | What does standard deviation tell us in non-normal distribution
It's the square root of the second central moment, the variance. The moments are related to characteristic functions(CF), which are called characteristic for a reason that they define the probability distribution. So, if you know all moments, you know CF, ... | What does standard deviation tell us in non-normal distribution
It's the square root of the second central moment, the variance. The moments are related to characteristic functions(CF), which are called characteristic for a reason that they define the probability |
3,378 | What does standard deviation tell us in non-normal distribution | The standard deviation is one particular measure of the variation. There are several others, Mean Absolute Deviation is fairly popular. The standard deviation is by no means special. What makes it appear special is that the Gaussian distribution is special.
As Pointed out in comments Chebyshev's inequality is useful fo... | What does standard deviation tell us in non-normal distribution | The standard deviation is one particular measure of the variation. There are several others, Mean Absolute Deviation is fairly popular. The standard deviation is by no means special. What makes it app | What does standard deviation tell us in non-normal distribution
The standard deviation is one particular measure of the variation. There are several others, Mean Absolute Deviation is fairly popular. The standard deviation is by no means special. What makes it appear special is that the Gaussian distribution is special... | What does standard deviation tell us in non-normal distribution
The standard deviation is one particular measure of the variation. There are several others, Mean Absolute Deviation is fairly popular. The standard deviation is by no means special. What makes it app |
3,379 | What does standard deviation tell us in non-normal distribution | The sample standard deviation is a measure of the deviance of the observed values from the mean, in the same units used to measure the data. Normal distribution, or not.
Specifically it is the square root of the mean squared deviance from the mean.
So the standard deviation tells you how spread out the data are from th... | What does standard deviation tell us in non-normal distribution | The sample standard deviation is a measure of the deviance of the observed values from the mean, in the same units used to measure the data. Normal distribution, or not.
Specifically it is the square | What does standard deviation tell us in non-normal distribution
The sample standard deviation is a measure of the deviance of the observed values from the mean, in the same units used to measure the data. Normal distribution, or not.
Specifically it is the square root of the mean squared deviance from the mean.
So the ... | What does standard deviation tell us in non-normal distribution
The sample standard deviation is a measure of the deviance of the observed values from the mean, in the same units used to measure the data. Normal distribution, or not.
Specifically it is the square |
3,380 | What is the most surprising characterization of the Gaussian (normal) distribution? | My personal most surprising is the one about the sample mean and variance, but here is another (maybe) surprising characterization: if $X$ and $Y$ are IID with finite variance with $X+Y$ and $X-Y$ independent, then $X$ and $Y$ are normal.
Intuitively, we can usually identify when variables are not independent with a sc... | What is the most surprising characterization of the Gaussian (normal) distribution? | My personal most surprising is the one about the sample mean and variance, but here is another (maybe) surprising characterization: if $X$ and $Y$ are IID with finite variance with $X+Y$ and $X-Y$ ind | What is the most surprising characterization of the Gaussian (normal) distribution?
My personal most surprising is the one about the sample mean and variance, but here is another (maybe) surprising characterization: if $X$ and $Y$ are IID with finite variance with $X+Y$ and $X-Y$ independent, then $X$ and $Y$ are norma... | What is the most surprising characterization of the Gaussian (normal) distribution?
My personal most surprising is the one about the sample mean and variance, but here is another (maybe) surprising characterization: if $X$ and $Y$ are IID with finite variance with $X+Y$ and $X-Y$ ind |
3,381 | What is the most surprising characterization of the Gaussian (normal) distribution? | The continuous distribution with fixed variance which maximizes differential entropy is the Gaussian distribution. | What is the most surprising characterization of the Gaussian (normal) distribution? | The continuous distribution with fixed variance which maximizes differential entropy is the Gaussian distribution. | What is the most surprising characterization of the Gaussian (normal) distribution?
The continuous distribution with fixed variance which maximizes differential entropy is the Gaussian distribution. | What is the most surprising characterization of the Gaussian (normal) distribution?
The continuous distribution with fixed variance which maximizes differential entropy is the Gaussian distribution. |
3,382 | What is the most surprising characterization of the Gaussian (normal) distribution? | There's an entire book written about this: "Characterizations of the normal probability law", A. M. Mathai & G. Perderzoli. A brief review in JASA (Dec. 1978) mentions the following:
Let $X_1, \ldots, X_n$ be independent random variables. Then $\sum_{i=1}^n{a_i x_i}$ and $\sum_{i=1}^n{b_i x_i}$ are independent, wher... | What is the most surprising characterization of the Gaussian (normal) distribution? | There's an entire book written about this: "Characterizations of the normal probability law", A. M. Mathai & G. Perderzoli. A brief review in JASA (Dec. 1978) mentions the following:
Let $X_1, \ldot | What is the most surprising characterization of the Gaussian (normal) distribution?
There's an entire book written about this: "Characterizations of the normal probability law", A. M. Mathai & G. Perderzoli. A brief review in JASA (Dec. 1978) mentions the following:
Let $X_1, \ldots, X_n$ be independent random variab... | What is the most surprising characterization of the Gaussian (normal) distribution?
There's an entire book written about this: "Characterizations of the normal probability law", A. M. Mathai & G. Perderzoli. A brief review in JASA (Dec. 1978) mentions the following:
Let $X_1, \ldot |
3,383 | What is the most surprising characterization of the Gaussian (normal) distribution? | Stein’s Lemma provides a very useful characterization. $Z$ is standard Gaussian iff
$$E f’(Z) = E Z f(Z)$$
for all absolutely continuous functions $f$ with $E|f’(Z)| < \infty$. | What is the most surprising characterization of the Gaussian (normal) distribution? | Stein’s Lemma provides a very useful characterization. $Z$ is standard Gaussian iff
$$E f’(Z) = E Z f(Z)$$
for all absolutely continuous functions $f$ with $E|f’(Z)| < \infty$. | What is the most surprising characterization of the Gaussian (normal) distribution?
Stein’s Lemma provides a very useful characterization. $Z$ is standard Gaussian iff
$$E f’(Z) = E Z f(Z)$$
for all absolutely continuous functions $f$ with $E|f’(Z)| < \infty$. | What is the most surprising characterization of the Gaussian (normal) distribution?
Stein’s Lemma provides a very useful characterization. $Z$ is standard Gaussian iff
$$E f’(Z) = E Z f(Z)$$
for all absolutely continuous functions $f$ with $E|f’(Z)| < \infty$. |
3,384 | What is the most surprising characterization of the Gaussian (normal) distribution? | Gaussian distributions are the only sum-stable distributions with finite variance. | What is the most surprising characterization of the Gaussian (normal) distribution? | Gaussian distributions are the only sum-stable distributions with finite variance. | What is the most surprising characterization of the Gaussian (normal) distribution?
Gaussian distributions are the only sum-stable distributions with finite variance. | What is the most surprising characterization of the Gaussian (normal) distribution?
Gaussian distributions are the only sum-stable distributions with finite variance. |
3,385 | What is the most surprising characterization of the Gaussian (normal) distribution? | Theorem [Herschel-Maxwell]: Let $Z \in \mathbb{R}^n$ be a random vector for which (i) projections into orthogonal subspaces are independent and (ii) the distribution of $Z$ depends only on the length $\|Z\|$. Then $Z$ is normally distributed.
Cited by George Cobb in Teaching statistics: Some important tensions (Chilean... | What is the most surprising characterization of the Gaussian (normal) distribution? | Theorem [Herschel-Maxwell]: Let $Z \in \mathbb{R}^n$ be a random vector for which (i) projections into orthogonal subspaces are independent and (ii) the distribution of $Z$ depends only on the length | What is the most surprising characterization of the Gaussian (normal) distribution?
Theorem [Herschel-Maxwell]: Let $Z \in \mathbb{R}^n$ be a random vector for which (i) projections into orthogonal subspaces are independent and (ii) the distribution of $Z$ depends only on the length $\|Z\|$. Then $Z$ is normally distri... | What is the most surprising characterization of the Gaussian (normal) distribution?
Theorem [Herschel-Maxwell]: Let $Z \in \mathbb{R}^n$ be a random vector for which (i) projections into orthogonal subspaces are independent and (ii) the distribution of $Z$ depends only on the length |
3,386 | What is the most surprising characterization of the Gaussian (normal) distribution? | This is not a characterization but a conjecture, which dates back from 1917 and is due to Cantelli:
If $f$ is a positive function on $\mathbb{R}$ and $X$ and $Y$ are $N(0,1)$ independent random variables such that $X+f(X)Y$ is normal, then $f$ is a constant almost everywhere.
Mentioned by Gérard Letac here. | What is the most surprising characterization of the Gaussian (normal) distribution? | This is not a characterization but a conjecture, which dates back from 1917 and is due to Cantelli:
If $f$ is a positive function on $\mathbb{R}$ and $X$ and $Y$ are $N(0,1)$ independent random vari | What is the most surprising characterization of the Gaussian (normal) distribution?
This is not a characterization but a conjecture, which dates back from 1917 and is due to Cantelli:
If $f$ is a positive function on $\mathbb{R}$ and $X$ and $Y$ are $N(0,1)$ independent random variables such that $X+f(X)Y$ is normal,... | What is the most surprising characterization of the Gaussian (normal) distribution?
This is not a characterization but a conjecture, which dates back from 1917 and is due to Cantelli:
If $f$ is a positive function on $\mathbb{R}$ and $X$ and $Y$ are $N(0,1)$ independent random vari |
3,387 | What is the most surprising characterization of the Gaussian (normal) distribution? | Let $\eta$ and $\xi$ be two independent random variables with a common symmetric distribution such that
$$ P\left ( \left |\frac{\xi+\eta}{\sqrt{2}}\right | \geq t \right )\leq P(|\xi|\geq t).$$
Then these random variables are gaussian. (Obviously, if the $\xi$ and $\eta$ are centered gaussian, it is true.)
This is ... | What is the most surprising characterization of the Gaussian (normal) distribution? | Let $\eta$ and $\xi$ be two independent random variables with a common symmetric distribution such that
$$ P\left ( \left |\frac{\xi+\eta}{\sqrt{2}}\right | \geq t \right )\leq P(|\xi|\geq t).$$
The | What is the most surprising characterization of the Gaussian (normal) distribution?
Let $\eta$ and $\xi$ be two independent random variables with a common symmetric distribution such that
$$ P\left ( \left |\frac{\xi+\eta}{\sqrt{2}}\right | \geq t \right )\leq P(|\xi|\geq t).$$
Then these random variables are gaussia... | What is the most surprising characterization of the Gaussian (normal) distribution?
Let $\eta$ and $\xi$ be two independent random variables with a common symmetric distribution such that
$$ P\left ( \left |\frac{\xi+\eta}{\sqrt{2}}\right | \geq t \right )\leq P(|\xi|\geq t).$$
The |
3,388 | What is the most surprising characterization of the Gaussian (normal) distribution? | Suppose one is estimating a location parameter using i.i.d. data $\{x_1,...,x_n\}$. If $\bar{x}$ is the maximum likelihood estimator, then the sampling distribution is Gaussian. According to Jaynes's Probability Theory: The Logic of Science pp. 202-4, this was how Gauss originally derived it. | What is the most surprising characterization of the Gaussian (normal) distribution? | Suppose one is estimating a location parameter using i.i.d. data $\{x_1,...,x_n\}$. If $\bar{x}$ is the maximum likelihood estimator, then the sampling distribution is Gaussian. According to Jaynes's | What is the most surprising characterization of the Gaussian (normal) distribution?
Suppose one is estimating a location parameter using i.i.d. data $\{x_1,...,x_n\}$. If $\bar{x}$ is the maximum likelihood estimator, then the sampling distribution is Gaussian. According to Jaynes's Probability Theory: The Logic of Sci... | What is the most surprising characterization of the Gaussian (normal) distribution?
Suppose one is estimating a location parameter using i.i.d. data $\{x_1,...,x_n\}$. If $\bar{x}$ is the maximum likelihood estimator, then the sampling distribution is Gaussian. According to Jaynes's |
3,389 | What is the most surprising characterization of the Gaussian (normal) distribution? | A more particular characterisation of the normal distribution among the class of infinitely divisible distributions is presented in Steutel and Van Harn (2004).
A non-degenerate infinitely divisible random variable $X$ has a normal distribution if and only if it satisfies
$$-\limsup_{x\rightarrow\infty}\dfrac{\log{\... | What is the most surprising characterization of the Gaussian (normal) distribution? | A more particular characterisation of the normal distribution among the class of infinitely divisible distributions is presented in Steutel and Van Harn (2004).
A non-degenerate infinitely divisible | What is the most surprising characterization of the Gaussian (normal) distribution?
A more particular characterisation of the normal distribution among the class of infinitely divisible distributions is presented in Steutel and Van Harn (2004).
A non-degenerate infinitely divisible random variable $X$ has a normal dis... | What is the most surprising characterization of the Gaussian (normal) distribution?
A more particular characterisation of the normal distribution among the class of infinitely divisible distributions is presented in Steutel and Van Harn (2004).
A non-degenerate infinitely divisible |
3,390 | What is the most surprising characterization of the Gaussian (normal) distribution? | In the context of image smoothing (e.g. scale space), the Gaussian is the only rotationally symmetric separable* kernel.
That is, if we require
$$F[x,y]=f[x]f[y]$$
where $[x,y]=r[\cos\theta,\sin\theta]$, then rotational symmetry requires
\begin{align}
F_\theta &= f'[x]f[y]x_\theta+f[x]f'[y]y_\theta \\
&= -f'[x]f[y]y+f... | What is the most surprising characterization of the Gaussian (normal) distribution? | In the context of image smoothing (e.g. scale space), the Gaussian is the only rotationally symmetric separable* kernel.
That is, if we require
$$F[x,y]=f[x]f[y]$$
where $[x,y]=r[\cos\theta,\sin\theta | What is the most surprising characterization of the Gaussian (normal) distribution?
In the context of image smoothing (e.g. scale space), the Gaussian is the only rotationally symmetric separable* kernel.
That is, if we require
$$F[x,y]=f[x]f[y]$$
where $[x,y]=r[\cos\theta,\sin\theta]$, then rotational symmetry require... | What is the most surprising characterization of the Gaussian (normal) distribution?
In the context of image smoothing (e.g. scale space), the Gaussian is the only rotationally symmetric separable* kernel.
That is, if we require
$$F[x,y]=f[x]f[y]$$
where $[x,y]=r[\cos\theta,\sin\theta |
3,391 | What is the most surprising characterization of the Gaussian (normal) distribution? | Recently Ejsmont [1] published article with new characterization of Gaussian:
Let $(X_1,\dots, X_m,Y) \textrm{ and } (X_{m+1},\dots,X_n,Z)$ be independent random vectors with all moments, where $X_i$ are
nondegenerate, and let statistic $\sum_{i=1}^na_iX_i+Y+Z$
have a distribution which depends only on $\sum_{i=1}^... | What is the most surprising characterization of the Gaussian (normal) distribution? | Recently Ejsmont [1] published article with new characterization of Gaussian:
Let $(X_1,\dots, X_m,Y) \textrm{ and } (X_{m+1},\dots,X_n,Z)$ be independent random vectors with all moments, where $X_ | What is the most surprising characterization of the Gaussian (normal) distribution?
Recently Ejsmont [1] published article with new characterization of Gaussian:
Let $(X_1,\dots, X_m,Y) \textrm{ and } (X_{m+1},\dots,X_n,Z)$ be independent random vectors with all moments, where $X_i$ are
nondegenerate, and let stati... | What is the most surprising characterization of the Gaussian (normal) distribution?
Recently Ejsmont [1] published article with new characterization of Gaussian:
Let $(X_1,\dots, X_m,Y) \textrm{ and } (X_{m+1},\dots,X_n,Z)$ be independent random vectors with all moments, where $X_ |
3,392 | What is the most surprising characterization of the Gaussian (normal) distribution? | Its characteristic function has the same form as its pdf. I am not sure of another distribution which does that. | What is the most surprising characterization of the Gaussian (normal) distribution? | Its characteristic function has the same form as its pdf. I am not sure of another distribution which does that. | What is the most surprising characterization of the Gaussian (normal) distribution?
Its characteristic function has the same form as its pdf. I am not sure of another distribution which does that. | What is the most surprising characterization of the Gaussian (normal) distribution?
Its characteristic function has the same form as its pdf. I am not sure of another distribution which does that. |
3,393 | What is the most surprising characterization of the Gaussian (normal) distribution? | The expectation plus minus the standard deviation are the saddle points of the function. | What is the most surprising characterization of the Gaussian (normal) distribution? | The expectation plus minus the standard deviation are the saddle points of the function. | What is the most surprising characterization of the Gaussian (normal) distribution?
The expectation plus minus the standard deviation are the saddle points of the function. | What is the most surprising characterization of the Gaussian (normal) distribution?
The expectation plus minus the standard deviation are the saddle points of the function. |
3,394 | Where did the frequentist-Bayesian debate go? | I actually mildly disagree with the premise. Everyone is a Bayesian, if they really do have a probability distribution handed to them as a prior. The trouble comes about when they don't, and I think there's still a pretty good-sized divide on that topic.
Having said that, though, I do agree that more and more people ... | Where did the frequentist-Bayesian debate go? | I actually mildly disagree with the premise. Everyone is a Bayesian, if they really do have a probability distribution handed to them as a prior. The trouble comes about when they don't, and I think | Where did the frequentist-Bayesian debate go?
I actually mildly disagree with the premise. Everyone is a Bayesian, if they really do have a probability distribution handed to them as a prior. The trouble comes about when they don't, and I think there's still a pretty good-sized divide on that topic.
Having said that,... | Where did the frequentist-Bayesian debate go?
I actually mildly disagree with the premise. Everyone is a Bayesian, if they really do have a probability distribution handed to them as a prior. The trouble comes about when they don't, and I think |
3,395 | Where did the frequentist-Bayesian debate go? | (The original answer is dated 2012).
This is a difficult question to answer. The number of people who truly do both is still very limited. Hard core Bayesians despise the users of mainstream statistics for their use of $p$-values, a nonsensical, internally inconsistent statistic for Bayesians; and the mainstream statis... | Where did the frequentist-Bayesian debate go? | (The original answer is dated 2012).
This is a difficult question to answer. The number of people who truly do both is still very limited. Hard core Bayesians despise the users of mainstream statistic | Where did the frequentist-Bayesian debate go?
(The original answer is dated 2012).
This is a difficult question to answer. The number of people who truly do both is still very limited. Hard core Bayesians despise the users of mainstream statistics for their use of $p$-values, a nonsensical, internally inconsistent stat... | Where did the frequentist-Bayesian debate go?
(The original answer is dated 2012).
This is a difficult question to answer. The number of people who truly do both is still very limited. Hard core Bayesians despise the users of mainstream statistic |
3,396 | Where did the frequentist-Bayesian debate go? | There is a good reason for still having both, which is that a good craftsman will want to select the best tool for the task at hand, and both Bayesian and frequentist methods have applications where they are the best tool for the job.
However, often the wrong tool for the job is used because frequentist statistics are ... | Where did the frequentist-Bayesian debate go? | There is a good reason for still having both, which is that a good craftsman will want to select the best tool for the task at hand, and both Bayesian and frequentist methods have applications where t | Where did the frequentist-Bayesian debate go?
There is a good reason for still having both, which is that a good craftsman will want to select the best tool for the task at hand, and both Bayesian and frequentist methods have applications where they are the best tool for the job.
However, often the wrong tool for the j... | Where did the frequentist-Bayesian debate go?
There is a good reason for still having both, which is that a good craftsman will want to select the best tool for the task at hand, and both Bayesian and frequentist methods have applications where t |
3,397 | Where did the frequentist-Bayesian debate go? | I don't think the Frequentists and Bayesians give different answers to the same questions. I think they are prepared to answer different questions. Therefore, I don't think it makes sense to talk much about one side winning, or even to talk about compromise.
Consider all the questions we might want to ask. Many are jus... | Where did the frequentist-Bayesian debate go? | I don't think the Frequentists and Bayesians give different answers to the same questions. I think they are prepared to answer different questions. Therefore, I don't think it makes sense to talk much | Where did the frequentist-Bayesian debate go?
I don't think the Frequentists and Bayesians give different answers to the same questions. I think they are prepared to answer different questions. Therefore, I don't think it makes sense to talk much about one side winning, or even to talk about compromise.
Consider all th... | Where did the frequentist-Bayesian debate go?
I don't think the Frequentists and Bayesians give different answers to the same questions. I think they are prepared to answer different questions. Therefore, I don't think it makes sense to talk much |
3,398 | Where did the frequentist-Bayesian debate go? | As you'll see, there's quite a lot of frequentist-Bayesian debate going on. In fact, I think it's hotter than ever, and less dogmatic. You might be interested in my blog:
http://errorstatistics.com | Where did the frequentist-Bayesian debate go? | As you'll see, there's quite a lot of frequentist-Bayesian debate going on. In fact, I think it's hotter than ever, and less dogmatic. You might be interested in my blog:
http://errorstatistics.com | Where did the frequentist-Bayesian debate go?
As you'll see, there's quite a lot of frequentist-Bayesian debate going on. In fact, I think it's hotter than ever, and less dogmatic. You might be interested in my blog:
http://errorstatistics.com | Where did the frequentist-Bayesian debate go?
As you'll see, there's quite a lot of frequentist-Bayesian debate going on. In fact, I think it's hotter than ever, and less dogmatic. You might be interested in my blog:
http://errorstatistics.com |
3,399 | Where did the frequentist-Bayesian debate go? | Many people (outside the specialist experts) who think they are frequentist are in fact Bayesian. This makes the debate a bit pointless. I think that Bayesianism won, but that there are still many Bayesians who think they are frequentist. There are some people who think that they don't use priors and hence they think t... | Where did the frequentist-Bayesian debate go? | Many people (outside the specialist experts) who think they are frequentist are in fact Bayesian. This makes the debate a bit pointless. I think that Bayesianism won, but that there are still many Bay | Where did the frequentist-Bayesian debate go?
Many people (outside the specialist experts) who think they are frequentist are in fact Bayesian. This makes the debate a bit pointless. I think that Bayesianism won, but that there are still many Bayesians who think they are frequentist. There are some people who think tha... | Where did the frequentist-Bayesian debate go?
Many people (outside the specialist experts) who think they are frequentist are in fact Bayesian. This makes the debate a bit pointless. I think that Bayesianism won, but that there are still many Bay |
3,400 | Where did the frequentist-Bayesian debate go? | These are actually apples and oranges if you dig deep enough.
The Frequentist vs. Bayesian approach dilemma is actually a philosophical question about what probabilities actually are.
Bayes discovered an useful tool to handle probabilities and treated them as primary entities in his mathematical background. Fisher, Pea... | Where did the frequentist-Bayesian debate go? | These are actually apples and oranges if you dig deep enough.
The Frequentist vs. Bayesian approach dilemma is actually a philosophical question about what probabilities actually are.
Bayes discovered | Where did the frequentist-Bayesian debate go?
These are actually apples and oranges if you dig deep enough.
The Frequentist vs. Bayesian approach dilemma is actually a philosophical question about what probabilities actually are.
Bayes discovered an useful tool to handle probabilities and treated them as primary entiti... | Where did the frequentist-Bayesian debate go?
These are actually apples and oranges if you dig deep enough.
The Frequentist vs. Bayesian approach dilemma is actually a philosophical question about what probabilities actually are.
Bayes discovered |
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