idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k β | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 β | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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3,601 | How exactly does a "random effects model" in econometrics relate to mixed models outside of econometrics? | In this answer, I would like to elaborate a little on Matthew's +1 answer regarding the GLS perspective on what the econometrics literature calls the random effects estimator.
GLS perspective
Consider the linear model
\begin{equation}
y_{it}=\alpha + X_{it}\beta+u_{it}\qquad i=1,\ldots,m,\quad t=1,\ldots,T
\end{equati... | How exactly does a "random effects model" in econometrics relate to mixed models outside of economet | In this answer, I would like to elaborate a little on Matthew's +1 answer regarding the GLS perspective on what the econometrics literature calls the random effects estimator.
GLS perspective
Conside | How exactly does a "random effects model" in econometrics relate to mixed models outside of econometrics?
In this answer, I would like to elaborate a little on Matthew's +1 answer regarding the GLS perspective on what the econometrics literature calls the random effects estimator.
GLS perspective
Consider the linear m... | How exactly does a "random effects model" in econometrics relate to mixed models outside of economet
In this answer, I would like to elaborate a little on Matthew's +1 answer regarding the GLS perspective on what the econometrics literature calls the random effects estimator.
GLS perspective
Conside |
3,602 | How exactly does a "random effects model" in econometrics relate to mixed models outside of econometrics? | I am not really familiar enough with R to comment on your code, but the simple random intercept mixed model should be identical to the RE MLE estimator, and very close to the RE GLS estimator, except when total $N = \sum_i T_i$ is small and the data are unbalanced. Hopefully, this will be useful in diagnosing the probl... | How exactly does a "random effects model" in econometrics relate to mixed models outside of economet | I am not really familiar enough with R to comment on your code, but the simple random intercept mixed model should be identical to the RE MLE estimator, and very close to the RE GLS estimator, except | How exactly does a "random effects model" in econometrics relate to mixed models outside of econometrics?
I am not really familiar enough with R to comment on your code, but the simple random intercept mixed model should be identical to the RE MLE estimator, and very close to the RE GLS estimator, except when total $N ... | How exactly does a "random effects model" in econometrics relate to mixed models outside of economet
I am not really familiar enough with R to comment on your code, but the simple random intercept mixed model should be identical to the RE MLE estimator, and very close to the RE GLS estimator, except |
3,603 | How exactly does a "random effects model" in econometrics relate to mixed models outside of econometrics? | Let me confuse things even more:
ECONOMETRICS - FIXED EFFECTS APPROACH
The "fixed effects" approach in econometrics for panel data, is a way to estimate the slope coefficients (the betas), by "by-passing" the existence of the individual effects variable $\alpha_i$, and so by not making any assumption as to whether it i... | How exactly does a "random effects model" in econometrics relate to mixed models outside of economet | Let me confuse things even more:
ECONOMETRICS - FIXED EFFECTS APPROACH
The "fixed effects" approach in econometrics for panel data, is a way to estimate the slope coefficients (the betas), by "by-pass | How exactly does a "random effects model" in econometrics relate to mixed models outside of econometrics?
Let me confuse things even more:
ECONOMETRICS - FIXED EFFECTS APPROACH
The "fixed effects" approach in econometrics for panel data, is a way to estimate the slope coefficients (the betas), by "by-passing" the exist... | How exactly does a "random effects model" in econometrics relate to mixed models outside of economet
Let me confuse things even more:
ECONOMETRICS - FIXED EFFECTS APPROACH
The "fixed effects" approach in econometrics for panel data, is a way to estimate the slope coefficients (the betas), by "by-pass |
3,604 | Explain the xkcd jelly bean comic: What makes it funny? | Humor is a very personal thing - some people will find it amusing, but it may not be funny to everyone - and attempts to explain what makes something funny often fail to convey the funny, even if they explain the underlying point. Indeed not all xkcd's are even intended to be actually funny. Many do, however make impor... | Explain the xkcd jelly bean comic: What makes it funny? | Humor is a very personal thing - some people will find it amusing, but it may not be funny to everyone - and attempts to explain what makes something funny often fail to convey the funny, even if they | Explain the xkcd jelly bean comic: What makes it funny?
Humor is a very personal thing - some people will find it amusing, but it may not be funny to everyone - and attempts to explain what makes something funny often fail to convey the funny, even if they explain the underlying point. Indeed not all xkcd's are even in... | Explain the xkcd jelly bean comic: What makes it funny?
Humor is a very personal thing - some people will find it amusing, but it may not be funny to everyone - and attempts to explain what makes something funny often fail to convey the funny, even if they |
3,605 | Explain the xkcd jelly bean comic: What makes it funny? | The effect of hypothesis testing on the decision to publish has been described more than fifty years ago in the 1959 JASA paper Publication Decisions and Their Possible Effects on Inferences Drawn from Tests of Significance - or Vice Versa (sorry for the paywall).
Overview of the Paper
The paper points out evidence tha... | Explain the xkcd jelly bean comic: What makes it funny? | The effect of hypothesis testing on the decision to publish has been described more than fifty years ago in the 1959 JASA paper Publication Decisions and Their Possible Effects on Inferences Drawn fro | Explain the xkcd jelly bean comic: What makes it funny?
The effect of hypothesis testing on the decision to publish has been described more than fifty years ago in the 1959 JASA paper Publication Decisions and Their Possible Effects on Inferences Drawn from Tests of Significance - or Vice Versa (sorry for the paywall).... | Explain the xkcd jelly bean comic: What makes it funny?
The effect of hypothesis testing on the decision to publish has been described more than fifty years ago in the 1959 JASA paper Publication Decisions and Their Possible Effects on Inferences Drawn fro |
3,606 | Explain the xkcd jelly bean comic: What makes it funny? | What people overlook is that the actual p-value for the green jelly bean case is not .05 but around .64. Only the pretend (nominal) p-value is .05. Thereβs a difference between actual and pretend p-values. The probability of finding 1 in 20 that reach the nominal level even if all the nulls are true is NOT .05, but .64... | Explain the xkcd jelly bean comic: What makes it funny? | What people overlook is that the actual p-value for the green jelly bean case is not .05 but around .64. Only the pretend (nominal) p-value is .05. Thereβs a difference between actual and pretend p-va | Explain the xkcd jelly bean comic: What makes it funny?
What people overlook is that the actual p-value for the green jelly bean case is not .05 but around .64. Only the pretend (nominal) p-value is .05. Thereβs a difference between actual and pretend p-values. The probability of finding 1 in 20 that reach the nominal ... | Explain the xkcd jelly bean comic: What makes it funny?
What people overlook is that the actual p-value for the green jelly bean case is not .05 but around .64. Only the pretend (nominal) p-value is .05. Thereβs a difference between actual and pretend p-va |
3,607 | Difference between Random Forest and Extremely Randomized Trees | The Extra-(Randomized)-Trees (ET) article contains a bias-variance analysis.
In Fig. 6 (on page 16), you can see a comparison with multiple methods including RF
on six tests (tree classification and three regression).
Both methods are about the same, with the ET being a bit worse when there is a high number of noisy fe... | Difference between Random Forest and Extremely Randomized Trees | The Extra-(Randomized)-Trees (ET) article contains a bias-variance analysis.
In Fig. 6 (on page 16), you can see a comparison with multiple methods including RF
on six tests (tree classification and t | Difference between Random Forest and Extremely Randomized Trees
The Extra-(Randomized)-Trees (ET) article contains a bias-variance analysis.
In Fig. 6 (on page 16), you can see a comparison with multiple methods including RF
on six tests (tree classification and three regression).
Both methods are about the same, with ... | Difference between Random Forest and Extremely Randomized Trees
The Extra-(Randomized)-Trees (ET) article contains a bias-variance analysis.
In Fig. 6 (on page 16), you can see a comparison with multiple methods including RF
on six tests (tree classification and t |
3,608 | Difference between Random Forest and Extremely Randomized Trees | ExtraTreesClassifier is like a brother of RandomForest but with 2 important differences.
We are building multiple decision trees. For building multiple trees, we need multiple datasets. Best practice is that we don't train the decision trees on the complete dataset but we train only on fraction of data (around 80%) fo... | Difference between Random Forest and Extremely Randomized Trees | ExtraTreesClassifier is like a brother of RandomForest but with 2 important differences.
We are building multiple decision trees. For building multiple trees, we need multiple datasets. Best practice | Difference between Random Forest and Extremely Randomized Trees
ExtraTreesClassifier is like a brother of RandomForest but with 2 important differences.
We are building multiple decision trees. For building multiple trees, we need multiple datasets. Best practice is that we don't train the decision trees on the comple... | Difference between Random Forest and Extremely Randomized Trees
ExtraTreesClassifier is like a brother of RandomForest but with 2 important differences.
We are building multiple decision trees. For building multiple trees, we need multiple datasets. Best practice |
3,609 | Difference between Random Forest and Extremely Randomized Trees | Thank you very much for the answers ! As I still had questions, I performed some numerical simulations to have more insights about the behavior of these two methods.
Extra trees seem to keep a higher performance in presence of noisy features.
The picture below shows the performance (evaluated with cross validation) a... | Difference between Random Forest and Extremely Randomized Trees | Thank you very much for the answers ! As I still had questions, I performed some numerical simulations to have more insights about the behavior of these two methods.
Extra trees seem to keep a higher | Difference between Random Forest and Extremely Randomized Trees
Thank you very much for the answers ! As I still had questions, I performed some numerical simulations to have more insights about the behavior of these two methods.
Extra trees seem to keep a higher performance in presence of noisy features.
The picture... | Difference between Random Forest and Extremely Randomized Trees
Thank you very much for the answers ! As I still had questions, I performed some numerical simulations to have more insights about the behavior of these two methods.
Extra trees seem to keep a higher |
3,610 | Difference between Random Forest and Extremely Randomized Trees | The answer is that it depends. I suggest you try both random forest and extra trees on your problem. Try large forest (1000 - 3000 trees/estimators, n_estimators in sklearn) and tune the number of features considered at each split (max_features in sklearn) as well as the the minimum samples per split (min_samples_split... | Difference between Random Forest and Extremely Randomized Trees | The answer is that it depends. I suggest you try both random forest and extra trees on your problem. Try large forest (1000 - 3000 trees/estimators, n_estimators in sklearn) and tune the number of fea | Difference between Random Forest and Extremely Randomized Trees
The answer is that it depends. I suggest you try both random forest and extra trees on your problem. Try large forest (1000 - 3000 trees/estimators, n_estimators in sklearn) and tune the number of features considered at each split (max_features in sklearn)... | Difference between Random Forest and Extremely Randomized Trees
The answer is that it depends. I suggest you try both random forest and extra trees on your problem. Try large forest (1000 - 3000 trees/estimators, n_estimators in sklearn) and tune the number of fea |
3,611 | Most famous statisticians | Reverend Thomas Bayes for discovering Bayes' theorem | Most famous statisticians | Reverend Thomas Bayes for discovering Bayes' theorem | Most famous statisticians
Reverend Thomas Bayes for discovering Bayes' theorem | Most famous statisticians
Reverend Thomas Bayes for discovering Bayes' theorem |
3,612 | Most famous statisticians | Ronald Fisher for his fundamental contributions to the way we analyze data, whether it be the analysis of variance framework, maximum likelihood, permutation tests, or any number of other ground-breaking discoveries. | Most famous statisticians | Ronald Fisher for his fundamental contributions to the way we analyze data, whether it be the analysis of variance framework, maximum likelihood, permutation tests, or any number of other ground-break | Most famous statisticians
Ronald Fisher for his fundamental contributions to the way we analyze data, whether it be the analysis of variance framework, maximum likelihood, permutation tests, or any number of other ground-breaking discoveries. | Most famous statisticians
Ronald Fisher for his fundamental contributions to the way we analyze data, whether it be the analysis of variance framework, maximum likelihood, permutation tests, or any number of other ground-break |
3,613 | Most famous statisticians | John Tukey for Fast Fourier Transforms, exploratory data analysis (EDA), box plots, projection pursuit, jackknife (along with Quenouille). Coined the words "software" and "bit". | Most famous statisticians | John Tukey for Fast Fourier Transforms, exploratory data analysis (EDA), box plots, projection pursuit, jackknife (along with Quenouille). Coined the words "software" and "bit". | Most famous statisticians
John Tukey for Fast Fourier Transforms, exploratory data analysis (EDA), box plots, projection pursuit, jackknife (along with Quenouille). Coined the words "software" and "bit". | Most famous statisticians
John Tukey for Fast Fourier Transforms, exploratory data analysis (EDA), box plots, projection pursuit, jackknife (along with Quenouille). Coined the words "software" and "bit". |
3,614 | Most famous statisticians | Karl Pearson for his work on mathematical statistics. Pearson correlation, Chi-square test, and principal components analysis are just a few of the incredibly important ideas that stem from his works. | Most famous statisticians | Karl Pearson for his work on mathematical statistics. Pearson correlation, Chi-square test, and principal components analysis are just a few of the incredibly important ideas that stem from his works | Most famous statisticians
Karl Pearson for his work on mathematical statistics. Pearson correlation, Chi-square test, and principal components analysis are just a few of the incredibly important ideas that stem from his works. | Most famous statisticians
Karl Pearson for his work on mathematical statistics. Pearson correlation, Chi-square test, and principal components analysis are just a few of the incredibly important ideas that stem from his works |
3,615 | Most famous statisticians | Carl Gauss for least squares estimation. | Most famous statisticians | Carl Gauss for least squares estimation. | Most famous statisticians
Carl Gauss for least squares estimation. | Most famous statisticians
Carl Gauss for least squares estimation. |
3,616 | Most famous statisticians | William Sealy Gosset for Student's t-distribution and the statistically-driven improvement of beer. | Most famous statisticians | William Sealy Gosset for Student's t-distribution and the statistically-driven improvement of beer. | Most famous statisticians
William Sealy Gosset for Student's t-distribution and the statistically-driven improvement of beer. | Most famous statisticians
William Sealy Gosset for Student's t-distribution and the statistically-driven improvement of beer. |
3,617 | Most famous statisticians | Bradley Efron for the Bootstrap - one of the most useful techniques in computational statistics. | Most famous statisticians | Bradley Efron for the Bootstrap - one of the most useful techniques in computational statistics. | Most famous statisticians
Bradley Efron for the Bootstrap - one of the most useful techniques in computational statistics. | Most famous statisticians
Bradley Efron for the Bootstrap - one of the most useful techniques in computational statistics. |
3,618 | Most famous statisticians | Andrey Nikolayevich Kolmogorov, for putting probability theory on a rigorous mathematical footing. While he was a mathematician, not a statistician, undoubtedly his work is important in many branches of statistics. | Most famous statisticians | Andrey Nikolayevich Kolmogorov, for putting probability theory on a rigorous mathematical footing. While he was a mathematician, not a statistician, undoubtedly his work is important in many branches | Most famous statisticians
Andrey Nikolayevich Kolmogorov, for putting probability theory on a rigorous mathematical footing. While he was a mathematician, not a statistician, undoubtedly his work is important in many branches of statistics. | Most famous statisticians
Andrey Nikolayevich Kolmogorov, for putting probability theory on a rigorous mathematical footing. While he was a mathematician, not a statistician, undoubtedly his work is important in many branches |
3,619 | Most famous statisticians | Pierre-Simon Laplace for work on fundamentals of (Bayesian) probability. | Most famous statisticians | Pierre-Simon Laplace for work on fundamentals of (Bayesian) probability. | Most famous statisticians
Pierre-Simon Laplace for work on fundamentals of (Bayesian) probability. | Most famous statisticians
Pierre-Simon Laplace for work on fundamentals of (Bayesian) probability. |
3,620 | Most famous statisticians | Francis Galton for discovering statistical correlation and promoting regression. | Most famous statisticians | Francis Galton for discovering statistical correlation and promoting regression. | Most famous statisticians
Francis Galton for discovering statistical correlation and promoting regression. | Most famous statisticians
Francis Galton for discovering statistical correlation and promoting regression. |
3,621 | Most famous statisticians | George Box for his work on time series, designed experiments and elucidating the iterative nature of scientific discovery (proposing and testing models). | Most famous statisticians | George Box for his work on time series, designed experiments and elucidating the iterative nature of scientific discovery (proposing and testing models). | Most famous statisticians
George Box for his work on time series, designed experiments and elucidating the iterative nature of scientific discovery (proposing and testing models). | Most famous statisticians
George Box for his work on time series, designed experiments and elucidating the iterative nature of scientific discovery (proposing and testing models). |
3,622 | Most famous statisticians | Andrey Markov for stochastic processes and markov chains. | Most famous statisticians | Andrey Markov for stochastic processes and markov chains. | Most famous statisticians
Andrey Markov for stochastic processes and markov chains. | Most famous statisticians
Andrey Markov for stochastic processes and markov chains. |
3,623 | Most famous statisticians | Jerzy Neyman and Egon Pearson for work on experimental design, hypothesis testing, confidence intervals, and the Neyman-Pearson lemma. | Most famous statisticians | Jerzy Neyman and Egon Pearson for work on experimental design, hypothesis testing, confidence intervals, and the Neyman-Pearson lemma. | Most famous statisticians
Jerzy Neyman and Egon Pearson for work on experimental design, hypothesis testing, confidence intervals, and the Neyman-Pearson lemma. | Most famous statisticians
Jerzy Neyman and Egon Pearson for work on experimental design, hypothesis testing, confidence intervals, and the Neyman-Pearson lemma. |
3,624 | Most famous statisticians | How has Sir David Roxbee Cox not been mentioned yet?
Some feats: Cox proportional hazards models, experimental design, he did a lot of work on stochastic processes and binary data. He also advised many students who went on to do great work (Hinkley, McCullagh, Little, Atkinson, etc.)
And the man was knighted! | Most famous statisticians | How has Sir David Roxbee Cox not been mentioned yet?
Some feats: Cox proportional hazards models, experimental design, he did a lot of work on stochastic processes and binary data. He also advise | Most famous statisticians
How has Sir David Roxbee Cox not been mentioned yet?
Some feats: Cox proportional hazards models, experimental design, he did a lot of work on stochastic processes and binary data. He also advised many students who went on to do great work (Hinkley, McCullagh, Little, Atkinson, etc.)
And ... | Most famous statisticians
How has Sir David Roxbee Cox not been mentioned yet?
Some feats: Cox proportional hazards models, experimental design, he did a lot of work on stochastic processes and binary data. He also advise |
3,625 | Most famous statisticians | Leo Breiman for CART, bagging, and random forests. | Most famous statisticians | Leo Breiman for CART, bagging, and random forests. | Most famous statisticians
Leo Breiman for CART, bagging, and random forests. | Most famous statisticians
Leo Breiman for CART, bagging, and random forests. |
3,626 | Most famous statisticians | Harold Jeffreys for revival of Bayesian interpretation of probability. | Most famous statisticians | Harold Jeffreys for revival of Bayesian interpretation of probability. | Most famous statisticians
Harold Jeffreys for revival of Bayesian interpretation of probability. | Most famous statisticians
Harold Jeffreys for revival of Bayesian interpretation of probability. |
3,627 | Most famous statisticians | Edwin Thompson Jaynes for work on objective Bayesian methods, particularly MaxEnt and transformation groups. | Most famous statisticians | Edwin Thompson Jaynes for work on objective Bayesian methods, particularly MaxEnt and transformation groups. | Most famous statisticians
Edwin Thompson Jaynes for work on objective Bayesian methods, particularly MaxEnt and transformation groups. | Most famous statisticians
Edwin Thompson Jaynes for work on objective Bayesian methods, particularly MaxEnt and transformation groups. |
3,628 | Most famous statisticians | C.R. Rao for the RaoβBlackwell theorem and the Cramer-Rao bound. | Most famous statisticians | C.R. Rao for the RaoβBlackwell theorem and the Cramer-Rao bound. | Most famous statisticians
C.R. Rao for the RaoβBlackwell theorem and the Cramer-Rao bound. | Most famous statisticians
C.R. Rao for the RaoβBlackwell theorem and the Cramer-Rao bound. |
3,629 | Most famous statisticians | Florence Nightingale for being "a true pioneer in the graphical representation of statistics" and developing the polar area diagram. Yes, that Florence Nightingale! | Most famous statisticians | Florence Nightingale for being "a true pioneer in the graphical representation of statistics" and developing the polar area diagram. Yes, that Florence Nightingale! | Most famous statisticians
Florence Nightingale for being "a true pioneer in the graphical representation of statistics" and developing the polar area diagram. Yes, that Florence Nightingale! | Most famous statisticians
Florence Nightingale for being "a true pioneer in the graphical representation of statistics" and developing the polar area diagram. Yes, that Florence Nightingale! |
3,630 | Most famous statisticians | Blaise Pascal and Pierre de Fermat for creating the theory of probability and inventing the idea of expected value (1654) in order to solve a problem grounded in statistical observations (from gambling). | Most famous statisticians | Blaise Pascal and Pierre de Fermat for creating the theory of probability and inventing the idea of expected value (1654) in order to solve a problem grounded in statistical observations (from gamblin | Most famous statisticians
Blaise Pascal and Pierre de Fermat for creating the theory of probability and inventing the idea of expected value (1654) in order to solve a problem grounded in statistical observations (from gambling). | Most famous statisticians
Blaise Pascal and Pierre de Fermat for creating the theory of probability and inventing the idea of expected value (1654) in order to solve a problem grounded in statistical observations (from gamblin |
3,631 | Most famous statisticians | Roderick Little and Donald Rubin for the contributions in Missing Data Analysis. | Most famous statisticians | Roderick Little and Donald Rubin for the contributions in Missing Data Analysis. | Most famous statisticians
Roderick Little and Donald Rubin for the contributions in Missing Data Analysis. | Most famous statisticians
Roderick Little and Donald Rubin for the contributions in Missing Data Analysis. |
3,632 | Most famous statisticians | W. Edwards Deming for promoting statistical process control | Most famous statisticians | W. Edwards Deming for promoting statistical process control | Most famous statisticians
W. Edwards Deming for promoting statistical process control | Most famous statisticians
W. Edwards Deming for promoting statistical process control |
3,633 | Most famous statisticians | George Dantzig for the Simplex Method, and for being the student who mistook two open statistics problems that Neyman had written on the board for homework problems, and in his "ignorance" solving them. I'd vote for him just for the story. | Most famous statisticians | George Dantzig for the Simplex Method, and for being the student who mistook two open statistics problems that Neyman had written on the board for homework problems, and in his "ignorance" solving the | Most famous statisticians
George Dantzig for the Simplex Method, and for being the student who mistook two open statistics problems that Neyman had written on the board for homework problems, and in his "ignorance" solving them. I'd vote for him just for the story. | Most famous statisticians
George Dantzig for the Simplex Method, and for being the student who mistook two open statistics problems that Neyman had written on the board for homework problems, and in his "ignorance" solving the |
3,634 | Most famous statisticians | Samuel S. Wilks was a leader in the development of mathematical statistics. He developed the theorem on the distribution of the likelihood ratio, a fundamental result that is used in a wide variety of situations.
He also helped found the Princeton statistics department, where he was Fred Mosteller's advisor, among ot... | Most famous statisticians | Samuel S. Wilks was a leader in the development of mathematical statistics. He developed the theorem on the distribution of the likelihood ratio, a fundamental result that is used in a wide variety of | Most famous statisticians
Samuel S. Wilks was a leader in the development of mathematical statistics. He developed the theorem on the distribution of the likelihood ratio, a fundamental result that is used in a wide variety of situations.
He also helped found the Princeton statistics department, where he was Fred Mos... | Most famous statisticians
Samuel S. Wilks was a leader in the development of mathematical statistics. He developed the theorem on the distribution of the likelihood ratio, a fundamental result that is used in a wide variety of |
3,635 | Most famous statisticians | Abraham Wald (1902-1950) for introducing the concept of Wald-tests and for his fundamental work on statistical decision theory. | Most famous statisticians | Abraham Wald (1902-1950) for introducing the concept of Wald-tests and for his fundamental work on statistical decision theory. | Most famous statisticians
Abraham Wald (1902-1950) for introducing the concept of Wald-tests and for his fundamental work on statistical decision theory. | Most famous statisticians
Abraham Wald (1902-1950) for introducing the concept of Wald-tests and for his fundamental work on statistical decision theory. |
3,636 | Most famous statisticians | John Nelder, for providing us the now omnipresent generalized linear model framework. By his approach of unifying various standard statistical models and its estimation method, the iteratively reweighted least squares method for ML, he gave us tools that we are using now in almost all applied and theoretical concepts t... | Most famous statisticians | John Nelder, for providing us the now omnipresent generalized linear model framework. By his approach of unifying various standard statistical models and its estimation method, the iteratively reweigh | Most famous statisticians
John Nelder, for providing us the now omnipresent generalized linear model framework. By his approach of unifying various standard statistical models and its estimation method, the iteratively reweighted least squares method for ML, he gave us tools that we are using now in almost all applied ... | Most famous statisticians
John Nelder, for providing us the now omnipresent generalized linear model framework. By his approach of unifying various standard statistical models and its estimation method, the iteratively reweigh |
3,637 | Most famous statisticians | Lucien Le Cam for his contribution to mathematical statistics. (maybe Local asymptotic normality and contiguity made him famous) | Most famous statisticians | Lucien Le Cam for his contribution to mathematical statistics. (maybe Local asymptotic normality and contiguity made him famous) | Most famous statisticians
Lucien Le Cam for his contribution to mathematical statistics. (maybe Local asymptotic normality and contiguity made him famous) | Most famous statisticians
Lucien Le Cam for his contribution to mathematical statistics. (maybe Local asymptotic normality and contiguity made him famous) |
3,638 | Most famous statisticians | Leland Wilkinson for his contribution to statistical graphics. | Most famous statisticians | Leland Wilkinson for his contribution to statistical graphics. | Most famous statisticians
Leland Wilkinson for his contribution to statistical graphics. | Most famous statisticians
Leland Wilkinson for his contribution to statistical graphics. |
3,639 | Most famous statisticians | David Donoho development of multiscale ideas in statistics, and a lot of theoretically justified while practically very efficient ideas in very high dimensional statistics, CHA: computational harmonic analysis,... | Most famous statisticians | David Donoho development of multiscale ideas in statistics, and a lot of theoretically justified while practically very efficient ideas in very high dimensional statistics, CHA: computational harmonic | Most famous statisticians
David Donoho development of multiscale ideas in statistics, and a lot of theoretically justified while practically very efficient ideas in very high dimensional statistics, CHA: computational harmonic analysis,... | Most famous statisticians
David Donoho development of multiscale ideas in statistics, and a lot of theoretically justified while practically very efficient ideas in very high dimensional statistics, CHA: computational harmonic |
3,640 | Most famous statisticians | Adolphe Quetelet for his work on the "average man", and for pioneering the use of statistics in the social sciences. Before him, statistics were largely confined to the physical sciences (astronomy, in particular). | Most famous statisticians | Adolphe Quetelet for his work on the "average man", and for pioneering the use of statistics in the social sciences. Before him, statistics were largely confined to the physical sciences (astronomy, | Most famous statisticians
Adolphe Quetelet for his work on the "average man", and for pioneering the use of statistics in the social sciences. Before him, statistics were largely confined to the physical sciences (astronomy, in particular). | Most famous statisticians
Adolphe Quetelet for his work on the "average man", and for pioneering the use of statistics in the social sciences. Before him, statistics were largely confined to the physical sciences (astronomy, |
3,641 | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | Failing to reject a null hypothesis is evidence that the null hypothesis is true, but it might not be particularly good evidence, and it certainly doesn't prove the null hypothesis.
Let's take a short detour. Consider for a moment the old clichΓ©:
Absence of evidence is not evidence of absence.
Notwithstanding its po... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | Failing to reject a null hypothesis is evidence that the null hypothesis is true, but it might not be particularly good evidence, and it certainly doesn't prove the null hypothesis.
Let's take a short | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
Failing to reject a null hypothesis is evidence that the null hypothesis is true, but it might not be particularly good evidence, and it certainly doesn't prove the null hypothesis.
Let's take a short detour. Consider for a mome... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
Failing to reject a null hypothesis is evidence that the null hypothesis is true, but it might not be particularly good evidence, and it certainly doesn't prove the null hypothesis.
Let's take a short |
3,642 | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | NHST relies on p-values, which tell us: Given the null hypothesis is true, what is the probability that we observe our data (or more extreme data)?
We assume that the null hypothesis is trueβit is baked into NHST that the null hypothesis is 100% correct. Small p-values tell us that, if the null hypothesis is true, our ... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | NHST relies on p-values, which tell us: Given the null hypothesis is true, what is the probability that we observe our data (or more extreme data)?
We assume that the null hypothesis is trueβit is bak | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
NHST relies on p-values, which tell us: Given the null hypothesis is true, what is the probability that we observe our data (or more extreme data)?
We assume that the null hypothesis is trueβit is baked into NHST that the null hy... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
NHST relies on p-values, which tell us: Given the null hypothesis is true, what is the probability that we observe our data (or more extreme data)?
We assume that the null hypothesis is trueβit is bak |
3,643 | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | To grasp what is wrong with the assumption, see the following example:
Imagine an enclosure in a zoo where you can't see its inhabitants. You want to test the hypothesis that it is inhabited by monkeys by putting a banana into the cage and check if it is gone the next day. This is repeated N times for enhanced statisti... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | To grasp what is wrong with the assumption, see the following example:
Imagine an enclosure in a zoo where you can't see its inhabitants. You want to test the hypothesis that it is inhabited by monkey | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
To grasp what is wrong with the assumption, see the following example:
Imagine an enclosure in a zoo where you can't see its inhabitants. You want to test the hypothesis that it is inhabited by monkeys by putting a banana into th... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
To grasp what is wrong with the assumption, see the following example:
Imagine an enclosure in a zoo where you can't see its inhabitants. You want to test the hypothesis that it is inhabited by monkey |
3,644 | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | In his famous paper Why Most Published Research Findings Are False, Ioannidis used Bayesian reasoning and the base rate-fallacy to argue that most findings are false-positives. Shortly, the post-study probability that a particular research hypothesis is true depends - among other things - on the pre-study probability o... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | In his famous paper Why Most Published Research Findings Are False, Ioannidis used Bayesian reasoning and the base rate-fallacy to argue that most findings are false-positives. Shortly, the post-study | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
In his famous paper Why Most Published Research Findings Are False, Ioannidis used Bayesian reasoning and the base rate-fallacy to argue that most findings are false-positives. Shortly, the post-study probability that a particula... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
In his famous paper Why Most Published Research Findings Are False, Ioannidis used Bayesian reasoning and the base rate-fallacy to argue that most findings are false-positives. Shortly, the post-study |
3,645 | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | The best explanation I've seen for this is from someone whose training is in mathematics.
Null-Hypothesis Significance Testing is basically a proof by contradiction: assume $H_0$, is there evidence for $H_1$? If there is evidence for $H_1$, reject $H_0$ and accept $H_1$. But if there isn't evidence for $H_1$, it's circ... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | The best explanation I've seen for this is from someone whose training is in mathematics.
Null-Hypothesis Significance Testing is basically a proof by contradiction: assume $H_0$, is there evidence fo | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
The best explanation I've seen for this is from someone whose training is in mathematics.
Null-Hypothesis Significance Testing is basically a proof by contradiction: assume $H_0$, is there evidence for $H_1$? If there is evidence... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
The best explanation I've seen for this is from someone whose training is in mathematics.
Null-Hypothesis Significance Testing is basically a proof by contradiction: assume $H_0$, is there evidence fo |
3,646 | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | If you do not like this consequence of hypothesis testing but are not prepared to make the full leap to Bayesian methods, how about a confidence interval?
Suppose you flip a coin $42078$ times and see $20913$ heads, leading to you saying that a 95% confidence interval for the probability of heads is $[0.492,0.502]$.
... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | If you do not like this consequence of hypothesis testing but are not prepared to make the full leap to Bayesian methods, how about a confidence interval?
Suppose you flip a coin $42078$ times and see | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
If you do not like this consequence of hypothesis testing but are not prepared to make the full leap to Bayesian methods, how about a confidence interval?
Suppose you flip a coin $42078$ times and see $20913$ heads, leading to yo... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
If you do not like this consequence of hypothesis testing but are not prepared to make the full leap to Bayesian methods, how about a confidence interval?
Suppose you flip a coin $42078$ times and see |
3,647 | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | It would perhaps be better to say that non-rejection of a null hypothesis is not in itself evidence for the null hypothesis. Once we consider the full likelihood of the data, which more explicitly considers the amount of the data, then the collected data may provide support for the parameters falling within the null hy... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | It would perhaps be better to say that non-rejection of a null hypothesis is not in itself evidence for the null hypothesis. Once we consider the full likelihood of the data, which more explicitly con | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
It would perhaps be better to say that non-rejection of a null hypothesis is not in itself evidence for the null hypothesis. Once we consider the full likelihood of the data, which more explicitly considers the amount of the data... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
It would perhaps be better to say that non-rejection of a null hypothesis is not in itself evidence for the null hypothesis. Once we consider the full likelihood of the data, which more explicitly con |
3,648 | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | It rather depends on how you are using language. Under Pearson and Neyman decision theory, it is not evidence for the null, but you are to behave as if the null is true.
The difficulty comes from modus tollens. Bayesian methods are a form of inductive reasoning and, as such, are a form of incomplete reasoning. Null ... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | It rather depends on how you are using language. Under Pearson and Neyman decision theory, it is not evidence for the null, but you are to behave as if the null is true.
The difficulty comes from mod | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
It rather depends on how you are using language. Under Pearson and Neyman decision theory, it is not evidence for the null, but you are to behave as if the null is true.
The difficulty comes from modus tollens. Bayesian methods... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
It rather depends on how you are using language. Under Pearson and Neyman decision theory, it is not evidence for the null, but you are to behave as if the null is true.
The difficulty comes from mod |
3,649 | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | I'll try to illustrate this with an example.
Let us think that we are sampling from a population, with an intention of test for its mean $\mu$. We get a sample with mean $\bar{x}$. If we get a non-significant p-value, we would also get non-significant p-values if we had tested for any other null hypothesis $H_0:\mu=\mu... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | I'll try to illustrate this with an example.
Let us think that we are sampling from a population, with an intention of test for its mean $\mu$. We get a sample with mean $\bar{x}$. If we get a non-sig | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
I'll try to illustrate this with an example.
Let us think that we are sampling from a population, with an intention of test for its mean $\mu$. We get a sample with mean $\bar{x}$. If we get a non-significant p-value, we would al... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
I'll try to illustrate this with an example.
Let us think that we are sampling from a population, with an intention of test for its mean $\mu$. We get a sample with mean $\bar{x}$. If we get a non-sig |
3,650 | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | Consider the small dataset (illustrated below) with mean $\bar x \approx 0$, say that you conducted a two-tailed $t$-test with $H_0: \bar x = \mu$, where $\mu = -0.5$. The test appears to be insignificant with $p > 0.05$. Does that signify that your $H_0$ is true? What if you tested against $\mu = 0.5$? Since the $t$ d... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | Consider the small dataset (illustrated below) with mean $\bar x \approx 0$, say that you conducted a two-tailed $t$-test with $H_0: \bar x = \mu$, where $\mu = -0.5$. The test appears to be insignifi | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
Consider the small dataset (illustrated below) with mean $\bar x \approx 0$, say that you conducted a two-tailed $t$-test with $H_0: \bar x = \mu$, where $\mu = -0.5$. The test appears to be insignificant with $p > 0.05$. Does th... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
Consider the small dataset (illustrated below) with mean $\bar x \approx 0$, say that you conducted a two-tailed $t$-test with $H_0: \bar x = \mu$, where $\mu = -0.5$. The test appears to be insignifi |
3,651 | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | Let's follow a simple example.
My null hypothesis is that my data follows a normal distribution. The alternative hypothesis is that the distribution for my data is not normal.
I draw two random samples from an uniform distribution on [0,1]. I can't do much with just two samples, thus I wouldn't be able to reject my nul... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | Let's follow a simple example.
My null hypothesis is that my data follows a normal distribution. The alternative hypothesis is that the distribution for my data is not normal.
I draw two random sample | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
Let's follow a simple example.
My null hypothesis is that my data follows a normal distribution. The alternative hypothesis is that the distribution for my data is not normal.
I draw two random samples from an uniform distributio... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
Let's follow a simple example.
My null hypothesis is that my data follows a normal distribution. The alternative hypothesis is that the distribution for my data is not normal.
I draw two random sample |
3,652 | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | Rejecting $H_0$ requires your study to have enough statistical power. If you're able to reject $H_0$, you can say that you have gathered sufficient data to draw a conclusion.
On the other hand, not rejecting $H_0$ doesn't require any data at all, since it's assumed to be true by default. So, if your study doesn't rejec... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | Rejecting $H_0$ requires your study to have enough statistical power. If you're able to reject $H_0$, you can say that you have gathered sufficient data to draw a conclusion.
On the other hand, not re | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
Rejecting $H_0$ requires your study to have enough statistical power. If you're able to reject $H_0$, you can say that you have gathered sufficient data to draw a conclusion.
On the other hand, not rejecting $H_0$ doesn't require... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
Rejecting $H_0$ requires your study to have enough statistical power. If you're able to reject $H_0$, you can say that you have gathered sufficient data to draw a conclusion.
On the other hand, not re |
3,653 | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | Both null and alternative hypothesis are models, and as such different from reality and never true. A rejection of the null hypothesis says that the data are not compatible with the null hypothesis, because if the null hypothesis were true, such data would not normally be observed. A non-rejection of the null hypothesi... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | Both null and alternative hypothesis are models, and as such different from reality and never true. A rejection of the null hypothesis says that the data are not compatible with the null hypothesis, b | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
Both null and alternative hypothesis are models, and as such different from reality and never true. A rejection of the null hypothesis says that the data are not compatible with the null hypothesis, because if the null hypothesis... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
Both null and alternative hypothesis are models, and as such different from reality and never true. A rejection of the null hypothesis says that the data are not compatible with the null hypothesis, b |
3,654 | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | No, it is not evidence unless you have evidence that it is evidence. I'm not trying to be cute, rather literal. You only have probability of seeing such data given your assumption the null is true. That is ALL you get from the p-value (if that, since the p-value is based on assumptions themselves).
Can you present a s... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null? | No, it is not evidence unless you have evidence that it is evidence. I'm not trying to be cute, rather literal. You only have probability of seeing such data given your assumption the null is true. Th | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
No, it is not evidence unless you have evidence that it is evidence. I'm not trying to be cute, rather literal. You only have probability of seeing such data given your assumption the null is true. That is ALL you get from the p-... | If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
No, it is not evidence unless you have evidence that it is evidence. I'm not trying to be cute, rather literal. You only have probability of seeing such data given your assumption the null is true. Th |
3,655 | Are bayesians slaves of the likelihood function? | I do not see much appeal in this example, esp. as a potential criticism of Bayesians and likelihood-wallahs.... The constant $c$ is known, being equal to
$$
1\big/ \int_\mathcal{X} g(x) \text{d}x
$$
If $c$ is the only "unknown" in the picture, given a sample $x_1,\ldots,x_n$, then there is no statistical issue about th... | Are bayesians slaves of the likelihood function? | I do not see much appeal in this example, esp. as a potential criticism of Bayesians and likelihood-wallahs.... The constant $c$ is known, being equal to
$$
1\big/ \int_\mathcal{X} g(x) \text{d}x
$$
I | Are bayesians slaves of the likelihood function?
I do not see much appeal in this example, esp. as a potential criticism of Bayesians and likelihood-wallahs.... The constant $c$ is known, being equal to
$$
1\big/ \int_\mathcal{X} g(x) \text{d}x
$$
If $c$ is the only "unknown" in the picture, given a sample $x_1,\ldots,... | Are bayesians slaves of the likelihood function?
I do not see much appeal in this example, esp. as a potential criticism of Bayesians and likelihood-wallahs.... The constant $c$ is known, being equal to
$$
1\big/ \int_\mathcal{X} g(x) \text{d}x
$$
I |
3,656 | Are bayesians slaves of the likelihood function? | This has been discussed in my paper (published only on the internet) "On an Example of Larry Wasserman" [1] and in a blog exchange between me, Wasserman, Robins, and some other commenters on Wasserman's blog: [2]
The short answer is that Wasserman (and Robins) generate paradoxes by suggesting that priors in high dimens... | Are bayesians slaves of the likelihood function? | This has been discussed in my paper (published only on the internet) "On an Example of Larry Wasserman" [1] and in a blog exchange between me, Wasserman, Robins, and some other commenters on Wasserman | Are bayesians slaves of the likelihood function?
This has been discussed in my paper (published only on the internet) "On an Example of Larry Wasserman" [1] and in a blog exchange between me, Wasserman, Robins, and some other commenters on Wasserman's blog: [2]
The short answer is that Wasserman (and Robins) generate p... | Are bayesians slaves of the likelihood function?
This has been discussed in my paper (published only on the internet) "On an Example of Larry Wasserman" [1] and in a blog exchange between me, Wasserman, Robins, and some other commenters on Wasserman |
3,657 | Are bayesians slaves of the likelihood function? | I agree that the example is weird.
I meant it to be more of a puzzle really.
(The example is actually due to Ed George.)
It does raise the question of what it means for something to be
"known". Christian says that $c$ is known. But, at least from the
purely subjective probability point of view, you don't know it
just b... | Are bayesians slaves of the likelihood function? | I agree that the example is weird.
I meant it to be more of a puzzle really.
(The example is actually due to Ed George.)
It does raise the question of what it means for something to be
"known". Christ | Are bayesians slaves of the likelihood function?
I agree that the example is weird.
I meant it to be more of a puzzle really.
(The example is actually due to Ed George.)
It does raise the question of what it means for something to be
"known". Christian says that $c$ is known. But, at least from the
purely subjective pr... | Are bayesians slaves of the likelihood function?
I agree that the example is weird.
I meant it to be more of a puzzle really.
(The example is actually due to Ed George.)
It does raise the question of what it means for something to be
"known". Christ |
3,658 | Are bayesians slaves of the likelihood function? | The proposed statistical model may be described as follows: You have a known nonnegative integrable function $g:\mathbb{R}\to\mathbb{R}$, and a nonnegative random variable $C$. The random variables $X_1,\dots,X_n$ are supposed to be conditionally independent and identically distributed, given that $C=c$, with condition... | Are bayesians slaves of the likelihood function? | The proposed statistical model may be described as follows: You have a known nonnegative integrable function $g:\mathbb{R}\to\mathbb{R}$, and a nonnegative random variable $C$. The random variables $X | Are bayesians slaves of the likelihood function?
The proposed statistical model may be described as follows: You have a known nonnegative integrable function $g:\mathbb{R}\to\mathbb{R}$, and a nonnegative random variable $C$. The random variables $X_1,\dots,X_n$ are supposed to be conditionally independent and identica... | Are bayesians slaves of the likelihood function?
The proposed statistical model may be described as follows: You have a known nonnegative integrable function $g:\mathbb{R}\to\mathbb{R}$, and a nonnegative random variable $C$. The random variables $X |
3,659 | Are bayesians slaves of the likelihood function? | There is an irony that the standard way to do Bayesian computation is to use frequentist analysis of MCMC samples. In this example we might consider $c$ to be closely related to the marginal likelihood, which we would like to calculate, but we are going to be Bayesian purists in the sense of to try to also do the comp... | Are bayesians slaves of the likelihood function? | There is an irony that the standard way to do Bayesian computation is to use frequentist analysis of MCMC samples. In this example we might consider $c$ to be closely related to the marginal likeliho | Are bayesians slaves of the likelihood function?
There is an irony that the standard way to do Bayesian computation is to use frequentist analysis of MCMC samples. In this example we might consider $c$ to be closely related to the marginal likelihood, which we would like to calculate, but we are going to be Bayesian p... | Are bayesians slaves of the likelihood function?
There is an irony that the standard way to do Bayesian computation is to use frequentist analysis of MCMC samples. In this example we might consider $c$ to be closely related to the marginal likeliho |
3,660 | Are bayesians slaves of the likelihood function? | The example is a little weird and contrived. The reason the likelihood goes awry is because g is a known function. The only unknown parameter is c which is not part of the likelihood. Also since g is known the data gives you no information about f. When do you see such a thing in practice? So the posterior is just... | Are bayesians slaves of the likelihood function? | The example is a little weird and contrived. The reason the likelihood goes awry is because g is a known function. The only unknown parameter is c which is not part of the likelihood. Also since g | Are bayesians slaves of the likelihood function?
The example is a little weird and contrived. The reason the likelihood goes awry is because g is a known function. The only unknown parameter is c which is not part of the likelihood. Also since g is known the data gives you no information about f. When do you see su... | Are bayesians slaves of the likelihood function?
The example is a little weird and contrived. The reason the likelihood goes awry is because g is a known function. The only unknown parameter is c which is not part of the likelihood. Also since g |
3,661 | Are bayesians slaves of the likelihood function? | We could extend the definition of possible knowns (analogous to the extension of data to allow for missing data for datum that was observed but lost) to include NULL (no data generated).
Suppose that you have a proper prior
$$
\pi(c) = \frac{1}{c^2} \,I_{[1,\infty)}(c) \, .
$$
Now define the data model for x
If $c... | Are bayesians slaves of the likelihood function? | We could extend the definition of possible knowns (analogous to the extension of data to allow for missing data for datum that was observed but lost) to include NULL (no data generated).
Suppose tha | Are bayesians slaves of the likelihood function?
We could extend the definition of possible knowns (analogous to the extension of data to allow for missing data for datum that was observed but lost) to include NULL (no data generated).
Suppose that you have a proper prior
$$
\pi(c) = \frac{1}{c^2} \,I_{[1,\infty)}(... | Are bayesians slaves of the likelihood function?
We could extend the definition of possible knowns (analogous to the extension of data to allow for missing data for datum that was observed but lost) to include NULL (no data generated).
Suppose tha |
3,662 | Are bayesians slaves of the likelihood function? | Wait, what? You have $$\pi(c|x) = \left( \Pi_i g(x_i) \right) \cdot c^n \pi(c) \,,$$ so it does depend on the values of $\{x_i\}$. Just because you hide the dependency in a "$\propto$" doesn't mean you can ignore it? | Are bayesians slaves of the likelihood function? | Wait, what? You have $$\pi(c|x) = \left( \Pi_i g(x_i) \right) \cdot c^n \pi(c) \,,$$ so it does depend on the values of $\{x_i\}$. Just because you hide the dependency in a "$\propto$" doesn't mean | Are bayesians slaves of the likelihood function?
Wait, what? You have $$\pi(c|x) = \left( \Pi_i g(x_i) \right) \cdot c^n \pi(c) \,,$$ so it does depend on the values of $\{x_i\}$. Just because you hide the dependency in a "$\propto$" doesn't mean you can ignore it? | Are bayesians slaves of the likelihood function?
Wait, what? You have $$\pi(c|x) = \left( \Pi_i g(x_i) \right) \cdot c^n \pi(c) \,,$$ so it does depend on the values of $\{x_i\}$. Just because you hide the dependency in a "$\propto$" doesn't mean |
3,663 | Why does collecting data until finding a significant result increase Type I error rate? | The problem is that you're giving yourself too many chances to pass the test. It's just a fancy version of this dialog:
I'll flip you to see who pays for dinner.
OK, I call heads.
Rats, you won. Best two out of three?
To understand this better, consider a simplified--but realistic--model of this sequential procedu... | Why does collecting data until finding a significant result increase Type I error rate? | The problem is that you're giving yourself too many chances to pass the test. It's just a fancy version of this dialog:
I'll flip you to see who pays for dinner.
OK, I call heads.
Rats, you won. Be | Why does collecting data until finding a significant result increase Type I error rate?
The problem is that you're giving yourself too many chances to pass the test. It's just a fancy version of this dialog:
I'll flip you to see who pays for dinner.
OK, I call heads.
Rats, you won. Best two out of three?
To unders... | Why does collecting data until finding a significant result increase Type I error rate?
The problem is that you're giving yourself too many chances to pass the test. It's just a fancy version of this dialog:
I'll flip you to see who pays for dinner.
OK, I call heads.
Rats, you won. Be |
3,664 | Why does collecting data until finding a significant result increase Type I error rate? | People who are new to hypothesis testing tend to think that once a p value goes below .05, adding more participants will only decrease the p value further. But this isn't true. Under the null hypothesis, a p value is uniformly distributed between 0 and 1 and can bounce around quite a bit in that range.
I've simulate... | Why does collecting data until finding a significant result increase Type I error rate? | People who are new to hypothesis testing tend to think that once a p value goes below .05, adding more participants will only decrease the p value further. But this isn't true. Under the null hypothes | Why does collecting data until finding a significant result increase Type I error rate?
People who are new to hypothesis testing tend to think that once a p value goes below .05, adding more participants will only decrease the p value further. But this isn't true. Under the null hypothesis, a p value is uniformly distr... | Why does collecting data until finding a significant result increase Type I error rate?
People who are new to hypothesis testing tend to think that once a p value goes below .05, adding more participants will only decrease the p value further. But this isn't true. Under the null hypothes |
3,665 | Why does collecting data until finding a significant result increase Type I error rate? | This answer only concerns the probability of ultimately getting a "significant" result and the distribution of the time to this event under @whuber's model.
As in the model of @whuber, let $S(t)=X_1 + X_2 + \dots + X_t$ denote the value of the test statistic after $t$ observations have been collected and assume that th... | Why does collecting data until finding a significant result increase Type I error rate? | This answer only concerns the probability of ultimately getting a "significant" result and the distribution of the time to this event under @whuber's model.
As in the model of @whuber, let $S(t)=X_1 + | Why does collecting data until finding a significant result increase Type I error rate?
This answer only concerns the probability of ultimately getting a "significant" result and the distribution of the time to this event under @whuber's model.
As in the model of @whuber, let $S(t)=X_1 + X_2 + \dots + X_t$ denote the v... | Why does collecting data until finding a significant result increase Type I error rate?
This answer only concerns the probability of ultimately getting a "significant" result and the distribution of the time to this event under @whuber's model.
As in the model of @whuber, let $S(t)=X_1 + |
3,666 | Why does collecting data until finding a significant result increase Type I error rate? | It needs to be said that the above discussion is for a frequentist world view for which multiplicity comes from the chances you give data to be more extreme, not from the chances you give an effect to exist. The root cause of the problem is that p-values and type I errors use backwards-time backwards-information flow ... | Why does collecting data until finding a significant result increase Type I error rate? | It needs to be said that the above discussion is for a frequentist world view for which multiplicity comes from the chances you give data to be more extreme, not from the chances you give an effect to | Why does collecting data until finding a significant result increase Type I error rate?
It needs to be said that the above discussion is for a frequentist world view for which multiplicity comes from the chances you give data to be more extreme, not from the chances you give an effect to exist. The root cause of the p... | Why does collecting data until finding a significant result increase Type I error rate?
It needs to be said that the above discussion is for a frequentist world view for which multiplicity comes from the chances you give data to be more extreme, not from the chances you give an effect to |
3,667 | Why does collecting data until finding a significant result increase Type I error rate? | We consider a researcher collecting a sample of size $n$, $x_1$, to test some hypothesis $\theta=\theta_0$. He rejects if a suitable test statistic $t$ exceeds its level-$\alpha$ critical value $c$. If it does not, he collects another sample of size $n$, $x_2$, and rejects if the test rejects for the combined sample $(... | Why does collecting data until finding a significant result increase Type I error rate? | We consider a researcher collecting a sample of size $n$, $x_1$, to test some hypothesis $\theta=\theta_0$. He rejects if a suitable test statistic $t$ exceeds its level-$\alpha$ critical value $c$. I | Why does collecting data until finding a significant result increase Type I error rate?
We consider a researcher collecting a sample of size $n$, $x_1$, to test some hypothesis $\theta=\theta_0$. He rejects if a suitable test statistic $t$ exceeds its level-$\alpha$ critical value $c$. If it does not, he collects anoth... | Why does collecting data until finding a significant result increase Type I error rate?
We consider a researcher collecting a sample of size $n$, $x_1$, to test some hypothesis $\theta=\theta_0$. He rejects if a suitable test statistic $t$ exceeds its level-$\alpha$ critical value $c$. I |
3,668 | Clustering with K-Means and EM: how are they related? | K means
Hard assign a data point to one particular cluster on convergence.
It makes use of the L2 norm when optimizing (Min {Theta} L2 norm point and its centroid coordinates).
EM
Soft assigns a point to clusters (so it give a probability of any point belonging to any centroid).
It doesn't depend on the L2 norm, bu... | Clustering with K-Means and EM: how are they related? | K means
Hard assign a data point to one particular cluster on convergence.
It makes use of the L2 norm when optimizing (Min {Theta} L2 norm point and its centroid coordinates).
EM
Soft assigns a p | Clustering with K-Means and EM: how are they related?
K means
Hard assign a data point to one particular cluster on convergence.
It makes use of the L2 norm when optimizing (Min {Theta} L2 norm point and its centroid coordinates).
EM
Soft assigns a point to clusters (so it give a probability of any point belonging ... | Clustering with K-Means and EM: how are they related?
K means
Hard assign a data point to one particular cluster on convergence.
It makes use of the L2 norm when optimizing (Min {Theta} L2 norm point and its centroid coordinates).
EM
Soft assigns a p |
3,669 | Clustering with K-Means and EM: how are they related? | There is no "k-means algorithm". There is MacQueens algorithm for k-means, the Lloyd/Forgy algorithm for k-means, the Hartigan-Wong method, ...
There also isn't "the" EM-algorithm. It is a general scheme of repeatedly expecting the likelihoods and then maximizing the model. The most popular variant of EM is also known ... | Clustering with K-Means and EM: how are they related? | There is no "k-means algorithm". There is MacQueens algorithm for k-means, the Lloyd/Forgy algorithm for k-means, the Hartigan-Wong method, ...
There also isn't "the" EM-algorithm. It is a general sch | Clustering with K-Means and EM: how are they related?
There is no "k-means algorithm". There is MacQueens algorithm for k-means, the Lloyd/Forgy algorithm for k-means, the Hartigan-Wong method, ...
There also isn't "the" EM-algorithm. It is a general scheme of repeatedly expecting the likelihoods and then maximizing th... | Clustering with K-Means and EM: how are they related?
There is no "k-means algorithm". There is MacQueens algorithm for k-means, the Lloyd/Forgy algorithm for k-means, the Hartigan-Wong method, ...
There also isn't "the" EM-algorithm. It is a general sch |
3,670 | Clustering with K-Means and EM: how are they related? | Here is an example, if I were doing this in mplus, which might be helpful and compliment more comprehensive answers:
Say I have 3 continuous variables and want to identify clusters based on these. I would specify a mixture model (more specficially in this case, a latent profile model), assuming conditional independence... | Clustering with K-Means and EM: how are they related? | Here is an example, if I were doing this in mplus, which might be helpful and compliment more comprehensive answers:
Say I have 3 continuous variables and want to identify clusters based on these. I w | Clustering with K-Means and EM: how are they related?
Here is an example, if I were doing this in mplus, which might be helpful and compliment more comprehensive answers:
Say I have 3 continuous variables and want to identify clusters based on these. I would specify a mixture model (more specficially in this case, a la... | Clustering with K-Means and EM: how are they related?
Here is an example, if I were doing this in mplus, which might be helpful and compliment more comprehensive answers:
Say I have 3 continuous variables and want to identify clusters based on these. I w |
3,671 | What are alternatives of Gradient Descent? | This is more a problem to do with the function being minimized than the method used, if finding the true global minimum is important, then use a method such a simulated annealing. This will be able to find the global minimum, but may take a very long time to do so.
In the case of neural nets, local minima are not nece... | What are alternatives of Gradient Descent? | This is more a problem to do with the function being minimized than the method used, if finding the true global minimum is important, then use a method such a simulated annealing. This will be able t | What are alternatives of Gradient Descent?
This is more a problem to do with the function being minimized than the method used, if finding the true global minimum is important, then use a method such a simulated annealing. This will be able to find the global minimum, but may take a very long time to do so.
In the cas... | What are alternatives of Gradient Descent?
This is more a problem to do with the function being minimized than the method used, if finding the true global minimum is important, then use a method such a simulated annealing. This will be able t |
3,672 | What are alternatives of Gradient Descent? | Gradient descent is an optimization algorithm.
There are many optimization algorithms that operate on a fixed number of real values that are correlated (non-separable). We can divide them roughly in 2 categories: gradient-based optimizers and derivative-free optimizers. Usually you want to use the gradient to optimize ... | What are alternatives of Gradient Descent? | Gradient descent is an optimization algorithm.
There are many optimization algorithms that operate on a fixed number of real values that are correlated (non-separable). We can divide them roughly in 2 | What are alternatives of Gradient Descent?
Gradient descent is an optimization algorithm.
There are many optimization algorithms that operate on a fixed number of real values that are correlated (non-separable). We can divide them roughly in 2 categories: gradient-based optimizers and derivative-free optimizers. Usuall... | What are alternatives of Gradient Descent?
Gradient descent is an optimization algorithm.
There are many optimization algorithms that operate on a fixed number of real values that are correlated (non-separable). We can divide them roughly in 2 |
3,673 | What are alternatives of Gradient Descent? | An interesting alternative to gradient descent is the population-based training algorithms such as the evolutionary algorithms (EA) and the particle swarm optimisation (PSO). The basic idea behind population-based approaches is that a population of candidate solutions (NN weight vectors) is created, and the candidate s... | What are alternatives of Gradient Descent? | An interesting alternative to gradient descent is the population-based training algorithms such as the evolutionary algorithms (EA) and the particle swarm optimisation (PSO). The basic idea behind pop | What are alternatives of Gradient Descent?
An interesting alternative to gradient descent is the population-based training algorithms such as the evolutionary algorithms (EA) and the particle swarm optimisation (PSO). The basic idea behind population-based approaches is that a population of candidate solutions (NN weig... | What are alternatives of Gradient Descent?
An interesting alternative to gradient descent is the population-based training algorithms such as the evolutionary algorithms (EA) and the particle swarm optimisation (PSO). The basic idea behind pop |
3,674 | What are alternatives of Gradient Descent? | I know this thread is quite old and others have done a great job to explain concepts like local minima, overfitting etc. However, as OP was looking for an alternative solution, I will try to contribute one and hope it will inspire more interesting ideas.
The idea is to replace every weight w to w + t, where t is a ran... | What are alternatives of Gradient Descent? | I know this thread is quite old and others have done a great job to explain concepts like local minima, overfitting etc. However, as OP was looking for an alternative solution, I will try to contribut | What are alternatives of Gradient Descent?
I know this thread is quite old and others have done a great job to explain concepts like local minima, overfitting etc. However, as OP was looking for an alternative solution, I will try to contribute one and hope it will inspire more interesting ideas.
The idea is to replac... | What are alternatives of Gradient Descent?
I know this thread is quite old and others have done a great job to explain concepts like local minima, overfitting etc. However, as OP was looking for an alternative solution, I will try to contribut |
3,675 | What are alternatives of Gradient Descent? | When it comes to Global Optimisation tasks (i.e. attempting to find a global minimum of an objective function) you might wanna take a look at:
Pattern Search (also known as direct search, derivative-free search, or black-box search), which uses a pattern (set of vectors ${\{v_i\}}$) to determine the points to search a... | What are alternatives of Gradient Descent? | When it comes to Global Optimisation tasks (i.e. attempting to find a global minimum of an objective function) you might wanna take a look at:
Pattern Search (also known as direct search, derivative- | What are alternatives of Gradient Descent?
When it comes to Global Optimisation tasks (i.e. attempting to find a global minimum of an objective function) you might wanna take a look at:
Pattern Search (also known as direct search, derivative-free search, or black-box search), which uses a pattern (set of vectors ${\{v... | What are alternatives of Gradient Descent?
When it comes to Global Optimisation tasks (i.e. attempting to find a global minimum of an objective function) you might wanna take a look at:
Pattern Search (also known as direct search, derivative- |
3,676 | What are alternatives of Gradient Descent? | Extreme Learning Machines Essentially they are a neural network where the weights connecting the inputs to the hidden nodes are assigned randomly and never updated. The weights between the hidden nodes and the outputs are learned in a single step by solving a linear equation (matrix inverse). | What are alternatives of Gradient Descent? | Extreme Learning Machines Essentially they are a neural network where the weights connecting the inputs to the hidden nodes are assigned randomly and never updated. The weights between the hidden node | What are alternatives of Gradient Descent?
Extreme Learning Machines Essentially they are a neural network where the weights connecting the inputs to the hidden nodes are assigned randomly and never updated. The weights between the hidden nodes and the outputs are learned in a single step by solving a linear equation (... | What are alternatives of Gradient Descent?
Extreme Learning Machines Essentially they are a neural network where the weights connecting the inputs to the hidden nodes are assigned randomly and never updated. The weights between the hidden node |
3,677 | What are alternatives of Gradient Descent? | (1) Bipropagation is a semi-gradient descent algorithm much faster than backpropagation. It solves the XOR problem each time and is 20 times faster than the fastest attempt of backpropagation.
(2) Border Pairs method (BPM) is totally non-gradient descent algorithm with many advantages over backpropagation:
it finds ne... | What are alternatives of Gradient Descent? | (1) Bipropagation is a semi-gradient descent algorithm much faster than backpropagation. It solves the XOR problem each time and is 20 times faster than the fastest attempt of backpropagation.
(2) Bor | What are alternatives of Gradient Descent?
(1) Bipropagation is a semi-gradient descent algorithm much faster than backpropagation. It solves the XOR problem each time and is 20 times faster than the fastest attempt of backpropagation.
(2) Border Pairs method (BPM) is totally non-gradient descent algorithm with many ad... | What are alternatives of Gradient Descent?
(1) Bipropagation is a semi-gradient descent algorithm much faster than backpropagation. It solves the XOR problem each time and is 20 times faster than the fastest attempt of backpropagation.
(2) Bor |
3,678 | What should I do when my neural network doesn't generalize well? | First of all, let's mention what does "my neural network doesn't generalize well" mean and what's the difference with saying "my neural network doesn't perform well".
When training a Neural Network, you are constantly evaluating it on a set of labelled data called the training set. If your model isn't working properly ... | What should I do when my neural network doesn't generalize well? | First of all, let's mention what does "my neural network doesn't generalize well" mean and what's the difference with saying "my neural network doesn't perform well".
When training a Neural Network, y | What should I do when my neural network doesn't generalize well?
First of all, let's mention what does "my neural network doesn't generalize well" mean and what's the difference with saying "my neural network doesn't perform well".
When training a Neural Network, you are constantly evaluating it on a set of labelled da... | What should I do when my neural network doesn't generalize well?
First of all, let's mention what does "my neural network doesn't generalize well" mean and what's the difference with saying "my neural network doesn't perform well".
When training a Neural Network, y |
3,679 | What should I do when my neural network doesn't generalize well? | There is plenty of empirical evidence that deep enough neural networks can memorize random labels on huge datasets (Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, Oriol Vinyals, "Understanding deep learning requires rethinking generalization"). Thus in principle by getting a big enough NN we can always reduc... | What should I do when my neural network doesn't generalize well? | There is plenty of empirical evidence that deep enough neural networks can memorize random labels on huge datasets (Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, Oriol Vinyals, "Understand | What should I do when my neural network doesn't generalize well?
There is plenty of empirical evidence that deep enough neural networks can memorize random labels on huge datasets (Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, Oriol Vinyals, "Understanding deep learning requires rethinking generalization").... | What should I do when my neural network doesn't generalize well?
There is plenty of empirical evidence that deep enough neural networks can memorize random labels on huge datasets (Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, Oriol Vinyals, "Understand |
3,680 | What should I do when my neural network doesn't generalize well? | A list of commonly used regularization techniques which I've seen in the literature are:
Using batch normalization, which is a surprisingly effective regularizer to the point where I rarely see dropout used anymore, because it is simply not necessary.
A small amount of weight decay.
Some more recent regularization tec... | What should I do when my neural network doesn't generalize well? | A list of commonly used regularization techniques which I've seen in the literature are:
Using batch normalization, which is a surprisingly effective regularizer to the point where I rarely see dropo | What should I do when my neural network doesn't generalize well?
A list of commonly used regularization techniques which I've seen in the literature are:
Using batch normalization, which is a surprisingly effective regularizer to the point where I rarely see dropout used anymore, because it is simply not necessary.
A ... | What should I do when my neural network doesn't generalize well?
A list of commonly used regularization techniques which I've seen in the literature are:
Using batch normalization, which is a surprisingly effective regularizer to the point where I rarely see dropo |
3,681 | What should I do when my neural network doesn't generalize well? | I feel like Djib2011, give great points about automated methods, but they don't really tackle the underlying issue of how do we know if the method employed to reduce overfitting did its job. So as an important footnote to DeltaIV answer, I wanted to include this based on recent research in the last 2 years. Overfitti... | What should I do when my neural network doesn't generalize well? | I feel like Djib2011, give great points about automated methods, but they don't really tackle the underlying issue of how do we know if the method employed to reduce overfitting did its job. So as an | What should I do when my neural network doesn't generalize well?
I feel like Djib2011, give great points about automated methods, but they don't really tackle the underlying issue of how do we know if the method employed to reduce overfitting did its job. So as an important footnote to DeltaIV answer, I wanted to incl... | What should I do when my neural network doesn't generalize well?
I feel like Djib2011, give great points about automated methods, but they don't really tackle the underlying issue of how do we know if the method employed to reduce overfitting did its job. So as an |
3,682 | What should I do when my neural network doesn't generalize well? | Reduce the number of parameters in the model.
The existing answers focus on different regularization strategies that can improve fit, given a model architecture that remains fixed (same configuration, number of layers, number of neurons in each layer).
However, the simplest and easiest step to reducing overfitting in a... | What should I do when my neural network doesn't generalize well? | Reduce the number of parameters in the model.
The existing answers focus on different regularization strategies that can improve fit, given a model architecture that remains fixed (same configuration, | What should I do when my neural network doesn't generalize well?
Reduce the number of parameters in the model.
The existing answers focus on different regularization strategies that can improve fit, given a model architecture that remains fixed (same configuration, number of layers, number of neurons in each layer).
Ho... | What should I do when my neural network doesn't generalize well?
Reduce the number of parameters in the model.
The existing answers focus on different regularization strategies that can improve fit, given a model architecture that remains fixed (same configuration, |
3,683 | What does having "constant variance" in a linear regression model mean? | It means that when you plot the individual error against the predicted value, the variance of the error predicted value should be constant. See the red arrows in the picture below, the length of the red lines (a proxy of its variance) are the same. | What does having "constant variance" in a linear regression model mean? | It means that when you plot the individual error against the predicted value, the variance of the error predicted value should be constant. See the red arrows in the picture below, the length of the r | What does having "constant variance" in a linear regression model mean?
It means that when you plot the individual error against the predicted value, the variance of the error predicted value should be constant. See the red arrows in the picture below, the length of the red lines (a proxy of its variance) are the same. | What does having "constant variance" in a linear regression model mean?
It means that when you plot the individual error against the predicted value, the variance of the error predicted value should be constant. See the red arrows in the picture below, the length of the r |
3,684 | What does having "constant variance" in a linear regression model mean? | This is a place where I've found looking at some formulas helps, even for people with some math anxiety (I'm not suggesting that you do, necessarily). The simple linear regression model is this:
$$
Y=\beta_0+\beta_1X+\varepsilon \\
\text{where } \varepsilon\sim\mathcal N(0, \sigma^2_\varepsilon)
$$
What's important t... | What does having "constant variance" in a linear regression model mean? | This is a place where I've found looking at some formulas helps, even for people with some math anxiety (I'm not suggesting that you do, necessarily). The simple linear regression model is this:
$$
Y | What does having "constant variance" in a linear regression model mean?
This is a place where I've found looking at some formulas helps, even for people with some math anxiety (I'm not suggesting that you do, necessarily). The simple linear regression model is this:
$$
Y=\beta_0+\beta_1X+\varepsilon \\
\text{where } ... | What does having "constant variance" in a linear regression model mean?
This is a place where I've found looking at some formulas helps, even for people with some math anxiety (I'm not suggesting that you do, necessarily). The simple linear regression model is this:
$$
Y |
3,685 | Does it ever make sense to treat categorical data as continuous? | I will assume that a "categorical" variable actually stands for an ordinal variable; otherwise it doesn't make much sense to treat it as a continuous one, unless it's a binary variable (coded 0/1) as pointed by @Rob. Then, I would say that the problem is not that much the way we treat the variable, although many models... | Does it ever make sense to treat categorical data as continuous? | I will assume that a "categorical" variable actually stands for an ordinal variable; otherwise it doesn't make much sense to treat it as a continuous one, unless it's a binary variable (coded 0/1) as | Does it ever make sense to treat categorical data as continuous?
I will assume that a "categorical" variable actually stands for an ordinal variable; otherwise it doesn't make much sense to treat it as a continuous one, unless it's a binary variable (coded 0/1) as pointed by @Rob. Then, I would say that the problem is ... | Does it ever make sense to treat categorical data as continuous?
I will assume that a "categorical" variable actually stands for an ordinal variable; otherwise it doesn't make much sense to treat it as a continuous one, unless it's a binary variable (coded 0/1) as |
3,686 | Does it ever make sense to treat categorical data as continuous? | If there are only two categories, then transforming them to (0,1) makes sense. In fact, this is commonly done where the resulting dummy variable is used in regression models.
If there are more than two categories, then I think it only makes sense if the data are ordinal, and then only in very specific circumstances. Fo... | Does it ever make sense to treat categorical data as continuous? | If there are only two categories, then transforming them to (0,1) makes sense. In fact, this is commonly done where the resulting dummy variable is used in regression models.
If there are more than tw | Does it ever make sense to treat categorical data as continuous?
If there are only two categories, then transforming them to (0,1) makes sense. In fact, this is commonly done where the resulting dummy variable is used in regression models.
If there are more than two categories, then I think it only makes sense if the d... | Does it ever make sense to treat categorical data as continuous?
If there are only two categories, then transforming them to (0,1) makes sense. In fact, this is commonly done where the resulting dummy variable is used in regression models.
If there are more than tw |
3,687 | Does it ever make sense to treat categorical data as continuous? | It is common practice to treat ordered categorical variables with many categories as continuous. Examples of this:
Number of items correct on a 100 item test
A summated psychological scale (e.g., that is the mean of 10 items each on a five point scale)
And by "treating as continuous" I mean including the variable in ... | Does it ever make sense to treat categorical data as continuous? | It is common practice to treat ordered categorical variables with many categories as continuous. Examples of this:
Number of items correct on a 100 item test
A summated psychological scale (e.g., tha | Does it ever make sense to treat categorical data as continuous?
It is common practice to treat ordered categorical variables with many categories as continuous. Examples of this:
Number of items correct on a 100 item test
A summated psychological scale (e.g., that is the mean of 10 items each on a five point scale)
... | Does it ever make sense to treat categorical data as continuous?
It is common practice to treat ordered categorical variables with many categories as continuous. Examples of this:
Number of items correct on a 100 item test
A summated psychological scale (e.g., tha |
3,688 | Does it ever make sense to treat categorical data as continuous? | A very simple example often overlooked that should lie within the experience of many readers concerns the marks or grades given to academic work. Often marks for individual assignments are in essence judgement-based ordinal measurements, even when as a matter of convention they are given as (say) percent marks or marks... | Does it ever make sense to treat categorical data as continuous? | A very simple example often overlooked that should lie within the experience of many readers concerns the marks or grades given to academic work. Often marks for individual assignments are in essence | Does it ever make sense to treat categorical data as continuous?
A very simple example often overlooked that should lie within the experience of many readers concerns the marks or grades given to academic work. Often marks for individual assignments are in essence judgement-based ordinal measurements, even when as a ma... | Does it ever make sense to treat categorical data as continuous?
A very simple example often overlooked that should lie within the experience of many readers concerns the marks or grades given to academic work. Often marks for individual assignments are in essence |
3,689 | Does it ever make sense to treat categorical data as continuous? | In an analysis of ranking by frequency, as with a Pareto chart and associated values (eg how many categories make up the top 80% of product faults) | Does it ever make sense to treat categorical data as continuous? | In an analysis of ranking by frequency, as with a Pareto chart and associated values (eg how many categories make up the top 80% of product faults) | Does it ever make sense to treat categorical data as continuous?
In an analysis of ranking by frequency, as with a Pareto chart and associated values (eg how many categories make up the top 80% of product faults) | Does it ever make sense to treat categorical data as continuous?
In an analysis of ranking by frequency, as with a Pareto chart and associated values (eg how many categories make up the top 80% of product faults) |
3,690 | Does it ever make sense to treat categorical data as continuous? | I'm going to make the argument that treating a truly categorical, non-ordinal variable as continuous can sometimes make sense.
If you are building decision trees based on large datasets, it may be costly in terms of processing power and memory to convert categorical variables into dummy variables. Furthermore, some mo... | Does it ever make sense to treat categorical data as continuous? | I'm going to make the argument that treating a truly categorical, non-ordinal variable as continuous can sometimes make sense.
If you are building decision trees based on large datasets, it may be cos | Does it ever make sense to treat categorical data as continuous?
I'm going to make the argument that treating a truly categorical, non-ordinal variable as continuous can sometimes make sense.
If you are building decision trees based on large datasets, it may be costly in terms of processing power and memory to convert ... | Does it ever make sense to treat categorical data as continuous?
I'm going to make the argument that treating a truly categorical, non-ordinal variable as continuous can sometimes make sense.
If you are building decision trees based on large datasets, it may be cos |
3,691 | Does it ever make sense to treat categorical data as continuous? | A very nice summary of this topic can be found here.
"When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under sub-optimal conditions."
Mijke Rhemtulla, Patricia Γ. Brosseau-Liard, and Victoria Savalei
They investigate about 60 pages' worth ... | Does it ever make sense to treat categorical data as continuous? | A very nice summary of this topic can be found here.
"When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under sub-optima | Does it ever make sense to treat categorical data as continuous?
A very nice summary of this topic can be found here.
"When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under sub-optimal conditions."
Mijke Rhemtulla, Patricia Γ. Brosseau-Li... | Does it ever make sense to treat categorical data as continuous?
A very nice summary of this topic can be found here.
"When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under sub-optima |
3,692 | Does it ever make sense to treat categorical data as continuous? | There is another case when it makes sense: when the data is sampled from continuous data (for example through an analogue-to-digital converter). For older instruments the ADCs would often be 10-bit, giving what is nominally 1024-category ordinal data, but can for most purposes be treated as real (though there will be s... | Does it ever make sense to treat categorical data as continuous? | There is another case when it makes sense: when the data is sampled from continuous data (for example through an analogue-to-digital converter). For older instruments the ADCs would often be 10-bit, g | Does it ever make sense to treat categorical data as continuous?
There is another case when it makes sense: when the data is sampled from continuous data (for example through an analogue-to-digital converter). For older instruments the ADCs would often be 10-bit, giving what is nominally 1024-category ordinal data, but... | Does it ever make sense to treat categorical data as continuous?
There is another case when it makes sense: when the data is sampled from continuous data (for example through an analogue-to-digital converter). For older instruments the ADCs would often be 10-bit, g |
3,693 | Training a decision tree against unbalanced data | This is an interesting and very frequent problem in classification - not just in decision trees but in virtually all classification algorithms.
As you found empirically, a training set consisting of different numbers of representatives from either class may result in a classifier that is biased towards the majority cla... | Training a decision tree against unbalanced data | This is an interesting and very frequent problem in classification - not just in decision trees but in virtually all classification algorithms.
As you found empirically, a training set consisting of d | Training a decision tree against unbalanced data
This is an interesting and very frequent problem in classification - not just in decision trees but in virtually all classification algorithms.
As you found empirically, a training set consisting of different numbers of representatives from either class may result in a c... | Training a decision tree against unbalanced data
This is an interesting and very frequent problem in classification - not just in decision trees but in virtually all classification algorithms.
As you found empirically, a training set consisting of d |
3,694 | Training a decision tree against unbalanced data | The following four ideas may help you tackle this problem.
Select an appropriate performance measure and then fine tune the hyperparameters of your model --e.g. regularization-- to attain satisfactory results on the Cross-Validation dataset and once satisfied, test your model on the testing dataset. For these purpose... | Training a decision tree against unbalanced data | The following four ideas may help you tackle this problem.
Select an appropriate performance measure and then fine tune the hyperparameters of your model --e.g. regularization-- to attain satisfactor | Training a decision tree against unbalanced data
The following four ideas may help you tackle this problem.
Select an appropriate performance measure and then fine tune the hyperparameters of your model --e.g. regularization-- to attain satisfactory results on the Cross-Validation dataset and once satisfied, test your... | Training a decision tree against unbalanced data
The following four ideas may help you tackle this problem.
Select an appropriate performance measure and then fine tune the hyperparameters of your model --e.g. regularization-- to attain satisfactor |
3,695 | Training a decision tree against unbalanced data | Adding to @Kay 's answer 1st solution strategy :
Synthetic Minority Oversampling (SMOTE) usually does better than under or over sampling from my experience as I think it kind of creates a compromise between both. It creates synthetic samples of the minority class using the data points plotted on the multivariate predi... | Training a decision tree against unbalanced data | Adding to @Kay 's answer 1st solution strategy :
Synthetic Minority Oversampling (SMOTE) usually does better than under or over sampling from my experience as I think it kind of creates a compromise | Training a decision tree against unbalanced data
Adding to @Kay 's answer 1st solution strategy :
Synthetic Minority Oversampling (SMOTE) usually does better than under or over sampling from my experience as I think it kind of creates a compromise between both. It creates synthetic samples of the minority class using ... | Training a decision tree against unbalanced data
Adding to @Kay 's answer 1st solution strategy :
Synthetic Minority Oversampling (SMOTE) usually does better than under or over sampling from my experience as I think it kind of creates a compromise |
3,696 | Training a decision tree against unbalanced data | I gave an answer in recent topic:
What we do is pick a sample with different proportions. In aforementioned example, that would be 1000 cases of "YES" and, for instance, 9000 of "NO" cases. This approach gives more stable models. However, it has to be tested on a real sample (that with 1,000,000 rows).
Not only does ... | Training a decision tree against unbalanced data | I gave an answer in recent topic:
What we do is pick a sample with different proportions. In aforementioned example, that would be 1000 cases of "YES" and, for instance, 9000 of "NO" cases. This appr | Training a decision tree against unbalanced data
I gave an answer in recent topic:
What we do is pick a sample with different proportions. In aforementioned example, that would be 1000 cases of "YES" and, for instance, 9000 of "NO" cases. This approach gives more stable models. However, it has to be tested on a real s... | Training a decision tree against unbalanced data
I gave an answer in recent topic:
What we do is pick a sample with different proportions. In aforementioned example, that would be 1000 cases of "YES" and, for instance, 9000 of "NO" cases. This appr |
3,697 | Training a decision tree against unbalanced data | My follow up with the the 3 approaches @Kay mentioned above is that to deal with unbalanced data, no matter you use undersampling/oversampling or weighted cost function, it is shifting your fit in the original feature space v.s. original data. So "undersampling/oversampling" and "weighted cost" are essentially the same... | Training a decision tree against unbalanced data | My follow up with the the 3 approaches @Kay mentioned above is that to deal with unbalanced data, no matter you use undersampling/oversampling or weighted cost function, it is shifting your fit in the | Training a decision tree against unbalanced data
My follow up with the the 3 approaches @Kay mentioned above is that to deal with unbalanced data, no matter you use undersampling/oversampling or weighted cost function, it is shifting your fit in the original feature space v.s. original data. So "undersampling/oversampl... | Training a decision tree against unbalanced data
My follow up with the the 3 approaches @Kay mentioned above is that to deal with unbalanced data, no matter you use undersampling/oversampling or weighted cost function, it is shifting your fit in the |
3,698 | What is the variance of the weighted mixture of two gaussians? | The variance is the second moment minus the square of the first moment, so it suffices to compute moments of mixtures.
In general, given distributions with PDFs $f_i$ and constant (non-random) weights $p_i$, the PDF of the mixture is
$$f(x) = \sum_i{p_i f_i(x)},$$
from which it follows immediately for any moment $k$ th... | What is the variance of the weighted mixture of two gaussians? | The variance is the second moment minus the square of the first moment, so it suffices to compute moments of mixtures.
In general, given distributions with PDFs $f_i$ and constant (non-random) weights | What is the variance of the weighted mixture of two gaussians?
The variance is the second moment minus the square of the first moment, so it suffices to compute moments of mixtures.
In general, given distributions with PDFs $f_i$ and constant (non-random) weights $p_i$, the PDF of the mixture is
$$f(x) = \sum_i{p_i f_i... | What is the variance of the weighted mixture of two gaussians?
The variance is the second moment minus the square of the first moment, so it suffices to compute moments of mixtures.
In general, given distributions with PDFs $f_i$ and constant (non-random) weights |
3,699 | What is the variance of the weighted mixture of two gaussians? | The solution of whuber is perfect but it seems that something lacks to join this result with the LTV (law of total variance). The previous result
$$\sigma^2=p_A \sigma_A^2+p_B \sigma_B^2+p_A \mu_A^2+p_B \mu_B^2β\mu^2$$
can be rewritten taking into account that $2p_A\mu_A\mu +2p_B\mu_B\mu=2\mu(p_A\mu_A+p_B\mu_B)=2\mu^2$... | What is the variance of the weighted mixture of two gaussians? | The solution of whuber is perfect but it seems that something lacks to join this result with the LTV (law of total variance). The previous result
$$\sigma^2=p_A \sigma_A^2+p_B \sigma_B^2+p_A \mu_A^2+p | What is the variance of the weighted mixture of two gaussians?
The solution of whuber is perfect but it seems that something lacks to join this result with the LTV (law of total variance). The previous result
$$\sigma^2=p_A \sigma_A^2+p_B \sigma_B^2+p_A \mu_A^2+p_B \mu_B^2β\mu^2$$
can be rewritten taking into account t... | What is the variance of the weighted mixture of two gaussians?
The solution of whuber is perfect but it seems that something lacks to join this result with the LTV (law of total variance). The previous result
$$\sigma^2=p_A \sigma_A^2+p_B \sigma_B^2+p_A \mu_A^2+p |
3,700 | What is the variance of the weighted mixture of two gaussians? | The solution of whuber is perfect. I just want to add that the term in the square brackets has another nice and simple expression, so
$$\sigma^2=p_A\sigma_A^2+p_B\sigma_B^2+p_Ap_B(\mu_A-\mu_B)^2.$$ | What is the variance of the weighted mixture of two gaussians? | The solution of whuber is perfect. I just want to add that the term in the square brackets has another nice and simple expression, so
$$\sigma^2=p_A\sigma_A^2+p_B\sigma_B^2+p_Ap_B(\mu_A-\mu_B)^2.$$ | What is the variance of the weighted mixture of two gaussians?
The solution of whuber is perfect. I just want to add that the term in the square brackets has another nice and simple expression, so
$$\sigma^2=p_A\sigma_A^2+p_B\sigma_B^2+p_Ap_B(\mu_A-\mu_B)^2.$$ | What is the variance of the weighted mixture of two gaussians?
The solution of whuber is perfect. I just want to add that the term in the square brackets has another nice and simple expression, so
$$\sigma^2=p_A\sigma_A^2+p_B\sigma_B^2+p_Ap_B(\mu_A-\mu_B)^2.$$ |
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