idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
|---|---|---|---|---|---|---|
35,801 | p-value as a distance? | I believe the answer is yes.
One could think of the "similarity" between two variables to be measured by (say) correlation. And for the p-value to be the significance of the correlation being different than 0. In such a case, a small p-value (nearing zero) is one that reflects a large distance ("difference") between ... | p-value as a distance? | I believe the answer is yes.
One could think of the "similarity" between two variables to be measured by (say) correlation. And for the p-value to be the significance of the correlation being differe | p-value as a distance?
I believe the answer is yes.
One could think of the "similarity" between two variables to be measured by (say) correlation. And for the p-value to be the significance of the correlation being different than 0. In such a case, a small p-value (nearing zero) is one that reflects a large distance ... | p-value as a distance?
I believe the answer is yes.
One could think of the "similarity" between two variables to be measured by (say) correlation. And for the p-value to be the significance of the correlation being differe |
35,802 | p-value as a distance? | I am not sure what you mean by "p-values between multiple pair-wise tests ". The p-value is a measure of how likely / unlikely for a particular test it would be to see a value as extreme or more extreme than what was actually observed if the null hypothesis is true. When doing pairwise testing there is no particular ... | p-value as a distance? | I am not sure what you mean by "p-values between multiple pair-wise tests ". The p-value is a measure of how likely / unlikely for a particular test it would be to see a value as extreme or more extr | p-value as a distance?
I am not sure what you mean by "p-values between multiple pair-wise tests ". The p-value is a measure of how likely / unlikely for a particular test it would be to see a value as extreme or more extreme than what was actually observed if the null hypothesis is true. When doing pairwise testing ... | p-value as a distance?
I am not sure what you mean by "p-values between multiple pair-wise tests ". The p-value is a measure of how likely / unlikely for a particular test it would be to see a value as extreme or more extr |
35,803 | Estimating ability using IRT when the model parameters are known | I can't find a way to do this in the ltm package, though it's relatively straightforward if you are willing to use the mirt package.
First, write out some arbitrary matrix or data frame consisting of possible but random response patterns. You can include the actual response patterns you are interested in as well for l... | Estimating ability using IRT when the model parameters are known | I can't find a way to do this in the ltm package, though it's relatively straightforward if you are willing to use the mirt package.
First, write out some arbitrary matrix or data frame consisting of | Estimating ability using IRT when the model parameters are known
I can't find a way to do this in the ltm package, though it's relatively straightforward if you are willing to use the mirt package.
First, write out some arbitrary matrix or data frame consisting of possible but random response patterns. You can include... | Estimating ability using IRT when the model parameters are known
I can't find a way to do this in the ltm package, though it's relatively straightforward if you are willing to use the mirt package.
First, write out some arbitrary matrix or data frame consisting of |
35,804 | Estimating ability using IRT when the model parameters are known | Try thetaEst from catR.
From the manual: This command returns the ability estimate for a given response pattern and a given matrix of item parameters. | Estimating ability using IRT when the model parameters are known | Try thetaEst from catR.
From the manual: This command returns the ability estimate for a given response pattern and a given matrix of item parameters. | Estimating ability using IRT when the model parameters are known
Try thetaEst from catR.
From the manual: This command returns the ability estimate for a given response pattern and a given matrix of item parameters. | Estimating ability using IRT when the model parameters are known
Try thetaEst from catR.
From the manual: This command returns the ability estimate for a given response pattern and a given matrix of item parameters. |
35,805 | How to draw mean, median and mode lines in R that end at density? | The density is represented as a polyline, which is a pair of parallel arrays, one for $x$, one for $y$, forming vertices along the graph of the density (with equal spacings in the $x$ direction). As such it is a discrete approximation to the idealized continuous density and we can use discrete versions of the relevant ... | How to draw mean, median and mode lines in R that end at density? | The density is represented as a polyline, which is a pair of parallel arrays, one for $x$, one for $y$, forming vertices along the graph of the density (with equal spacings in the $x$ direction). As s | How to draw mean, median and mode lines in R that end at density?
The density is represented as a polyline, which is a pair of parallel arrays, one for $x$, one for $y$, forming vertices along the graph of the density (with equal spacings in the $x$ direction). As such it is a discrete approximation to the idealized co... | How to draw mean, median and mode lines in R that end at density?
The density is represented as a polyline, which is a pair of parallel arrays, one for $x$, one for $y$, forming vertices along the graph of the density (with equal spacings in the $x$ direction). As s |
35,806 | Using ARMA when data is missing | There is no need to do anything. An ARMA model can easily be estimated with missing values within the time series. You need to use the state space representation of an ARMA model to compute the likelihood. If you use R, this is already handled automatically via the arima() function. | Using ARMA when data is missing | There is no need to do anything. An ARMA model can easily be estimated with missing values within the time series. You need to use the state space representation of an ARMA model to compute the likeli | Using ARMA when data is missing
There is no need to do anything. An ARMA model can easily be estimated with missing values within the time series. You need to use the state space representation of an ARMA model to compute the likelihood. If you use R, this is already handled automatically via the arima() function. | Using ARMA when data is missing
There is no need to do anything. An ARMA model can easily be estimated with missing values within the time series. You need to use the state space representation of an ARMA model to compute the likeli |
35,807 | How to interpret the output for calculating concordance index (c-index)? | The index of concordance is a "global" index for validating the predictive ability of a survival model. It is the fraction of pairs in your data, where the observation with the higher survival time has the higher probability of survival predicted by your model. As far as I remember it it equivalent to a rank correlatio... | How to interpret the output for calculating concordance index (c-index)? | The index of concordance is a "global" index for validating the predictive ability of a survival model. It is the fraction of pairs in your data, where the observation with the higher survival time ha | How to interpret the output for calculating concordance index (c-index)?
The index of concordance is a "global" index for validating the predictive ability of a survival model. It is the fraction of pairs in your data, where the observation with the higher survival time has the higher probability of survival predicted ... | How to interpret the output for calculating concordance index (c-index)?
The index of concordance is a "global" index for validating the predictive ability of a survival model. It is the fraction of pairs in your data, where the observation with the higher survival time ha |
35,808 | How to interpret the output for calculating concordance index (c-index)? | High risk by your definition means likely to have short survival times. | How to interpret the output for calculating concordance index (c-index)? | High risk by your definition means likely to have short survival times. | How to interpret the output for calculating concordance index (c-index)?
High risk by your definition means likely to have short survival times. | How to interpret the output for calculating concordance index (c-index)?
High risk by your definition means likely to have short survival times. |
35,809 | Flexible version of logistic regression | This problem surfaces in virtually all classification approaches, whether logistic regression, support vector classification, or Naive Bayes classification. There are two intertwined issues:
A model trained on an imbalanced dataset may overfit in the sense of acquiring a bias in favour of the majority class.
When eval... | Flexible version of logistic regression | This problem surfaces in virtually all classification approaches, whether logistic regression, support vector classification, or Naive Bayes classification. There are two intertwined issues:
A model | Flexible version of logistic regression
This problem surfaces in virtually all classification approaches, whether logistic regression, support vector classification, or Naive Bayes classification. There are two intertwined issues:
A model trained on an imbalanced dataset may overfit in the sense of acquiring a bias in... | Flexible version of logistic regression
This problem surfaces in virtually all classification approaches, whether logistic regression, support vector classification, or Naive Bayes classification. There are two intertwined issues:
A model |
35,810 | Flexible version of logistic regression | That it doesn't work does not come from the unbalanced size of the groups, but from the smallness of one of the groups. Downsampling the larger group is ok but does not help with overfitting. (BTW, there is an easy and elegant way to correct the predictions from the downsampled model, by adding ±log(r) to the linear te... | Flexible version of logistic regression | That it doesn't work does not come from the unbalanced size of the groups, but from the smallness of one of the groups. Downsampling the larger group is ok but does not help with overfitting. (BTW, th | Flexible version of logistic regression
That it doesn't work does not come from the unbalanced size of the groups, but from the smallness of one of the groups. Downsampling the larger group is ok but does not help with overfitting. (BTW, there is an easy and elegant way to correct the predictions from the downsampled m... | Flexible version of logistic regression
That it doesn't work does not come from the unbalanced size of the groups, but from the smallness of one of the groups. Downsampling the larger group is ok but does not help with overfitting. (BTW, th |
35,811 | Flexible version of logistic regression | Do you mean the distribution of response, i.e. you have 70 cases of "YES" and 10000 of "NO"?
If so, that is a common problem in data mining applications. Imagine a database with 1,000,000 instances, where only about 1,000 cases are "YES". Response rate of 1% and even less is a common thing in a business predictive mode... | Flexible version of logistic regression | Do you mean the distribution of response, i.e. you have 70 cases of "YES" and 10000 of "NO"?
If so, that is a common problem in data mining applications. Imagine a database with 1,000,000 instances, w | Flexible version of logistic regression
Do you mean the distribution of response, i.e. you have 70 cases of "YES" and 10000 of "NO"?
If so, that is a common problem in data mining applications. Imagine a database with 1,000,000 instances, where only about 1,000 cases are "YES". Response rate of 1% and even less is a co... | Flexible version of logistic regression
Do you mean the distribution of response, i.e. you have 70 cases of "YES" and 10000 of "NO"?
If so, that is a common problem in data mining applications. Imagine a database with 1,000,000 instances, w |
35,812 | Flexible version of logistic regression | If you want a classification technique that is insensitive to the relative proportion of examples from different classes, Support Vector Machines have that property as do decision trees. | Flexible version of logistic regression | If you want a classification technique that is insensitive to the relative proportion of examples from different classes, Support Vector Machines have that property as do decision trees. | Flexible version of logistic regression
If you want a classification technique that is insensitive to the relative proportion of examples from different classes, Support Vector Machines have that property as do decision trees. | Flexible version of logistic regression
If you want a classification technique that is insensitive to the relative proportion of examples from different classes, Support Vector Machines have that property as do decision trees. |
35,813 | How does glm.nb work? | Thanks for clarifying. So, it appears you want to have the inner workings of GLM estimation explained. I can give a sketch, but I doubt it will help you much. It's probably better to read a book on GLM, e.g McCullagh and Nelder's book.
Anyway:
Question 1
The standard error for the $β_j$ in a GLM that uses Fischer scori... | How does glm.nb work? | Thanks for clarifying. So, it appears you want to have the inner workings of GLM estimation explained. I can give a sketch, but I doubt it will help you much. It's probably better to read a book on GL | How does glm.nb work?
Thanks for clarifying. So, it appears you want to have the inner workings of GLM estimation explained. I can give a sketch, but I doubt it will help you much. It's probably better to read a book on GLM, e.g McCullagh and Nelder's book.
Anyway:
Question 1
The standard error for the $β_j$ in a GLM t... | How does glm.nb work?
Thanks for clarifying. So, it appears you want to have the inner workings of GLM estimation explained. I can give a sketch, but I doubt it will help you much. It's probably better to read a book on GL |
35,814 | Why is my replication of Silver & Dunlap 1987 not working out? | To me, the r bias entry for rho of 0.5 in the Silver & Dunlap table looks the most suspiciously different to me. However, that said, it does match your estimated value quite closely.
Unfortunately, I don't have access to the Silver & Dunlap paper at the moment, but a Google search did turn up a recent paper that perfor... | Why is my replication of Silver & Dunlap 1987 not working out? | To me, the r bias entry for rho of 0.5 in the Silver & Dunlap table looks the most suspiciously different to me. However, that said, it does match your estimated value quite closely.
Unfortunately, I | Why is my replication of Silver & Dunlap 1987 not working out?
To me, the r bias entry for rho of 0.5 in the Silver & Dunlap table looks the most suspiciously different to me. However, that said, it does match your estimated value quite closely.
Unfortunately, I don't have access to the Silver & Dunlap paper at the mom... | Why is my replication of Silver & Dunlap 1987 not working out?
To me, the r bias entry for rho of 0.5 in the Silver & Dunlap table looks the most suspiciously different to me. However, that said, it does match your estimated value quite closely.
Unfortunately, I |
35,815 | Can simple vector distance work as a SVM kernel? | No, this kernel doesn't give a positive (semi-) definite Gram matrix, so it is not a valid kernel (the first randomly generated Gram matrix $\matrix{K}$ and vector $\vec{v}$ I tried gave $\vec{v}'\matrix{K}\vec{v} < 0$ so $\matrix{K}$ isn't positive semi-definite. If you infer from that that I am an engineer - you are... | Can simple vector distance work as a SVM kernel? | No, this kernel doesn't give a positive (semi-) definite Gram matrix, so it is not a valid kernel (the first randomly generated Gram matrix $\matrix{K}$ and vector $\vec{v}$ I tried gave $\vec{v}'\mat | Can simple vector distance work as a SVM kernel?
No, this kernel doesn't give a positive (semi-) definite Gram matrix, so it is not a valid kernel (the first randomly generated Gram matrix $\matrix{K}$ and vector $\vec{v}$ I tried gave $\vec{v}'\matrix{K}\vec{v} < 0$ so $\matrix{K}$ isn't positive semi-definite. If yo... | Can simple vector distance work as a SVM kernel?
No, this kernel doesn't give a positive (semi-) definite Gram matrix, so it is not a valid kernel (the first randomly generated Gram matrix $\matrix{K}$ and vector $\vec{v}$ I tried gave $\vec{v}'\mat |
35,816 | Are these populations non-random and different? | For question 2, I would start by looking at the distributions of the percentages of each group that have a given trait. e.g.:
A <- c(126,86,63,54,47,40,32,32,29,29,27,26,20,18,14)
B <- c(357,196,185,137,95,74,45,69,64,49,54,80,62,41,56)
C <- c(348,139,162,126,82,69,35,63,40,42,40,55,44,29,35)
N <- c(382,207,193,143,10... | Are these populations non-random and different? | For question 2, I would start by looking at the distributions of the percentages of each group that have a given trait. e.g.:
A <- c(126,86,63,54,47,40,32,32,29,29,27,26,20,18,14)
B <- c(357,196,185, | Are these populations non-random and different?
For question 2, I would start by looking at the distributions of the percentages of each group that have a given trait. e.g.:
A <- c(126,86,63,54,47,40,32,32,29,29,27,26,20,18,14)
B <- c(357,196,185,137,95,74,45,69,64,49,54,80,62,41,56)
C <- c(348,139,162,126,82,69,35,63... | Are these populations non-random and different?
For question 2, I would start by looking at the distributions of the percentages of each group that have a given trait. e.g.:
A <- c(126,86,63,54,47,40,32,32,29,29,27,26,20,18,14)
B <- c(357,196,185, |
35,817 | Are these populations non-random and different? | i'm not sure if i understand the problem correctly - so correct me if i'm wrong but here's my thoughts:
So, is spottiness non-random for members in a group? And does spottiness vary significantly between the groups?
I'm not sure if the first question is answerable with the data presented. If the data was available in... | Are these populations non-random and different? | i'm not sure if i understand the problem correctly - so correct me if i'm wrong but here's my thoughts:
So, is spottiness non-random for members in a group? And does spottiness vary significantly bet | Are these populations non-random and different?
i'm not sure if i understand the problem correctly - so correct me if i'm wrong but here's my thoughts:
So, is spottiness non-random for members in a group? And does spottiness vary significantly between the groups?
I'm not sure if the first question is answerable with ... | Are these populations non-random and different?
i'm not sure if i understand the problem correctly - so correct me if i'm wrong but here's my thoughts:
So, is spottiness non-random for members in a group? And does spottiness vary significantly bet |
35,818 | Are these populations non-random and different? | I'm not sure I fully understand the situation (your data or your question). @Zach has some good ideas, so I thought I'd follow his lead and throw out some information and we'll see if something helps.
1) To determine if data are random, the runs test can be used. A run is a series of data points that are similar in s... | Are these populations non-random and different? | I'm not sure I fully understand the situation (your data or your question). @Zach has some good ideas, so I thought I'd follow his lead and throw out some information and we'll see if something helps | Are these populations non-random and different?
I'm not sure I fully understand the situation (your data or your question). @Zach has some good ideas, so I thought I'd follow his lead and throw out some information and we'll see if something helps.
1) To determine if data are random, the runs test can be used. A run ... | Are these populations non-random and different?
I'm not sure I fully understand the situation (your data or your question). @Zach has some good ideas, so I thought I'd follow his lead and throw out some information and we'll see if something helps |
35,819 | Textbooks on the numerical solution of stochastic differential equations | In addition to the Kloeden and Platen books already mentioned, the book Simulation and Inference for Stochastic Differential Equations by Stefano Iacus is good. He is also the author of the sde package for R. | Textbooks on the numerical solution of stochastic differential equations | In addition to the Kloeden and Platen books already mentioned, the book Simulation and Inference for Stochastic Differential Equations by Stefano Iacus is good. He is also the author of the sde packag | Textbooks on the numerical solution of stochastic differential equations
In addition to the Kloeden and Platen books already mentioned, the book Simulation and Inference for Stochastic Differential Equations by Stefano Iacus is good. He is also the author of the sde package for R. | Textbooks on the numerical solution of stochastic differential equations
In addition to the Kloeden and Platen books already mentioned, the book Simulation and Inference for Stochastic Differential Equations by Stefano Iacus is good. He is also the author of the sde packag |
35,820 | Textbooks on the numerical solution of stochastic differential equations | These two books may be a good starting point
Numerical Solution of Stochastic Differential Equations (Stochastic Modelling and Applied Probability, 23) by Peter E. Kloeden and Eckhard Platen.
Numerical Solution of SDE Through Computer Experiments (Universitext) by Peter Eris Kloeden, Eckhard Platen and Henri Schur... | Textbooks on the numerical solution of stochastic differential equations | These two books may be a good starting point
Numerical Solution of Stochastic Differential Equations (Stochastic Modelling and Applied Probability, 23) by Peter E. Kloeden and Eckhard Platen.
Numeri | Textbooks on the numerical solution of stochastic differential equations
These two books may be a good starting point
Numerical Solution of Stochastic Differential Equations (Stochastic Modelling and Applied Probability, 23) by Peter E. Kloeden and Eckhard Platen.
Numerical Solution of SDE Through Computer Experiment... | Textbooks on the numerical solution of stochastic differential equations
These two books may be a good starting point
Numerical Solution of Stochastic Differential Equations (Stochastic Modelling and Applied Probability, 23) by Peter E. Kloeden and Eckhard Platen.
Numeri |
35,821 | Testing homoscedasticity with Breusch-Pagan test | The problem isn't heteroskedasticity, that's why it's passing the test. The problem is that your model doesn't work well for (at least some of) your observations.
I've never seen anyone analyze stock prices without looking at their differences. Try a Dickey-Fuller test for a unit root---I bet that you can't reject tha... | Testing homoscedasticity with Breusch-Pagan test | The problem isn't heteroskedasticity, that's why it's passing the test. The problem is that your model doesn't work well for (at least some of) your observations.
I've never seen anyone analyze stock | Testing homoscedasticity with Breusch-Pagan test
The problem isn't heteroskedasticity, that's why it's passing the test. The problem is that your model doesn't work well for (at least some of) your observations.
I've never seen anyone analyze stock prices without looking at their differences. Try a Dickey-Fuller test ... | Testing homoscedasticity with Breusch-Pagan test
The problem isn't heteroskedasticity, that's why it's passing the test. The problem is that your model doesn't work well for (at least some of) your observations.
I've never seen anyone analyze stock |
35,822 | What to do in case of low inter-rater reliability (ICC)? | I'd rather answer on the grounds of the methodology itself, rather than how to "fix" the situation. In another context, I assisted in working on a ratings and classification system, and found that inter-rater agreement was disappointingly low. Two paths were considered
Change how rating agreements were defined and i... | What to do in case of low inter-rater reliability (ICC)? | I'd rather answer on the grounds of the methodology itself, rather than how to "fix" the situation. In another context, I assisted in working on a ratings and classification system, and found that in | What to do in case of low inter-rater reliability (ICC)?
I'd rather answer on the grounds of the methodology itself, rather than how to "fix" the situation. In another context, I assisted in working on a ratings and classification system, and found that inter-rater agreement was disappointingly low. Two paths were co... | What to do in case of low inter-rater reliability (ICC)?
I'd rather answer on the grounds of the methodology itself, rather than how to "fix" the situation. In another context, I assisted in working on a ratings and classification system, and found that in |
35,823 | What to do in case of low inter-rater reliability (ICC)? | Cherry-picking the best ICC value out of 28 possible pairs is definitely NOT a good idea, as that estimate of ICC is certainly optimistic.
Neuendorf's The Content Analysis Handbook has a pretty good discussion of options for dealing with poor reliability in coding. Citation is:
Neuendorf, Kimberly A. The Content An... | What to do in case of low inter-rater reliability (ICC)? | Cherry-picking the best ICC value out of 28 possible pairs is definitely NOT a good idea, as that estimate of ICC is certainly optimistic.
Neuendorf's The Content Analysis Handbook has a pretty good | What to do in case of low inter-rater reliability (ICC)?
Cherry-picking the best ICC value out of 28 possible pairs is definitely NOT a good idea, as that estimate of ICC is certainly optimistic.
Neuendorf's The Content Analysis Handbook has a pretty good discussion of options for dealing with poor reliability in cod... | What to do in case of low inter-rater reliability (ICC)?
Cherry-picking the best ICC value out of 28 possible pairs is definitely NOT a good idea, as that estimate of ICC is certainly optimistic.
Neuendorf's The Content Analysis Handbook has a pretty good |
35,824 | Preferred methods for graphing time-series data to present "averages"? | I suggest adding an example or two of what you are presently doing so we can better see what you are dealing with.
What you are concerned with is an important issue: how do you convey the "overall" pattern in the time series data while also not misleading viewers by showing just average values? One way I have dealt wit... | Preferred methods for graphing time-series data to present "averages"? | I suggest adding an example or two of what you are presently doing so we can better see what you are dealing with.
What you are concerned with is an important issue: how do you convey the "overall" pa | Preferred methods for graphing time-series data to present "averages"?
I suggest adding an example or two of what you are presently doing so we can better see what you are dealing with.
What you are concerned with is an important issue: how do you convey the "overall" pattern in the time series data while also not misl... | Preferred methods for graphing time-series data to present "averages"?
I suggest adding an example or two of what you are presently doing so we can better see what you are dealing with.
What you are concerned with is an important issue: how do you convey the "overall" pa |
35,825 | Preferred methods for graphing time-series data to present "averages"? | Have you considered a scatterplot of the data themselves? That's an approach I really like. It lets the viewer make their own conclusions about the presence and significance of trends, and it doesn't conceal variability or outliers. Alpha-blending the points will help if you have serious overplotting (which it sound... | Preferred methods for graphing time-series data to present "averages"? | Have you considered a scatterplot of the data themselves? That's an approach I really like. It lets the viewer make their own conclusions about the presence and significance of trends, and it doesn' | Preferred methods for graphing time-series data to present "averages"?
Have you considered a scatterplot of the data themselves? That's an approach I really like. It lets the viewer make their own conclusions about the presence and significance of trends, and it doesn't conceal variability or outliers. Alpha-blendin... | Preferred methods for graphing time-series data to present "averages"?
Have you considered a scatterplot of the data themselves? That's an approach I really like. It lets the viewer make their own conclusions about the presence and significance of trends, and it doesn' |
35,826 | Multinomial choice with binary observations | Unless I misunderstood the question, this refers to paired preference (1) or pair comparison data. A well-known example of such a model is the Bradley-Terry model (2), which shares some connections with item scaling in psychometrics (3). There is an R package, BradleyTerry2, described in the JSS (2005) 12(1), Bradley-T... | Multinomial choice with binary observations | Unless I misunderstood the question, this refers to paired preference (1) or pair comparison data. A well-known example of such a model is the Bradley-Terry model (2), which shares some connections wi | Multinomial choice with binary observations
Unless I misunderstood the question, this refers to paired preference (1) or pair comparison data. A well-known example of such a model is the Bradley-Terry model (2), which shares some connections with item scaling in psychometrics (3). There is an R package, BradleyTerry2, ... | Multinomial choice with binary observations
Unless I misunderstood the question, this refers to paired preference (1) or pair comparison data. A well-known example of such a model is the Bradley-Terry model (2), which shares some connections wi |
35,827 | Anscombe transform and normal approximation | Here is a sketch of a proof which combines three ideas: (a) the delta method, (b) variance-stabilization transformations and (c) the closure of the Poisson distribution under independent sums.
First, let's consider a sequence of iid Poisson random variables $X_1, X_2, \ldots$ with mean $\lambda > 0$. Then, the Central ... | Anscombe transform and normal approximation | Here is a sketch of a proof which combines three ideas: (a) the delta method, (b) variance-stabilization transformations and (c) the closure of the Poisson distribution under independent sums.
First, | Anscombe transform and normal approximation
Here is a sketch of a proof which combines three ideas: (a) the delta method, (b) variance-stabilization transformations and (c) the closure of the Poisson distribution under independent sums.
First, let's consider a sequence of iid Poisson random variables $X_1, X_2, \ldots$... | Anscombe transform and normal approximation
Here is a sketch of a proof which combines three ideas: (a) the delta method, (b) variance-stabilization transformations and (c) the closure of the Poisson distribution under independent sums.
First, |
35,828 | Power calculation for likelihood ratio test | You can do this using simulation.
Write a function that does your test and accepts the lambdas and sample size(s) as arguments (you have a good start above).
Now for a given set of lambdas and sample size(s) run the function a bunch of times (the replicate function in R is great for that). Then the power is just the p... | Power calculation for likelihood ratio test | You can do this using simulation.
Write a function that does your test and accepts the lambdas and sample size(s) as arguments (you have a good start above).
Now for a given set of lambdas and sample | Power calculation for likelihood ratio test
You can do this using simulation.
Write a function that does your test and accepts the lambdas and sample size(s) as arguments (you have a good start above).
Now for a given set of lambdas and sample size(s) run the function a bunch of times (the replicate function in R is gr... | Power calculation for likelihood ratio test
You can do this using simulation.
Write a function that does your test and accepts the lambdas and sample size(s) as arguments (you have a good start above).
Now for a given set of lambdas and sample |
35,829 | Symbolic computer algebra for statistics | Support for matrix algebra. The vast majority of practiced statistics is multivariate and involves matrices, and often simplifying matrix forms requires special rules that aren't easily translated from a univariate case, so good matrix support would be really helpful. | Symbolic computer algebra for statistics | Support for matrix algebra. The vast majority of practiced statistics is multivariate and involves matrices, and often simplifying matrix forms requires special rules that aren't easily translated fro | Symbolic computer algebra for statistics
Support for matrix algebra. The vast majority of practiced statistics is multivariate and involves matrices, and often simplifying matrix forms requires special rules that aren't easily translated from a univariate case, so good matrix support would be really helpful. | Symbolic computer algebra for statistics
Support for matrix algebra. The vast majority of practiced statistics is multivariate and involves matrices, and often simplifying matrix forms requires special rules that aren't easily translated fro |
35,830 | Estimating Lambda for Box Cox transformation for ANOVA | It is not appropriate to do ordinary ANOVA after using the same dataset to fit lambda. The analysis should be unified, penalizing for uncertainty in lambda (a parameter to be estimated, and included in the covariance matrix). | Estimating Lambda for Box Cox transformation for ANOVA | It is not appropriate to do ordinary ANOVA after using the same dataset to fit lambda. The analysis should be unified, penalizing for uncertainty in lambda (a parameter to be estimated, and included | Estimating Lambda for Box Cox transformation for ANOVA
It is not appropriate to do ordinary ANOVA after using the same dataset to fit lambda. The analysis should be unified, penalizing for uncertainty in lambda (a parameter to be estimated, and included in the covariance matrix). | Estimating Lambda for Box Cox transformation for ANOVA
It is not appropriate to do ordinary ANOVA after using the same dataset to fit lambda. The analysis should be unified, penalizing for uncertainty in lambda (a parameter to be estimated, and included |
35,831 | Estimating Lambda for Box Cox transformation for ANOVA | The Box-Cox transformation tries to improve the normality of the residuals. Since that is the assumption of ANOVA as well, you should run it on the model that you are actually going to use, i.e. the full model. For example, if you have two well separated groups, the distribution of the response variable will be strongl... | Estimating Lambda for Box Cox transformation for ANOVA | The Box-Cox transformation tries to improve the normality of the residuals. Since that is the assumption of ANOVA as well, you should run it on the model that you are actually going to use, i.e. the f | Estimating Lambda for Box Cox transformation for ANOVA
The Box-Cox transformation tries to improve the normality of the residuals. Since that is the assumption of ANOVA as well, you should run it on the model that you are actually going to use, i.e. the full model. For example, if you have two well separated groups, th... | Estimating Lambda for Box Cox transformation for ANOVA
The Box-Cox transformation tries to improve the normality of the residuals. Since that is the assumption of ANOVA as well, you should run it on the model that you are actually going to use, i.e. the f |
35,832 | Two-stage clustering in R | The closest package that I can think of is birch, but it is not available on CRAN anymore so you have to get the source and install it yourself (R CMD install birch_1.1-3.tar.gz works fine for me, OS X 10.6 with R version 2.13.0 (2011-04-13)). It implements the original algorithm described in
Zhang, T. and Ramakrishn... | Two-stage clustering in R | The closest package that I can think of is birch, but it is not available on CRAN anymore so you have to get the source and install it yourself (R CMD install birch_1.1-3.tar.gz works fine for me, OS | Two-stage clustering in R
The closest package that I can think of is birch, but it is not available on CRAN anymore so you have to get the source and install it yourself (R CMD install birch_1.1-3.tar.gz works fine for me, OS X 10.6 with R version 2.13.0 (2011-04-13)). It implements the original algorithm described in ... | Two-stage clustering in R
The closest package that I can think of is birch, but it is not available on CRAN anymore so you have to get the source and install it yourself (R CMD install birch_1.1-3.tar.gz works fine for me, OS |
35,833 | Two-stage clustering in R | Maybe this also can help: https://cran.r-project.org/web/packages/prcr/
Provides an easy-to-use yet adaptable set of tools to conduct person-center analysis using a two-step clustering procedure. As described in Bergman and El-Khouri (1999) doi:10.1002/(SICI)1521-4036(199910)41:6%3C753::AID-BIMJ753%3E3.0.CO;2-K, hiera... | Two-stage clustering in R | Maybe this also can help: https://cran.r-project.org/web/packages/prcr/
Provides an easy-to-use yet adaptable set of tools to conduct person-center analysis using a two-step clustering procedure. As | Two-stage clustering in R
Maybe this also can help: https://cran.r-project.org/web/packages/prcr/
Provides an easy-to-use yet adaptable set of tools to conduct person-center analysis using a two-step clustering procedure. As described in Bergman and El-Khouri (1999) doi:10.1002/(SICI)1521-4036(199910)41:6%3C753::AID-B... | Two-stage clustering in R
Maybe this also can help: https://cran.r-project.org/web/packages/prcr/
Provides an easy-to-use yet adaptable set of tools to conduct person-center analysis using a two-step clustering procedure. As |
35,834 | Two-stage clustering in R | If you are looking for something akin to a 2-step, have you considered looking into Self Organizing Maps. I think it is based on similar (but not the same) principle as 2-step. | Two-stage clustering in R | If you are looking for something akin to a 2-step, have you considered looking into Self Organizing Maps. I think it is based on similar (but not the same) principle as 2-step. | Two-stage clustering in R
If you are looking for something akin to a 2-step, have you considered looking into Self Organizing Maps. I think it is based on similar (but not the same) principle as 2-step. | Two-stage clustering in R
If you are looking for something akin to a 2-step, have you considered looking into Self Organizing Maps. I think it is based on similar (but not the same) principle as 2-step. |
35,835 | What method is preferred, a bootstrapping test or a nonparametric rank-based test? | You just described the difference. No one can know in advance outcome differences because it greatly depends on the nature of your data.
Do you know the non-normal distribution you're working with? If so, you could simulate some results and see what the typical error rates for the different tests were and how they ... | What method is preferred, a bootstrapping test or a nonparametric rank-based test? | You just described the difference. No one can know in advance outcome differences because it greatly depends on the nature of your data.
Do you know the non-normal distribution you're working with? | What method is preferred, a bootstrapping test or a nonparametric rank-based test?
You just described the difference. No one can know in advance outcome differences because it greatly depends on the nature of your data.
Do you know the non-normal distribution you're working with? If so, you could simulate some resu... | What method is preferred, a bootstrapping test or a nonparametric rank-based test?
You just described the difference. No one can know in advance outcome differences because it greatly depends on the nature of your data.
Do you know the non-normal distribution you're working with? |
35,836 | What method is preferred, a bootstrapping test or a nonparametric rank-based test? | This answer may be helpful, and/or it may be annoying. Your welcome and my apologies at the same time :)
One thing to remember when using a normal distribution, is that it has a set of sufficient statistics, namely the mean and variance. What this indicates is that only the mean and variance matter in the inference. ... | What method is preferred, a bootstrapping test or a nonparametric rank-based test? | This answer may be helpful, and/or it may be annoying. Your welcome and my apologies at the same time :)
One thing to remember when using a normal distribution, is that it has a set of sufficient sta | What method is preferred, a bootstrapping test or a nonparametric rank-based test?
This answer may be helpful, and/or it may be annoying. Your welcome and my apologies at the same time :)
One thing to remember when using a normal distribution, is that it has a set of sufficient statistics, namely the mean and variance... | What method is preferred, a bootstrapping test or a nonparametric rank-based test?
This answer may be helpful, and/or it may be annoying. Your welcome and my apologies at the same time :)
One thing to remember when using a normal distribution, is that it has a set of sufficient sta |
35,837 | What method is preferred, a bootstrapping test or a nonparametric rank-based test? | The inferences generated by Wilcoxon vs bootstrapping cannot be compared as they pertain to different data. Wilcoxon is a rank test, thus generates inferences that pertain to ranks. Bootstrapping applies to the raw data, and thus generates inferences that pertain to the raw data. If you dislike bootstrapping but want i... | What method is preferred, a bootstrapping test or a nonparametric rank-based test? | The inferences generated by Wilcoxon vs bootstrapping cannot be compared as they pertain to different data. Wilcoxon is a rank test, thus generates inferences that pertain to ranks. Bootstrapping appl | What method is preferred, a bootstrapping test or a nonparametric rank-based test?
The inferences generated by Wilcoxon vs bootstrapping cannot be compared as they pertain to different data. Wilcoxon is a rank test, thus generates inferences that pertain to ranks. Bootstrapping applies to the raw data, and thus generat... | What method is preferred, a bootstrapping test or a nonparametric rank-based test?
The inferences generated by Wilcoxon vs bootstrapping cannot be compared as they pertain to different data. Wilcoxon is a rank test, thus generates inferences that pertain to ranks. Bootstrapping appl |
35,838 | What method is preferred, a bootstrapping test or a nonparametric rank-based test? | I have two notes and one suggestion.
The first note is that testing theory is typically done by setting an acceptable level where you would reject a true hypothesis (Type I error), then minimize the risk of accepting a false hypothesis (Type II error). There are two reasons for this, first is that all your tests use th... | What method is preferred, a bootstrapping test or a nonparametric rank-based test? | I have two notes and one suggestion.
The first note is that testing theory is typically done by setting an acceptable level where you would reject a true hypothesis (Type I error), then minimize the r | What method is preferred, a bootstrapping test or a nonparametric rank-based test?
I have two notes and one suggestion.
The first note is that testing theory is typically done by setting an acceptable level where you would reject a true hypothesis (Type I error), then minimize the risk of accepting a false hypothesis (... | What method is preferred, a bootstrapping test or a nonparametric rank-based test?
I have two notes and one suggestion.
The first note is that testing theory is typically done by setting an acceptable level where you would reject a true hypothesis (Type I error), then minimize the r |
35,839 | How to identify invalid online survey responses? | 1) Flag all responses with duplicate IP addresses. Create a new variable for this purpose -- say FLAG1, which takes on values of 1 or 0.
2) Choose a threshold for an impossibly fast response time based on common sense (e.g., less than 1 second per question) and the aid of a histogram of response times -- flag people fa... | How to identify invalid online survey responses? | 1) Flag all responses with duplicate IP addresses. Create a new variable for this purpose -- say FLAG1, which takes on values of 1 or 0.
2) Choose a threshold for an impossibly fast response time base | How to identify invalid online survey responses?
1) Flag all responses with duplicate IP addresses. Create a new variable for this purpose -- say FLAG1, which takes on values of 1 or 0.
2) Choose a threshold for an impossibly fast response time based on common sense (e.g., less than 1 second per question) and the aid o... | How to identify invalid online survey responses?
1) Flag all responses with duplicate IP addresses. Create a new variable for this purpose -- say FLAG1, which takes on values of 1 or 0.
2) Choose a threshold for an impossibly fast response time base |
35,840 | Efficient way to populate matrix in R? [closed] | Generally tables are handled as matrices or arrays and matrix indexing allows two column arguments as (i,j)-indexing (and if the object being indexed has higher dimensions then matrices with more columns are used) so:
> inp.mtx <- as.matrix(inp)
> mat[inp.mtx[,1:2] ]<- inp.mtx[,3]
> mat
[,1] [,2] [,3]
[1,] NA 0... | Efficient way to populate matrix in R? [closed] | Generally tables are handled as matrices or arrays and matrix indexing allows two column arguments as (i,j)-indexing (and if the object being indexed has higher dimensions then matrices with more colu | Efficient way to populate matrix in R? [closed]
Generally tables are handled as matrices or arrays and matrix indexing allows two column arguments as (i,j)-indexing (and if the object being indexed has higher dimensions then matrices with more columns are used) so:
> inp.mtx <- as.matrix(inp)
> mat[inp.mtx[,1:2] ]<- in... | Efficient way to populate matrix in R? [closed]
Generally tables are handled as matrices or arrays and matrix indexing allows two column arguments as (i,j)-indexing (and if the object being indexed has higher dimensions then matrices with more colu |
35,841 | Efficient way to populate matrix in R? [closed] | mat <- matrix(c(1, 1, 2, 2, 3, 3, 0.05, 0.04, 0.001), nrow = 3, ncol = 3)
mat
mat1 <- matrix(c(rep(NA,6), 0.05, 0.04, 0.001), nrow = 3, ncol = 3)
mat1
mat2 <- matrix(NA, nrow = 3, ncol = 3)
mat2
mat2[,3] <- c(0.05, 0.04, 0.001)
mat2
df <- data.frame(x=c(1, 1, 2), y=c(2, 3, 3), z=c(0.05, 0.04, 0.001))
df
... | Efficient way to populate matrix in R? [closed] | mat <- matrix(c(1, 1, 2, 2, 3, 3, 0.05, 0.04, 0.001), nrow = 3, ncol = 3)
mat
mat1 <- matrix(c(rep(NA,6), 0.05, 0.04, 0.001), nrow = 3, ncol = 3)
mat1
mat2 <- matrix(NA, nrow = 3, ncol = 3)
mat | Efficient way to populate matrix in R? [closed]
mat <- matrix(c(1, 1, 2, 2, 3, 3, 0.05, 0.04, 0.001), nrow = 3, ncol = 3)
mat
mat1 <- matrix(c(rep(NA,6), 0.05, 0.04, 0.001), nrow = 3, ncol = 3)
mat1
mat2 <- matrix(NA, nrow = 3, ncol = 3)
mat2
mat2[,3] <- c(0.05, 0.04, 0.001)
mat2
df <- data.frame(x=c(1, 1,... | Efficient way to populate matrix in R? [closed]
mat <- matrix(c(1, 1, 2, 2, 3, 3, 0.05, 0.04, 0.001), nrow = 3, ncol = 3)
mat
mat1 <- matrix(c(rep(NA,6), 0.05, 0.04, 0.001), nrow = 3, ncol = 3)
mat1
mat2 <- matrix(NA, nrow = 3, ncol = 3)
mat |
35,842 | Proof that CRF models and logistic models are convex functions | One trick is to rewrite objective functions in terms of functions which are known to be convex.
Objective function of ML trained log-linear model is a sum of negative log-likelihoods, so it's sufficient to show that negative log-likelihood for each datapoint is convex.
Considering datapoint fixed, we can write its nega... | Proof that CRF models and logistic models are convex functions | One trick is to rewrite objective functions in terms of functions which are known to be convex.
Objective function of ML trained log-linear model is a sum of negative log-likelihoods, so it's sufficie | Proof that CRF models and logistic models are convex functions
One trick is to rewrite objective functions in terms of functions which are known to be convex.
Objective function of ML trained log-linear model is a sum of negative log-likelihoods, so it's sufficient to show that negative log-likelihood for each datapoin... | Proof that CRF models and logistic models are convex functions
One trick is to rewrite objective functions in terms of functions which are known to be convex.
Objective function of ML trained log-linear model is a sum of negative log-likelihoods, so it's sufficie |
35,843 | Proof that CRF models and logistic models are convex functions | First, convexity is not only a feature of a function, but rather, a function and the domain over which it is defined.
To address your question more directly, another trick (rather another formulation) is to compute the Hessian matrix of your likelihood function. A per wiki a continuous, twice differentiable function of... | Proof that CRF models and logistic models are convex functions | First, convexity is not only a feature of a function, but rather, a function and the domain over which it is defined.
To address your question more directly, another trick (rather another formulation) | Proof that CRF models and logistic models are convex functions
First, convexity is not only a feature of a function, but rather, a function and the domain over which it is defined.
To address your question more directly, another trick (rather another formulation) is to compute the Hessian matrix of your likelihood func... | Proof that CRF models and logistic models are convex functions
First, convexity is not only a feature of a function, but rather, a function and the domain over which it is defined.
To address your question more directly, another trick (rather another formulation) |
35,844 | How should one define the sample variance for scalar input? | Scalars can't 'have' a population variance although they can be single samples from population that has a (population) variance. If you want to estimate that then you need at least: more than one data point in the sample, another sample from the same distribution, or some prior information about the population varianc... | How should one define the sample variance for scalar input? | Scalars can't 'have' a population variance although they can be single samples from population that has a (population) variance. If you want to estimate that then you need at least: more than one dat | How should one define the sample variance for scalar input?
Scalars can't 'have' a population variance although they can be single samples from population that has a (population) variance. If you want to estimate that then you need at least: more than one data point in the sample, another sample from the same distribu... | How should one define the sample variance for scalar input?
Scalars can't 'have' a population variance although they can be single samples from population that has a (population) variance. If you want to estimate that then you need at least: more than one dat |
35,845 | How should one define the sample variance for scalar input? | I am sure people in this forum will have better answers, here is what I think:
I think R's answer is logical. The random variable has a population variance, but it turns out that with 1 sample you don't have enough degrees of freedom to estimate sample variance i-e- you are trying to extract information that is NOT the... | How should one define the sample variance for scalar input? | I am sure people in this forum will have better answers, here is what I think:
I think R's answer is logical. The random variable has a population variance, but it turns out that with 1 sample you don | How should one define the sample variance for scalar input?
I am sure people in this forum will have better answers, here is what I think:
I think R's answer is logical. The random variable has a population variance, but it turns out that with 1 sample you don't have enough degrees of freedom to estimate sample varianc... | How should one define the sample variance for scalar input?
I am sure people in this forum will have better answers, here is what I think:
I think R's answer is logical. The random variable has a population variance, but it turns out that with 1 sample you don |
35,846 | How should one define the sample variance for scalar input? | I think Matlab is using the following logic for a scalar (analogous to how we define population variance) to avoid having to deal with NA and NAN.
$Var(x) = \frac{(x - \bar{x})^2}{1} = 0$
The above follows as for a scalar: $\bar{x} = x$.
Their definition is probably a programming convention that may perhaps make some a... | How should one define the sample variance for scalar input? | I think Matlab is using the following logic for a scalar (analogous to how we define population variance) to avoid having to deal with NA and NAN.
$Var(x) = \frac{(x - \bar{x})^2}{1} = 0$
The above fo | How should one define the sample variance for scalar input?
I think Matlab is using the following logic for a scalar (analogous to how we define population variance) to avoid having to deal with NA and NAN.
$Var(x) = \frac{(x - \bar{x})^2}{1} = 0$
The above follows as for a scalar: $\bar{x} = x$.
Their definition is pr... | How should one define the sample variance for scalar input?
I think Matlab is using the following logic for a scalar (analogous to how we define population variance) to avoid having to deal with NA and NAN.
$Var(x) = \frac{(x - \bar{x})^2}{1} = 0$
The above fo |
35,847 | Recommendations for visualization type when data has an extremely wide variance | A standard approach to dealing with data that has a wide variance is to use a log scale (or some other kind of scaling approach) regardless of the visualization itself. This could be applied in any graphical package (including a JS library like Protovis).
Another strategy is to use bands, and fold the data over severa... | Recommendations for visualization type when data has an extremely wide variance | A standard approach to dealing with data that has a wide variance is to use a log scale (or some other kind of scaling approach) regardless of the visualization itself. This could be applied in any g | Recommendations for visualization type when data has an extremely wide variance
A standard approach to dealing with data that has a wide variance is to use a log scale (or some other kind of scaling approach) regardless of the visualization itself. This could be applied in any graphical package (including a JS library... | Recommendations for visualization type when data has an extremely wide variance
A standard approach to dealing with data that has a wide variance is to use a log scale (or some other kind of scaling approach) regardless of the visualization itself. This could be applied in any g |
35,848 | What are the examples for stochastic processes in Electrical Engineering and Computer Science? | What about monitoring network congestion. An underlying stochastic process is assumed to be driving the congestion, and the process has reached an equilibrium state and is stationary. That is, process characteristics such as the mean level does not depend on time. You can then use this the stochastic process to give yo... | What are the examples for stochastic processes in Electrical Engineering and Computer Science? | What about monitoring network congestion. An underlying stochastic process is assumed to be driving the congestion, and the process has reached an equilibrium state and is stationary. That is, process | What are the examples for stochastic processes in Electrical Engineering and Computer Science?
What about monitoring network congestion. An underlying stochastic process is assumed to be driving the congestion, and the process has reached an equilibrium state and is stationary. That is, process characteristics such as ... | What are the examples for stochastic processes in Electrical Engineering and Computer Science?
What about monitoring network congestion. An underlying stochastic process is assumed to be driving the congestion, and the process has reached an equilibrium state and is stationary. That is, process |
35,849 | What are the examples for stochastic processes in Electrical Engineering and Computer Science? | Google's Pagerank algorithm is a stochastic approximation (through Markov's stationary state) of the proportion of visits received asymptotically by website $x_i$. | What are the examples for stochastic processes in Electrical Engineering and Computer Science? | Google's Pagerank algorithm is a stochastic approximation (through Markov's stationary state) of the proportion of visits received asymptotically by website $x_i$. | What are the examples for stochastic processes in Electrical Engineering and Computer Science?
Google's Pagerank algorithm is a stochastic approximation (through Markov's stationary state) of the proportion of visits received asymptotically by website $x_i$. | What are the examples for stochastic processes in Electrical Engineering and Computer Science?
Google's Pagerank algorithm is a stochastic approximation (through Markov's stationary state) of the proportion of visits received asymptotically by website $x_i$. |
35,850 | What are the examples for stochastic processes in Electrical Engineering and Computer Science? | As you have alluded to, communications engineering (and signal processing in general) is filled with stochastic processes. See, for example:
Chapter 9 and later of Communications Systems by Carlson and Crilly
Chapter 13 of A Course in Digtial Signal Processing by Porat
This is only two textbook examples. You will fi... | What are the examples for stochastic processes in Electrical Engineering and Computer Science? | As you have alluded to, communications engineering (and signal processing in general) is filled with stochastic processes. See, for example:
Chapter 9 and later of Communications Systems by Carlson a | What are the examples for stochastic processes in Electrical Engineering and Computer Science?
As you have alluded to, communications engineering (and signal processing in general) is filled with stochastic processes. See, for example:
Chapter 9 and later of Communications Systems by Carlson and Crilly
Chapter 13 of ... | What are the examples for stochastic processes in Electrical Engineering and Computer Science?
As you have alluded to, communications engineering (and signal processing in general) is filled with stochastic processes. See, for example:
Chapter 9 and later of Communications Systems by Carlson a |
35,851 | The expected value of random variable on tosses of a coin | If n is large enough, your expected
value should approach the mean of the
distribution.
Yes that's correct.
So probability that value is greater
than expected value should be 0.5.
This would only be correct if the distribution is symmetric - which in your game isn't the case. You can see this easily if you th... | The expected value of random variable on tosses of a coin | If n is large enough, your expected
value should approach the mean of the
distribution.
Yes that's correct.
So probability that value is greater
than expected value should be 0.5.
This would | The expected value of random variable on tosses of a coin
If n is large enough, your expected
value should approach the mean of the
distribution.
Yes that's correct.
So probability that value is greater
than expected value should be 0.5.
This would only be correct if the distribution is symmetric - which in y... | The expected value of random variable on tosses of a coin
If n is large enough, your expected
value should approach the mean of the
distribution.
Yes that's correct.
So probability that value is greater
than expected value should be 0.5.
This would |
35,852 | The expected value of random variable on tosses of a coin | Let $S_k$ be the wealth after $k$ plays of this game, where we assume $S_0 = 1.$ The temptation here is to take $X_k = \log{S_k}$, and study $X_k$ as a symmetric random walk, with innovations of size $\pm \log{2}$. This, as it turns out, will be fine for the second question, but not the first. A bit of work will show t... | The expected value of random variable on tosses of a coin | Let $S_k$ be the wealth after $k$ plays of this game, where we assume $S_0 = 1.$ The temptation here is to take $X_k = \log{S_k}$, and study $X_k$ as a symmetric random walk, with innovations of size | The expected value of random variable on tosses of a coin
Let $S_k$ be the wealth after $k$ plays of this game, where we assume $S_0 = 1.$ The temptation here is to take $X_k = \log{S_k}$, and study $X_k$ as a symmetric random walk, with innovations of size $\pm \log{2}$. This, as it turns out, will be fine for the sec... | The expected value of random variable on tosses of a coin
Let $S_k$ be the wealth after $k$ plays of this game, where we assume $S_0 = 1.$ The temptation here is to take $X_k = \log{S_k}$, and study $X_k$ as a symmetric random walk, with innovations of size |
35,853 | The expected value of random variable on tosses of a coin | You're right about the expectation.
You actually also have the right answer to the probability of getting more than your original stake back, although not the right proof. Consider, instead of the raw amount of money you have, its base-2 logarithm. This turns out to be the number of times you've doubled your money, mi... | The expected value of random variable on tosses of a coin | You're right about the expectation.
You actually also have the right answer to the probability of getting more than your original stake back, although not the right proof. Consider, instead of the raw | The expected value of random variable on tosses of a coin
You're right about the expectation.
You actually also have the right answer to the probability of getting more than your original stake back, although not the right proof. Consider, instead of the raw amount of money you have, its base-2 logarithm. This turns o... | The expected value of random variable on tosses of a coin
You're right about the expectation.
You actually also have the right answer to the probability of getting more than your original stake back, although not the right proof. Consider, instead of the raw |
35,854 | How to deal with the effect of the order of observations in a non hierarchical cluster analysis? | A "right" answer cannot depend on an arbitrary ordering of some method you are using.
You need to consider all possible orderings (or some representative sample) and estimate your parameters for every case. This will give you distributions for the parameters you are trying to estimate. Estimate the "true" parameter val... | How to deal with the effect of the order of observations in a non hierarchical cluster analysis? | A "right" answer cannot depend on an arbitrary ordering of some method you are using.
You need to consider all possible orderings (or some representative sample) and estimate your parameters for every | How to deal with the effect of the order of observations in a non hierarchical cluster analysis?
A "right" answer cannot depend on an arbitrary ordering of some method you are using.
You need to consider all possible orderings (or some representative sample) and estimate your parameters for every case. This will give y... | How to deal with the effect of the order of observations in a non hierarchical cluster analysis?
A "right" answer cannot depend on an arbitrary ordering of some method you are using.
You need to consider all possible orderings (or some representative sample) and estimate your parameters for every |
35,855 | How to deal with the effect of the order of observations in a non hierarchical cluster analysis? | What you're discovering is a degree of instability in either the algorithm or the data itself. The approach termed 'consensus' or 'ensemble' clustering is a way of dealing with the problem. The problem there is: given a collection of clusterings, find a "consensus" clustering that is in some sense the "average" of the ... | How to deal with the effect of the order of observations in a non hierarchical cluster analysis? | What you're discovering is a degree of instability in either the algorithm or the data itself. The approach termed 'consensus' or 'ensemble' clustering is a way of dealing with the problem. The proble | How to deal with the effect of the order of observations in a non hierarchical cluster analysis?
What you're discovering is a degree of instability in either the algorithm or the data itself. The approach termed 'consensus' or 'ensemble' clustering is a way of dealing with the problem. The problem there is: given a col... | How to deal with the effect of the order of observations in a non hierarchical cluster analysis?
What you're discovering is a degree of instability in either the algorithm or the data itself. The approach termed 'consensus' or 'ensemble' clustering is a way of dealing with the problem. The proble |
35,856 | How to deal with the effect of the order of observations in a non hierarchical cluster analysis? | Which flat-clustering algorithm are you using? It might also be the case that the different results are because maybe it's not your data but your algorithm itself is non-deterministic (e.g., using K-means with random initialization, or using a model-based clustering with EM or MCMC for inference with random initializat... | How to deal with the effect of the order of observations in a non hierarchical cluster analysis? | Which flat-clustering algorithm are you using? It might also be the case that the different results are because maybe it's not your data but your algorithm itself is non-deterministic (e.g., using K-m | How to deal with the effect of the order of observations in a non hierarchical cluster analysis?
Which flat-clustering algorithm are you using? It might also be the case that the different results are because maybe it's not your data but your algorithm itself is non-deterministic (e.g., using K-means with random initia... | How to deal with the effect of the order of observations in a non hierarchical cluster analysis?
Which flat-clustering algorithm are you using? It might also be the case that the different results are because maybe it's not your data but your algorithm itself is non-deterministic (e.g., using K-m |
35,857 | Why do we need normality test if we already have CLT? | 1. The CLT certainly doesn't solve all problems. For example:
(a) There are distributions for which the CLT doesn't hold.
Here's an example:
This density is a mixture of a symmetric 4-parameter beta and a $t_2$. There's a normal distribution that looks visually pretty close to it (e.g. in the way that a Kolmogorov-Smi... | Why do we need normality test if we already have CLT? | 1. The CLT certainly doesn't solve all problems. For example:
(a) There are distributions for which the CLT doesn't hold.
Here's an example:
This density is a mixture of a symmetric 4-parameter beta | Why do we need normality test if we already have CLT?
1. The CLT certainly doesn't solve all problems. For example:
(a) There are distributions for which the CLT doesn't hold.
Here's an example:
This density is a mixture of a symmetric 4-parameter beta and a $t_2$. There's a normal distribution that looks visually pre... | Why do we need normality test if we already have CLT?
1. The CLT certainly doesn't solve all problems. For example:
(a) There are distributions for which the CLT doesn't hold.
Here's an example:
This density is a mixture of a symmetric 4-parameter beta |
35,858 | Median of the squared difference from the median of a Cauchy random variable | Suppose $F$ is the distribution function of a random variable $X$ with median $m.$
By definition, a median is any number for which $F(m)\ge 1/2$ and $F(x) \le 1/2$ for all $x \lt m.$
For any non-negative number $y,$ let
$$G(y) = F(m+y) - F(m-y) = \Pr(X \in (m-y, m+y]).$$
Clearly (by the probability axioms) $G(0)=0$ a... | Median of the squared difference from the median of a Cauchy random variable | Suppose $F$ is the distribution function of a random variable $X$ with median $m.$
By definition, a median is any number for which $F(m)\ge 1/2$ and $F(x) \le 1/2$ for all $x \lt m.$
For any non-neg | Median of the squared difference from the median of a Cauchy random variable
Suppose $F$ is the distribution function of a random variable $X$ with median $m.$
By definition, a median is any number for which $F(m)\ge 1/2$ and $F(x) \le 1/2$ for all $x \lt m.$
For any non-negative number $y,$ let
$$G(y) = F(m+y) - F(m... | Median of the squared difference from the median of a Cauchy random variable
Suppose $F$ is the distribution function of a random variable $X$ with median $m.$
By definition, a median is any number for which $F(m)\ge 1/2$ and $F(x) \le 1/2$ for all $x \lt m.$
For any non-neg |
35,859 | Probability of collision: mathematical vs probabilistic modeling | Related scattering theory and free path length
Change frame of reference
You can compute your method 1 more easily by switching the frame of reference to a co-moving frame along with the stream of cars.
If the car 1 has the velocity $\vec{v}_1$ and car 2 have the velocity $\vec{v}_2$ then in the co-moving frame the re... | Probability of collision: mathematical vs probabilistic modeling | Related scattering theory and free path length
Change frame of reference
You can compute your method 1 more easily by switching the frame of reference to a co-moving frame along with the stream of car | Probability of collision: mathematical vs probabilistic modeling
Related scattering theory and free path length
Change frame of reference
You can compute your method 1 more easily by switching the frame of reference to a co-moving frame along with the stream of cars.
If the car 1 has the velocity $\vec{v}_1$ and car 2... | Probability of collision: mathematical vs probabilistic modeling
Related scattering theory and free path length
Change frame of reference
You can compute your method 1 more easily by switching the frame of reference to a co-moving frame along with the stream of car |
35,860 | Probability of collision: mathematical vs probabilistic modeling | First, once you know where you are in this picture relative to the position of the car 1, there's nothing probabilistic left in the problem: you know exactly whether you're colliding or not. So the event of collision and its probability boils down to what is random about your relative location.
Reduction to 1D
Let's de... | Probability of collision: mathematical vs probabilistic modeling | First, once you know where you are in this picture relative to the position of the car 1, there's nothing probabilistic left in the problem: you know exactly whether you're colliding or not. So the ev | Probability of collision: mathematical vs probabilistic modeling
First, once you know where you are in this picture relative to the position of the car 1, there's nothing probabilistic left in the problem: you know exactly whether you're colliding or not. So the event of collision and its probability boils down to what... | Probability of collision: mathematical vs probabilistic modeling
First, once you know where you are in this picture relative to the position of the car 1, there's nothing probabilistic left in the problem: you know exactly whether you're colliding or not. So the ev |
35,861 | Interpreting nonlinear regression $R^2$ | NO
Let’s start by deriving $R^2$ in the linear case.
Notation
$y_i$ is observation $i$ of some response variable $Y$.
$\hat{y}_i$ is the value of $y_i$ predicted by the regression.
$\bar{y}$ is the average of all observations of the response variable.
$$ y_i-\bar{y} = (y_i - \hat{y_i} + \hat{y_i} - \bar{y}) = (y_i - \h... | Interpreting nonlinear regression $R^2$ | NO
Let’s start by deriving $R^2$ in the linear case.
Notation
$y_i$ is observation $i$ of some response variable $Y$.
$\hat{y}_i$ is the value of $y_i$ predicted by the regression.
$\bar{y}$ is the av | Interpreting nonlinear regression $R^2$
NO
Let’s start by deriving $R^2$ in the linear case.
Notation
$y_i$ is observation $i$ of some response variable $Y$.
$\hat{y}_i$ is the value of $y_i$ predicted by the regression.
$\bar{y}$ is the average of all observations of the response variable.
$$ y_i-\bar{y} = (y_i - \hat... | Interpreting nonlinear regression $R^2$
NO
Let’s start by deriving $R^2$ in the linear case.
Notation
$y_i$ is observation $i$ of some response variable $Y$.
$\hat{y}_i$ is the value of $y_i$ predicted by the regression.
$\bar{y}$ is the av |
35,862 | Can a (possibly infinite) mixture of Gaussians be Gaussian? | Copying from the Wikipedia page on compound distributions
Gaussian scale mixtures:
Compounding a normal distribution with variance distributed according to an inverse gamma distribution (or equivalently, with
precision distributed as a gamma distribution) yields a
non-standardized Student's t-distribution. This distr... | Can a (possibly infinite) mixture of Gaussians be Gaussian? | Copying from the Wikipedia page on compound distributions
Gaussian scale mixtures:
Compounding a normal distribution with variance distributed according to an inverse gamma distribution (or equivale | Can a (possibly infinite) mixture of Gaussians be Gaussian?
Copying from the Wikipedia page on compound distributions
Gaussian scale mixtures:
Compounding a normal distribution with variance distributed according to an inverse gamma distribution (or equivalently, with
precision distributed as a gamma distribution) yi... | Can a (possibly infinite) mixture of Gaussians be Gaussian?
Copying from the Wikipedia page on compound distributions
Gaussian scale mixtures:
Compounding a normal distribution with variance distributed according to an inverse gamma distribution (or equivale |
35,863 | If $20 $ random numbers are selected independently from the interval $(0,1) $ probability that the sum of these numbers is at least $8$? [closed] | It can be helpful to have a "gross reality check" (or grc) ((some people call it a sanity check)) that comes at the problem side-ways and can tell you if you are doing something wrong.
Here is R-code to simulate the problem, and give an estimate:
set.seed(1)
temp <- numeric(length=20000)
for(i in 1:20000){
# ... | If $20 $ random numbers are selected independently from the interval $(0,1) $ probability that the s | It can be helpful to have a "gross reality check" (or grc) ((some people call it a sanity check)) that comes at the problem side-ways and can tell you if you are doing something wrong.
Here is R-code | If $20 $ random numbers are selected independently from the interval $(0,1) $ probability that the sum of these numbers is at least $8$? [closed]
It can be helpful to have a "gross reality check" (or grc) ((some people call it a sanity check)) that comes at the problem side-ways and can tell you if you are doing someth... | If $20 $ random numbers are selected independently from the interval $(0,1) $ probability that the s
It can be helpful to have a "gross reality check" (or grc) ((some people call it a sanity check)) that comes at the problem side-ways and can tell you if you are doing something wrong.
Here is R-code |
35,864 | If $20 $ random numbers are selected independently from the interval $(0,1) $ probability that the sum of these numbers is at least $8$? [closed] | Let $ \ X_i $ be the $ \ i^{th}$ number selected where $\ i= 1,2,3,4...20 $
$To $ $ calculate $
$ \ P( \sum_{i=1}^{20} X_i \ge 8 ) $
$ E(\ X_i) = \frac{(0+1)}{2} $ $ [uniform $ $ distribution ] $
$ E(\ X_i) = \frac{1}{2} $
$ E(\sum_{i=1}^{20} X_i) = 20/2 = 10 $
$ Var(\ X_i) = \frac{\ (1-0)^2}{12} $ $ [uniform $ $ dist... | If $20 $ random numbers are selected independently from the interval $(0,1) $ probability that the s | Let $ \ X_i $ be the $ \ i^{th}$ number selected where $\ i= 1,2,3,4...20 $
$To $ $ calculate $
$ \ P( \sum_{i=1}^{20} X_i \ge 8 ) $
$ E(\ X_i) = \frac{(0+1)}{2} $ $ [uniform $ $ distribution ] $
$ E | If $20 $ random numbers are selected independently from the interval $(0,1) $ probability that the sum of these numbers is at least $8$? [closed]
Let $ \ X_i $ be the $ \ i^{th}$ number selected where $\ i= 1,2,3,4...20 $
$To $ $ calculate $
$ \ P( \sum_{i=1}^{20} X_i \ge 8 ) $
$ E(\ X_i) = \frac{(0+1)}{2} $ $ [unifor... | If $20 $ random numbers are selected independently from the interval $(0,1) $ probability that the s
Let $ \ X_i $ be the $ \ i^{th}$ number selected where $\ i= 1,2,3,4...20 $
$To $ $ calculate $
$ \ P( \sum_{i=1}^{20} X_i \ge 8 ) $
$ E(\ X_i) = \frac{(0+1)}{2} $ $ [uniform $ $ distribution ] $
$ E |
35,865 | If $20 $ random numbers are selected independently from the interval $(0,1) $ probability that the sum of these numbers is at least $8$? [closed] | Here is a histogram of 100,000 simulations each taking the sum of 20 uniform random deviates. Based on this simulation the sum of uniform deviates is well approximated by a normal distribution with an estimated mean of 10.004 and an estimated variance of 1.680. Using the normal approximation the probability that $\su... | If $20 $ random numbers are selected independently from the interval $(0,1) $ probability that the s | Here is a histogram of 100,000 simulations each taking the sum of 20 uniform random deviates. Based on this simulation the sum of uniform deviates is well approximated by a normal distribution with a | If $20 $ random numbers are selected independently from the interval $(0,1) $ probability that the sum of these numbers is at least $8$? [closed]
Here is a histogram of 100,000 simulations each taking the sum of 20 uniform random deviates. Based on this simulation the sum of uniform deviates is well approximated by a ... | If $20 $ random numbers are selected independently from the interval $(0,1) $ probability that the s
Here is a histogram of 100,000 simulations each taking the sum of 20 uniform random deviates. Based on this simulation the sum of uniform deviates is well approximated by a normal distribution with a |
35,866 | MCMC sampling for a model with a multinomial choice--so the parameters need to sum to 1 | The problem does not seem to stand with MCMC but with the prior modelling. If the data comes from a Multinomial distribution
$$\mathcal D_k(n,p_1,\ldots,p_k)$$
where the probability vector $\mathbf{p}=(p_1,\ldots,p_k)$ belongs to the $k$-dimensional simplex, the prior on $\mathbf{p}$ must put some mass on the simplex (... | MCMC sampling for a model with a multinomial choice--so the parameters need to sum to 1 | The problem does not seem to stand with MCMC but with the prior modelling. If the data comes from a Multinomial distribution
$$\mathcal D_k(n,p_1,\ldots,p_k)$$
where the probability vector $\mathbf{p} | MCMC sampling for a model with a multinomial choice--so the parameters need to sum to 1
The problem does not seem to stand with MCMC but with the prior modelling. If the data comes from a Multinomial distribution
$$\mathcal D_k(n,p_1,\ldots,p_k)$$
where the probability vector $\mathbf{p}=(p_1,\ldots,p_k)$ belongs to th... | MCMC sampling for a model with a multinomial choice--so the parameters need to sum to 1
The problem does not seem to stand with MCMC but with the prior modelling. If the data comes from a Multinomial distribution
$$\mathcal D_k(n,p_1,\ldots,p_k)$$
where the probability vector $\mathbf{p} |
35,867 | Multivariate normal distribution vs. sampling multiple times from univariate normal distribution | What you propose ignores correlations. When marginals have correlation (say positive for now), then when one is high, the others will tend to be high.
Example
Marginals are $X,Y\sim N(0,1)$. Draw from $X$ and $Y$ independently and get $X = 1.5$ and $Y=-1$. So far so good, right? Maybe the values are a little unusual an... | Multivariate normal distribution vs. sampling multiple times from univariate normal distribution | What you propose ignores correlations. When marginals have correlation (say positive for now), then when one is high, the others will tend to be high.
Example
Marginals are $X,Y\sim N(0,1)$. Draw from | Multivariate normal distribution vs. sampling multiple times from univariate normal distribution
What you propose ignores correlations. When marginals have correlation (say positive for now), then when one is high, the others will tend to be high.
Example
Marginals are $X,Y\sim N(0,1)$. Draw from $X$ and $Y$ independen... | Multivariate normal distribution vs. sampling multiple times from univariate normal distribution
What you propose ignores correlations. When marginals have correlation (say positive for now), then when one is high, the others will tend to be high.
Example
Marginals are $X,Y\sim N(0,1)$. Draw from |
35,868 | Does zero Spearman's rho imply zero Covariance? | Counterexample:
X Y
1 500
2 1
3 2
4 3
5 4
For these values,
Pearson's $r \approx -0.70$
Spearman's $\rho = 0$
That single large Y value affects the covariance much more than it affects Spearman's rank correlation coefficient. | Does zero Spearman's rho imply zero Covariance? | Counterexample:
X Y
1 500
2 1
3 2
4 3
5 4
For these values,
Pearson's $r \approx -0.70$
Spearman's $\rho = 0$
That single large Y value affects the covariance much more than it affects Spearman's r | Does zero Spearman's rho imply zero Covariance?
Counterexample:
X Y
1 500
2 1
3 2
4 3
5 4
For these values,
Pearson's $r \approx -0.70$
Spearman's $\rho = 0$
That single large Y value affects the covariance much more than it affects Spearman's rank correlation coefficient. | Does zero Spearman's rho imply zero Covariance?
Counterexample:
X Y
1 500
2 1
3 2
4 3
5 4
For these values,
Pearson's $r \approx -0.70$
Spearman's $\rho = 0$
That single large Y value affects the covariance much more than it affects Spearman's r |
35,869 | Does zero Spearman's rho imply zero Covariance? | No. Easy to see why. The use case of rank correlation is when we’re not satisfied with Pearson correlation, e.g. with its proneness to fall for outliers. Therefore, clearly Spearman correlation should not correspond to Pearson correlation outcomes.
Sometimes zero spearman correlation coincides with zero Pearson correla... | Does zero Spearman's rho imply zero Covariance? | No. Easy to see why. The use case of rank correlation is when we’re not satisfied with Pearson correlation, e.g. with its proneness to fall for outliers. Therefore, clearly Spearman correlation should | Does zero Spearman's rho imply zero Covariance?
No. Easy to see why. The use case of rank correlation is when we’re not satisfied with Pearson correlation, e.g. with its proneness to fall for outliers. Therefore, clearly Spearman correlation should not correspond to Pearson correlation outcomes.
Sometimes zero spearman... | Does zero Spearman's rho imply zero Covariance?
No. Easy to see why. The use case of rank correlation is when we’re not satisfied with Pearson correlation, e.g. with its proneness to fall for outliers. Therefore, clearly Spearman correlation should |
35,870 | Probability that the sample comes from a certain distribution | phibog's goal is to find out the probability that a set of data samples belongs to the distribution with pdf $f(x)$. It can be expressed as $P(f(x)|x_1,x_2,...,x_n)$. From Bayes theorem,
$P(f(x)|x_1,x_2,...,x_n)=\frac{P(x_1,x_2,...,x_n|f(x))P(f(x))}{P(x_1,x_2,...,x_n|f(x))P(f(x))+P(x_1,x_2,...,x_n|g(x))P(g(x))},$
where... | Probability that the sample comes from a certain distribution | phibog's goal is to find out the probability that a set of data samples belongs to the distribution with pdf $f(x)$. It can be expressed as $P(f(x)|x_1,x_2,...,x_n)$. From Bayes theorem,
$P(f(x)|x_1,x | Probability that the sample comes from a certain distribution
phibog's goal is to find out the probability that a set of data samples belongs to the distribution with pdf $f(x)$. It can be expressed as $P(f(x)|x_1,x_2,...,x_n)$. From Bayes theorem,
$P(f(x)|x_1,x_2,...,x_n)=\frac{P(x_1,x_2,...,x_n|f(x))P(f(x))}{P(x_1,x_... | Probability that the sample comes from a certain distribution
phibog's goal is to find out the probability that a set of data samples belongs to the distribution with pdf $f(x)$. It can be expressed as $P(f(x)|x_1,x_2,...,x_n)$. From Bayes theorem,
$P(f(x)|x_1,x |
35,871 | Probability that the sample comes from a certain distribution | A simple method here is to use Bayesian analysis. For notational simplicity, let's "parameterise" your family of (two) distributions by defining the probability density $h$ by:
$$h(x|\theta) = \begin{cases}
f(x) & & & \text{if } \theta = 0, \\[6pt]
g(x) & & & \text{if } \theta = 1. \\[6pt]
\end{cases}$$
The binary par... | Probability that the sample comes from a certain distribution | A simple method here is to use Bayesian analysis. For notational simplicity, let's "parameterise" your family of (two) distributions by defining the probability density $h$ by:
$$h(x|\theta) = \begin | Probability that the sample comes from a certain distribution
A simple method here is to use Bayesian analysis. For notational simplicity, let's "parameterise" your family of (two) distributions by defining the probability density $h$ by:
$$h(x|\theta) = \begin{cases}
f(x) & & & \text{if } \theta = 0, \\[6pt]
g(x) & &... | Probability that the sample comes from a certain distribution
A simple method here is to use Bayesian analysis. For notational simplicity, let's "parameterise" your family of (two) distributions by defining the probability density $h$ by:
$$h(x|\theta) = \begin |
35,872 | Probability that the sample comes from a certain distribution | If one of your distribution is a more/less restricted version of the other, then the Likelihood-ratio test might be what you want. More specifically:
Assuming $H_0$ is true, there is a fundamental result by Samuel S. Wilks: As the sample size $n$ approaches $\infty$, the test statistic $-2\log(\lambda)$ asymptotically... | Probability that the sample comes from a certain distribution | If one of your distribution is a more/less restricted version of the other, then the Likelihood-ratio test might be what you want. More specifically:
Assuming $H_0$ is true, there is a fundamental re | Probability that the sample comes from a certain distribution
If one of your distribution is a more/less restricted version of the other, then the Likelihood-ratio test might be what you want. More specifically:
Assuming $H_0$ is true, there is a fundamental result by Samuel S. Wilks: As the sample size $n$ approaches... | Probability that the sample comes from a certain distribution
If one of your distribution is a more/less restricted version of the other, then the Likelihood-ratio test might be what you want. More specifically:
Assuming $H_0$ is true, there is a fundamental re |
35,873 | Probability that the sample comes from a certain distribution | The data either come from the specified model or they do not. There is no probability regarding this concern. The candidate model serves as a convenient yet imperfect representation of the data generative process. To compare how competing models fit your data you can use a criterion such as AIC based on the likeliho... | Probability that the sample comes from a certain distribution | The data either come from the specified model or they do not. There is no probability regarding this concern. The candidate model serves as a convenient yet imperfect representation of the data gene | Probability that the sample comes from a certain distribution
The data either come from the specified model or they do not. There is no probability regarding this concern. The candidate model serves as a convenient yet imperfect representation of the data generative process. To compare how competing models fit your ... | Probability that the sample comes from a certain distribution
The data either come from the specified model or they do not. There is no probability regarding this concern. The candidate model serves as a convenient yet imperfect representation of the data gene |
35,874 | Probability that the sample comes from a certain distribution | To answer your question, you can select from a few available tests. To quote Wikipedia on the Kolmogorov–Smirnov test where other competitive tests are also cited (placed in bold):
Kolmogorov–Smirnov test (K–S test or KS test) is a nonparametric test of the equality of continuous (or discontinuous, see Section 2.2), o... | Probability that the sample comes from a certain distribution | To answer your question, you can select from a few available tests. To quote Wikipedia on the Kolmogorov–Smirnov test where other competitive tests are also cited (placed in bold):
Kolmogorov–Smirnov | Probability that the sample comes from a certain distribution
To answer your question, you can select from a few available tests. To quote Wikipedia on the Kolmogorov–Smirnov test where other competitive tests are also cited (placed in bold):
Kolmogorov–Smirnov test (K–S test or KS test) is a nonparametric test of the... | Probability that the sample comes from a certain distribution
To answer your question, you can select from a few available tests. To quote Wikipedia on the Kolmogorov–Smirnov test where other competitive tests are also cited (placed in bold):
Kolmogorov–Smirnov |
35,875 | Parsimonious Mixed Models | Yes, your understanding is correct, but it if probabily a good idea to understand that background of that paper. Following the publication of the "Keep it Maximal" paper by Barr etc al (2013), which is referenced substantially by Bates, practitioners were increasingly confronted with models that convereged with a singu... | Parsimonious Mixed Models | Yes, your understanding is correct, but it if probabily a good idea to understand that background of that paper. Following the publication of the "Keep it Maximal" paper by Barr etc al (2013), which i | Parsimonious Mixed Models
Yes, your understanding is correct, but it if probabily a good idea to understand that background of that paper. Following the publication of the "Keep it Maximal" paper by Barr etc al (2013), which is referenced substantially by Bates, practitioners were increasingly confronted with models th... | Parsimonious Mixed Models
Yes, your understanding is correct, but it if probabily a good idea to understand that background of that paper. Following the publication of the "Keep it Maximal" paper by Barr etc al (2013), which i |
35,876 | Proving that logistic regression on $I(X>c)$ by $X$ itself recovers decision boundary $c$ when $X$ is normal | Let's lead off with a wonderful approximation. Here is a plot of two functions.
The underlying tan curve is the graph of $\Phi,$ the standard Normal CDF. The overplotted blue curve is the graph of $\Lambda:z \to 1/(1 + \exp(-7z/4)),$ a scaled version of the logistic function.
To see how well they approximate each ot... | Proving that logistic regression on $I(X>c)$ by $X$ itself recovers decision boundary $c$ when $X$ i | Let's lead off with a wonderful approximation. Here is a plot of two functions.
The underlying tan curve is the graph of $\Phi,$ the standard Normal CDF. The overplotted blue curve is the graph of | Proving that logistic regression on $I(X>c)$ by $X$ itself recovers decision boundary $c$ when $X$ is normal
Let's lead off with a wonderful approximation. Here is a plot of two functions.
The underlying tan curve is the graph of $\Phi,$ the standard Normal CDF. The overplotted blue curve is the graph of $\Lambda:z ... | Proving that logistic regression on $I(X>c)$ by $X$ itself recovers decision boundary $c$ when $X$ i
Let's lead off with a wonderful approximation. Here is a plot of two functions.
The underlying tan curve is the graph of $\Phi,$ the standard Normal CDF. The overplotted blue curve is the graph of |
35,877 | Proving that logistic regression on $I(X>c)$ by $X$ itself recovers decision boundary $c$ when $X$ is normal | Indipendently on the distribution of $X$, if $C$ is computed in that deterministic way, estimation won't converge because there is no couple of parameters $\beta$ for which likelihood is maximized.
It is easy to notice that $\hat c = -\frac{\hat \beta_0}{\hat \beta_1}$ maximises the likelihood at some middle value bet... | Proving that logistic regression on $I(X>c)$ by $X$ itself recovers decision boundary $c$ when $X$ i | Indipendently on the distribution of $X$, if $C$ is computed in that deterministic way, estimation won't converge because there is no couple of parameters $\beta$ for which likelihood is maximized.
I | Proving that logistic regression on $I(X>c)$ by $X$ itself recovers decision boundary $c$ when $X$ is normal
Indipendently on the distribution of $X$, if $C$ is computed in that deterministic way, estimation won't converge because there is no couple of parameters $\beta$ for which likelihood is maximized.
It is easy t... | Proving that logistic regression on $I(X>c)$ by $X$ itself recovers decision boundary $c$ when $X$ i
Indipendently on the distribution of $X$, if $C$ is computed in that deterministic way, estimation won't converge because there is no couple of parameters $\beta$ for which likelihood is maximized.
I |
35,878 | Proving that logistic regression on $I(X>c)$ by $X$ itself recovers decision boundary $c$ when $X$ is normal | One way to understand the solution to the problem - the answers by carlo, whuber and comments already say a lot of this - is to re-express the logit expression as $\exp(\beta_1 (\gamma+X))\over 1+\exp(\beta_1(\gamma+X))$, where $\gamma={\beta_0\over \beta_1}$. Doing so, you can maximize the likelihood
$$
\max_{\beta_1... | Proving that logistic regression on $I(X>c)$ by $X$ itself recovers decision boundary $c$ when $X$ i | One way to understand the solution to the problem - the answers by carlo, whuber and comments already say a lot of this - is to re-express the logit expression as $\exp(\beta_1 (\gamma+X))\over 1+\exp | Proving that logistic regression on $I(X>c)$ by $X$ itself recovers decision boundary $c$ when $X$ is normal
One way to understand the solution to the problem - the answers by carlo, whuber and comments already say a lot of this - is to re-express the logit expression as $\exp(\beta_1 (\gamma+X))\over 1+\exp(\beta_1(\g... | Proving that logistic regression on $I(X>c)$ by $X$ itself recovers decision boundary $c$ when $X$ i
One way to understand the solution to the problem - the answers by carlo, whuber and comments already say a lot of this - is to re-express the logit expression as $\exp(\beta_1 (\gamma+X))\over 1+\exp |
35,879 | How to choose delta parameter in Huber Loss function? | Huber loss will clip gradients to delta for residual (abs) values larger than delta. You want that when some part of your data points poorly fit the model and you would like to limit their influence. Also, clipping the grads is a common way to make optimization stable (not necessarily with huber).
Set delta to the val... | How to choose delta parameter in Huber Loss function? | Huber loss will clip gradients to delta for residual (abs) values larger than delta. You want that when some part of your data points poorly fit the model and you would like to limit their influence. | How to choose delta parameter in Huber Loss function?
Huber loss will clip gradients to delta for residual (abs) values larger than delta. You want that when some part of your data points poorly fit the model and you would like to limit their influence. Also, clipping the grads is a common way to make optimization sta... | How to choose delta parameter in Huber Loss function?
Huber loss will clip gradients to delta for residual (abs) values larger than delta. You want that when some part of your data points poorly fit the model and you would like to limit their influence. |
35,880 | How to choose delta parameter in Huber Loss function? | As Alex Kreimer said you want to set $\delta$ as a measure of spread of the inliers. Most of the time (for example in R) it is done using the MADN (median absolute deviation about the median renormalized to be efficient at the Gaussian), the other possibility is to choose $\delta=1.35$ because it is what you would choo... | How to choose delta parameter in Huber Loss function? | As Alex Kreimer said you want to set $\delta$ as a measure of spread of the inliers. Most of the time (for example in R) it is done using the MADN (median absolute deviation about the median renormali | How to choose delta parameter in Huber Loss function?
As Alex Kreimer said you want to set $\delta$ as a measure of spread of the inliers. Most of the time (for example in R) it is done using the MADN (median absolute deviation about the median renormalized to be efficient at the Gaussian), the other possibility is to ... | How to choose delta parameter in Huber Loss function?
As Alex Kreimer said you want to set $\delta$ as a measure of spread of the inliers. Most of the time (for example in R) it is done using the MADN (median absolute deviation about the median renormali |
35,881 | Hypothesis testing for difference in medians vs. median difference | Data. There are some minor discrepancies (maybe from rounding) in your data table.
The table below is what I get from inputting your x1 and x2. These are
the values I will use:
x1 x2 d
[1,] 1.37 1.68 -0.31
[2,] 2.18 2.99 -0.81
[3,] 1.16 3.24 -2.08
[4,] 3.60 3.08 0.52
[5,] 2.33 2.19 0.14
Sample means and... | Hypothesis testing for difference in medians vs. median difference | Data. There are some minor discrepancies (maybe from rounding) in your data table.
The table below is what I get from inputting your x1 and x2. These are
the values I will use:
x1 x2 d
[1 | Hypothesis testing for difference in medians vs. median difference
Data. There are some minor discrepancies (maybe from rounding) in your data table.
The table below is what I get from inputting your x1 and x2. These are
the values I will use:
x1 x2 d
[1,] 1.37 1.68 -0.31
[2,] 2.18 2.99 -0.81
[3,] 1.16 3.2... | Hypothesis testing for difference in medians vs. median difference
Data. There are some minor discrepancies (maybe from rounding) in your data table.
The table below is what I get from inputting your x1 and x2. These are
the values I will use:
x1 x2 d
[1 |
35,882 | Is the t distribution a member of the exponential family? | No, the t distribution is not an exponential family. Exponential family distributions do have existing moment generating functions, and the t distribution do not. See also Why doesn't the exponential family include all distributions? | Is the t distribution a member of the exponential family? | No, the t distribution is not an exponential family. Exponential family distributions do have existing moment generating functions, and the t distribution do not. See also Why doesn't the exponent | Is the t distribution a member of the exponential family?
No, the t distribution is not an exponential family. Exponential family distributions do have existing moment generating functions, and the t distribution do not. See also Why doesn't the exponential family include all distributions? | Is the t distribution a member of the exponential family?
No, the t distribution is not an exponential family. Exponential family distributions do have existing moment generating functions, and the t distribution do not. See also Why doesn't the exponent |
35,883 | Do I need a second validation set to select model class? | Prior to the revival of deep learning in the last few years, hyperparameter tuning used to be called model selection. The purpose of the validation set is to choose among several model candidates. It shouldn't make a difference whether these models have the same architecture with different hyperparameters or are comple... | Do I need a second validation set to select model class? | Prior to the revival of deep learning in the last few years, hyperparameter tuning used to be called model selection. The purpose of the validation set is to choose among several model candidates. It | Do I need a second validation set to select model class?
Prior to the revival of deep learning in the last few years, hyperparameter tuning used to be called model selection. The purpose of the validation set is to choose among several model candidates. It shouldn't make a difference whether these models have the same ... | Do I need a second validation set to select model class?
Prior to the revival of deep learning in the last few years, hyperparameter tuning used to be called model selection. The purpose of the validation set is to choose among several model candidates. It |
35,884 | Do I need a second validation set to select model class? | I am actually doing this right now too! :) I have 3 model classes, logistic, random forest and GP.
My design is this (with 5-fold crossvalidation):
training data set - optimize parameters and hyperparameters (not sure if we have the same definition of hyperparameters; in my case these are the length-scales for GP cova... | Do I need a second validation set to select model class? | I am actually doing this right now too! :) I have 3 model classes, logistic, random forest and GP.
My design is this (with 5-fold crossvalidation):
training data set - optimize parameters and hyperpa | Do I need a second validation set to select model class?
I am actually doing this right now too! :) I have 3 model classes, logistic, random forest and GP.
My design is this (with 5-fold crossvalidation):
training data set - optimize parameters and hyperparameters (not sure if we have the same definition of hyperparam... | Do I need a second validation set to select model class?
I am actually doing this right now too! :) I have 3 model classes, logistic, random forest and GP.
My design is this (with 5-fold crossvalidation):
training data set - optimize parameters and hyperpa |
35,885 | How to use PCA to detect outliers? | One approach is to consider outliers those points that can not be well reconstructed using the principal vectors that you have selected.
The procedure goes like this:
1.Fix two positive numbers, a and b (see the next steps for there meaning an to understand how to select them; to be refined using cross-validation).
Co... | How to use PCA to detect outliers? | One approach is to consider outliers those points that can not be well reconstructed using the principal vectors that you have selected.
The procedure goes like this:
1.Fix two positive numbers, a and | How to use PCA to detect outliers?
One approach is to consider outliers those points that can not be well reconstructed using the principal vectors that you have selected.
The procedure goes like this:
1.Fix two positive numbers, a and b (see the next steps for there meaning an to understand how to select them; to be r... | How to use PCA to detect outliers?
One approach is to consider outliers those points that can not be well reconstructed using the principal vectors that you have selected.
The procedure goes like this:
1.Fix two positive numbers, a and |
35,886 | advantages and disadvantages of IPTW vs propensity score matching? | Despite some similarities, propensity score matching (PSM) and inverse probability of treatment weighting (IPTW) behave differently, mainly because matching selects some cases/controls and discards others, while IPTW includes all study units.
The scholarly literature suggests indeed that PSM and IPTW have similar accur... | advantages and disadvantages of IPTW vs propensity score matching? | Despite some similarities, propensity score matching (PSM) and inverse probability of treatment weighting (IPTW) behave differently, mainly because matching selects some cases/controls and discards ot | advantages and disadvantages of IPTW vs propensity score matching?
Despite some similarities, propensity score matching (PSM) and inverse probability of treatment weighting (IPTW) behave differently, mainly because matching selects some cases/controls and discards others, while IPTW includes all study units.
The schola... | advantages and disadvantages of IPTW vs propensity score matching?
Despite some similarities, propensity score matching (PSM) and inverse probability of treatment weighting (IPTW) behave differently, mainly because matching selects some cases/controls and discards ot |
35,887 | advantages and disadvantages of IPTW vs propensity score matching? | The choice between propensity score matching and weighting seems to be a widely debated topic among statistical sholars. Some thoughts, after having read through many papers of infuriated statisticians:
Propensity score matching
Advantages:
Often used, thus familiar to non-statisticians
Simple and intuitive subject to... | advantages and disadvantages of IPTW vs propensity score matching? | The choice between propensity score matching and weighting seems to be a widely debated topic among statistical sholars. Some thoughts, after having read through many papers of infuriated statistician | advantages and disadvantages of IPTW vs propensity score matching?
The choice between propensity score matching and weighting seems to be a widely debated topic among statistical sholars. Some thoughts, after having read through many papers of infuriated statisticians:
Propensity score matching
Advantages:
Often used,... | advantages and disadvantages of IPTW vs propensity score matching?
The choice between propensity score matching and weighting seems to be a widely debated topic among statistical sholars. Some thoughts, after having read through many papers of infuriated statistician |
35,888 | KL divergence between gaussian and uniform distribution | The KL divergence
$$
KL\left(P \middle\| Q\right) = \int \log \frac{d P}{d Q }dP
$$
is only defined if the Radon-Nikodym derivative exists, which is when $P$ is dominated by $Q$ (written $P \ll Q$). This means that there can't be any sets $A$ where $P(A) > 0$ and $Q(A) = 0$, otherwise we would be dividing by zero.
In ... | KL divergence between gaussian and uniform distribution | The KL divergence
$$
KL\left(P \middle\| Q\right) = \int \log \frac{d P}{d Q }dP
$$
is only defined if the Radon-Nikodym derivative exists, which is when $P$ is dominated by $Q$ (written $P \ll Q$). | KL divergence between gaussian and uniform distribution
The KL divergence
$$
KL\left(P \middle\| Q\right) = \int \log \frac{d P}{d Q }dP
$$
is only defined if the Radon-Nikodym derivative exists, which is when $P$ is dominated by $Q$ (written $P \ll Q$). This means that there can't be any sets $A$ where $P(A) > 0$ and... | KL divergence between gaussian and uniform distribution
The KL divergence
$$
KL\left(P \middle\| Q\right) = \int \log \frac{d P}{d Q }dP
$$
is only defined if the Radon-Nikodym derivative exists, which is when $P$ is dominated by $Q$ (written $P \ll Q$). |
35,889 | KL divergence between gaussian and uniform distribution | How else can I calculate the distance of my gaussian to a 'maximum entropy' distribution if I can't use the uniform distribution?
You basically answered your question, you can use the entropy of the distribution as a measure of randomness. For a Gaussian distribution, it can be computed directly from the standard stan... | KL divergence between gaussian and uniform distribution | How else can I calculate the distance of my gaussian to a 'maximum entropy' distribution if I can't use the uniform distribution?
You basically answered your question, you can use the entropy of the | KL divergence between gaussian and uniform distribution
How else can I calculate the distance of my gaussian to a 'maximum entropy' distribution if I can't use the uniform distribution?
You basically answered your question, you can use the entropy of the distribution as a measure of randomness. For a Gaussian distribu... | KL divergence between gaussian and uniform distribution
How else can I calculate the distance of my gaussian to a 'maximum entropy' distribution if I can't use the uniform distribution?
You basically answered your question, you can use the entropy of the |
35,890 | Can small SGD batch size lead to faster overfitting? | Using "epoch" on the x-axis to compare "speed" of convergence while comparing different batch sizes makes no sense since the number of weight updates per epoch depends on the batch size. When using smaller batches, the learning algorithm performs more weight updates per epoch and it naturally it seems to converge faste... | Can small SGD batch size lead to faster overfitting? | Using "epoch" on the x-axis to compare "speed" of convergence while comparing different batch sizes makes no sense since the number of weight updates per epoch depends on the batch size. When using sm | Can small SGD batch size lead to faster overfitting?
Using "epoch" on the x-axis to compare "speed" of convergence while comparing different batch sizes makes no sense since the number of weight updates per epoch depends on the batch size. When using smaller batches, the learning algorithm performs more weight updates ... | Can small SGD batch size lead to faster overfitting?
Using "epoch" on the x-axis to compare "speed" of convergence while comparing different batch sizes makes no sense since the number of weight updates per epoch depends on the batch size. When using sm |
35,891 | How to approximate the student-t CDF at a point without the hypergeometric function? | The Wikipedia article on the $t$ distribution helpfully informs us that
If $X$ has a Student's t-distribution with degree of freedom $\nu$ then one can obtain a Beta distribution: $$\frac {\nu }{\nu +X^{2}}\sim \mathrm {B} \left({\frac {1}{2}},{\frac {\nu }{2}}\right).$$
Equivalently, $1-\nu/(\nu + X^2) = X^2/(\nu + ... | How to approximate the student-t CDF at a point without the hypergeometric function? | The Wikipedia article on the $t$ distribution helpfully informs us that
If $X$ has a Student's t-distribution with degree of freedom $\nu$ then one can obtain a Beta distribution: $$\frac {\nu }{\nu | How to approximate the student-t CDF at a point without the hypergeometric function?
The Wikipedia article on the $t$ distribution helpfully informs us that
If $X$ has a Student's t-distribution with degree of freedom $\nu$ then one can obtain a Beta distribution: $$\frac {\nu }{\nu +X^{2}}\sim \mathrm {B} \left({\fra... | How to approximate the student-t CDF at a point without the hypergeometric function?
The Wikipedia article on the $t$ distribution helpfully informs us that
If $X$ has a Student's t-distribution with degree of freedom $\nu$ then one can obtain a Beta distribution: $$\frac {\nu }{\nu |
35,892 | KNN parameter tuning with cross validation: score draw | This problem occurs when you have a small test set, which can cause multiple models to tie, by achieving the same number of correct predictions.
The method you said first should do. Because in CV each model sees each training sample once, I'd consider it unlikely for your 3 models to have the same accuracy. If this per... | KNN parameter tuning with cross validation: score draw | This problem occurs when you have a small test set, which can cause multiple models to tie, by achieving the same number of correct predictions.
The method you said first should do. Because in CV each | KNN parameter tuning with cross validation: score draw
This problem occurs when you have a small test set, which can cause multiple models to tie, by achieving the same number of correct predictions.
The method you said first should do. Because in CV each model sees each training sample once, I'd consider it unlikely f... | KNN parameter tuning with cross validation: score draw
This problem occurs when you have a small test set, which can cause multiple models to tie, by achieving the same number of correct predictions.
The method you said first should do. Because in CV each |
35,893 | KNN parameter tuning with cross validation: score draw | Occam's principle suggest's that you should go for the simplest model possible. So you should go for that one. But to get a better idea of the model's generalization, i would suggest you to use nested cross validation. | KNN parameter tuning with cross validation: score draw | Occam's principle suggest's that you should go for the simplest model possible. So you should go for that one. But to get a better idea of the model's generalization, i would suggest you to use nested | KNN parameter tuning with cross validation: score draw
Occam's principle suggest's that you should go for the simplest model possible. So you should go for that one. But to get a better idea of the model's generalization, i would suggest you to use nested cross validation. | KNN parameter tuning with cross validation: score draw
Occam's principle suggest's that you should go for the simplest model possible. So you should go for that one. But to get a better idea of the model's generalization, i would suggest you to use nested |
35,894 | Is there a universal approximation theorem for monotone functions? | I am not sure if a single hidden layer is sufficient, but it can be shown that if your input is in $\mathbb{R}^k$, you will need at most $k$ hidden layers. See Theorem 3.1 in https://ieeexplore.ieee.org/document/5443743
Theorem 3.1: For any continuous monotone nondecreasing
function $f : K \rightarrow \mathbb{R}$, ... | Is there a universal approximation theorem for monotone functions? | I am not sure if a single hidden layer is sufficient, but it can be shown that if your input is in $\mathbb{R}^k$, you will need at most $k$ hidden layers. See Theorem 3.1 in https://ieeexplore.ieee.o | Is there a universal approximation theorem for monotone functions?
I am not sure if a single hidden layer is sufficient, but it can be shown that if your input is in $\mathbb{R}^k$, you will need at most $k$ hidden layers. See Theorem 3.1 in https://ieeexplore.ieee.org/document/5443743
Theorem 3.1: For any continuous ... | Is there a universal approximation theorem for monotone functions?
I am not sure if a single hidden layer is sufficient, but it can be shown that if your input is in $\mathbb{R}^k$, you will need at most $k$ hidden layers. See Theorem 3.1 in https://ieeexplore.ieee.o |
35,895 | Are products of exchangeable RVs exchangeable? | The product does not have to be exchangeable. The following counterexample will show what can go wrong and why.
We will specify the joint distributions $P_1$ of $(X_1,Y_1)$ and $P_2$ of $(X_2,Y_2)$ and assume each of these bivariate random variables is independent. Thus, the $X_i$ will be exchangeable provided they a... | Are products of exchangeable RVs exchangeable? | The product does not have to be exchangeable. The following counterexample will show what can go wrong and why.
We will specify the joint distributions $P_1$ of $(X_1,Y_1)$ and $P_2$ of $(X_2,Y_2)$ a | Are products of exchangeable RVs exchangeable?
The product does not have to be exchangeable. The following counterexample will show what can go wrong and why.
We will specify the joint distributions $P_1$ of $(X_1,Y_1)$ and $P_2$ of $(X_2,Y_2)$ and assume each of these bivariate random variables is independent. Thus,... | Are products of exchangeable RVs exchangeable?
The product does not have to be exchangeable. The following counterexample will show what can go wrong and why.
We will specify the joint distributions $P_1$ of $(X_1,Y_1)$ and $P_2$ of $(X_2,Y_2)$ a |
35,896 | Are products of exchangeable RVs exchangeable? | No. Suppose that the sample space consists of three equally likely outomes for which $X$ takes values of
$$(1,0,0), (0,1,0), (0,0,1)$$
and for which $Y$ takes values of
$$(1,0,0), (0,0,1), (0,1,0).$$
Then $X_1,X_2,X_3$ are exchangeable and so are $Y_1,Y_2,Y_3$. But the corresponding values of $Z=(X_1 Y_1,\dots, X_3 Y... | Are products of exchangeable RVs exchangeable? | No. Suppose that the sample space consists of three equally likely outomes for which $X$ takes values of
$$(1,0,0), (0,1,0), (0,0,1)$$
and for which $Y$ takes values of
$$(1,0,0), (0,0,1), (0,1,0).$$ | Are products of exchangeable RVs exchangeable?
No. Suppose that the sample space consists of three equally likely outomes for which $X$ takes values of
$$(1,0,0), (0,1,0), (0,0,1)$$
and for which $Y$ takes values of
$$(1,0,0), (0,0,1), (0,1,0).$$
Then $X_1,X_2,X_3$ are exchangeable and so are $Y_1,Y_2,Y_3$. But the c... | Are products of exchangeable RVs exchangeable?
No. Suppose that the sample space consists of three equally likely outomes for which $X$ takes values of
$$(1,0,0), (0,1,0), (0,0,1)$$
and for which $Y$ takes values of
$$(1,0,0), (0,0,1), (0,1,0).$$ |
35,897 | McDonald's Omega: Assumptions, Coefficients and Interpretation | The topic is old, but the questions interesting, so I would like to include some of available information regarding some questions.
Statistical requirements/assumptions underlying Omega:
Omega and omega hierarchical are based on parameter estimates (i.e.,
estimates of factor loadings and factor variances) that are der... | McDonald's Omega: Assumptions, Coefficients and Interpretation | The topic is old, but the questions interesting, so I would like to include some of available information regarding some questions.
Statistical requirements/assumptions underlying Omega:
Omega and om | McDonald's Omega: Assumptions, Coefficients and Interpretation
The topic is old, but the questions interesting, so I would like to include some of available information regarding some questions.
Statistical requirements/assumptions underlying Omega:
Omega and omega hierarchical are based on parameter estimates (i.e.,
... | McDonald's Omega: Assumptions, Coefficients and Interpretation
The topic is old, but the questions interesting, so I would like to include some of available information regarding some questions.
Statistical requirements/assumptions underlying Omega:
Omega and om |
35,898 | McDonald's Omega: Assumptions, Coefficients and Interpretation | A useful source that alleviated some of my confusion around this topic was:
McNeish, Daniel. 2018. “Thanks Coefficient Alpha, We’ll Take It from
Here.” Psychological Methods 23(3):412–33. doi: 10.1037/met0000144.
One important note is that the Omega-function in the psych (refereed to as Revelle’s omega total. by the ... | McDonald's Omega: Assumptions, Coefficients and Interpretation | A useful source that alleviated some of my confusion around this topic was:
McNeish, Daniel. 2018. “Thanks Coefficient Alpha, We’ll Take It from
Here.” Psychological Methods 23(3):412–33. doi: 10.103 | McDonald's Omega: Assumptions, Coefficients and Interpretation
A useful source that alleviated some of my confusion around this topic was:
McNeish, Daniel. 2018. “Thanks Coefficient Alpha, We’ll Take It from
Here.” Psychological Methods 23(3):412–33. doi: 10.1037/met0000144.
One important note is that the Omega-funct... | McDonald's Omega: Assumptions, Coefficients and Interpretation
A useful source that alleviated some of my confusion around this topic was:
McNeish, Daniel. 2018. “Thanks Coefficient Alpha, We’ll Take It from
Here.” Psychological Methods 23(3):412–33. doi: 10.103 |
35,899 | Why does Off-Policy Monte Carlo Control only learn from the "Tails of Episodes"? | I still fail to see why all of the remaining actions after some point in an episode are guaranteed to be greedy,
It is not the case, there is no guarantee of any number of steps being greedy. The very last step can be non-greedy. In that case, then the only return that will get assessed in off-policy Monte Carlo cont... | Why does Off-Policy Monte Carlo Control only learn from the "Tails of Episodes"? | I still fail to see why all of the remaining actions after some point in an episode are guaranteed to be greedy,
It is not the case, there is no guarantee of any number of steps being greedy. The ve | Why does Off-Policy Monte Carlo Control only learn from the "Tails of Episodes"?
I still fail to see why all of the remaining actions after some point in an episode are guaranteed to be greedy,
It is not the case, there is no guarantee of any number of steps being greedy. The very last step can be non-greedy. In that... | Why does Off-Policy Monte Carlo Control only learn from the "Tails of Episodes"?
I still fail to see why all of the remaining actions after some point in an episode are guaranteed to be greedy,
It is not the case, there is no guarantee of any number of steps being greedy. The ve |
35,900 | Why does Off-Policy Monte Carlo Control only learn from the "Tails of Episodes"? | short
Lets say you recorded the following episode:
$$s_1, a_1^o, r_1,\quad s_2, a_2^o, r_2,\quad s_3, a_3^o, r_3,\quad s_4, a_4^p, r_4,\quad s_5, a_5^p, r_5,\quad s_6, a_6^p, r_6 $$
$a^o$ is an off-policy or non-greedy action and $a^p$ is the best action according to the current policy (greedy action).
If you lear... | Why does Off-Policy Monte Carlo Control only learn from the "Tails of Episodes"? | short
Lets say you recorded the following episode:
$$s_1, a_1^o, r_1,\quad s_2, a_2^o, r_2,\quad s_3, a_3^o, r_3,\quad s_4, a_4^p, r_4,\quad s_5, a_5^p, r_5,\quad s_6, a_6^p, r_6 $$
$a^o$ is an of | Why does Off-Policy Monte Carlo Control only learn from the "Tails of Episodes"?
short
Lets say you recorded the following episode:
$$s_1, a_1^o, r_1,\quad s_2, a_2^o, r_2,\quad s_3, a_3^o, r_3,\quad s_4, a_4^p, r_4,\quad s_5, a_5^p, r_5,\quad s_6, a_6^p, r_6 $$
$a^o$ is an off-policy or non-greedy action and $a^p$... | Why does Off-Policy Monte Carlo Control only learn from the "Tails of Episodes"?
short
Lets say you recorded the following episode:
$$s_1, a_1^o, r_1,\quad s_2, a_2^o, r_2,\quad s_3, a_3^o, r_3,\quad s_4, a_4^p, r_4,\quad s_5, a_5^p, r_5,\quad s_6, a_6^p, r_6 $$
$a^o$ is an of |
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