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 |
|---|---|---|---|---|---|---|
3,801 | Two-tailed tests... I'm just not convinced. What's the point? | Often a significance test is performed for the null hypothesis against an alternative hypothesis. This is when one-tailed versus two-tailed make a difference.
For p-values this (two or one sided) does not matter! The point is that you select a criterium that only occurs a fraction $\alpha$ of the time when the null h... | Two-tailed tests... I'm just not convinced. What's the point? | Often a significance test is performed for the null hypothesis against an alternative hypothesis. This is when one-tailed versus two-tailed make a difference.
For p-values this (two or one sided) do | Two-tailed tests... I'm just not convinced. What's the point?
Often a significance test is performed for the null hypothesis against an alternative hypothesis. This is when one-tailed versus two-tailed make a difference.
For p-values this (two or one sided) does not matter! The point is that you select a criterium th... | Two-tailed tests... I'm just not convinced. What's the point?
Often a significance test is performed for the null hypothesis against an alternative hypothesis. This is when one-tailed versus two-tailed make a difference.
For p-values this (two or one sided) do |
3,802 | Two-tailed tests... I'm just not convinced. What's the point? | So one more answer attempt:
I guess whether to take one-tailed or two-tailed depends completely on the Alternative hypothesis.
Consider the following example of testing mean in a t-test:
$H_0: \mu=0$
$H_a: \mu \neq 0$
Now if you observe a very negative sample mean or a very positive sample mean, your hypothesis is unl... | Two-tailed tests... I'm just not convinced. What's the point? | So one more answer attempt:
I guess whether to take one-tailed or two-tailed depends completely on the Alternative hypothesis.
Consider the following example of testing mean in a t-test:
$H_0: \mu=0$ | Two-tailed tests... I'm just not convinced. What's the point?
So one more answer attempt:
I guess whether to take one-tailed or two-tailed depends completely on the Alternative hypothesis.
Consider the following example of testing mean in a t-test:
$H_0: \mu=0$
$H_a: \mu \neq 0$
Now if you observe a very negative samp... | Two-tailed tests... I'm just not convinced. What's the point?
So one more answer attempt:
I guess whether to take one-tailed or two-tailed depends completely on the Alternative hypothesis.
Consider the following example of testing mean in a t-test:
$H_0: \mu=0$ |
3,803 | Two-tailed tests... I'm just not convinced. What's the point? | It's easy to see where the confusions comes from if you liberate yourself from a single dimension while remembering that a particular hypothesis you're testing is of significance of difference from 0. Whether your estimate $x$ is different from zero or not is your question here.
Ask yourself what would be the test if y... | Two-tailed tests... I'm just not convinced. What's the point? | It's easy to see where the confusions comes from if you liberate yourself from a single dimension while remembering that a particular hypothesis you're testing is of significance of difference from 0. | Two-tailed tests... I'm just not convinced. What's the point?
It's easy to see where the confusions comes from if you liberate yourself from a single dimension while remembering that a particular hypothesis you're testing is of significance of difference from 0. Whether your estimate $x$ is different from zero or not i... | Two-tailed tests... I'm just not convinced. What's the point?
It's easy to see where the confusions comes from if you liberate yourself from a single dimension while remembering that a particular hypothesis you're testing is of significance of difference from 0. |
3,804 | Are residuals "predicted minus actual" or "actual minus predicted" | The residuals are always actual minus predicted. The models are:
$$y=f(x;\beta)+\varepsilon$$
Hence, the residuals $\hat\varepsilon$, which are estimates of errors $\varepsilon$:
$$\hat\varepsilon=y-\hat y\\\hat y=f(x;\hat\beta)$$
I agree with @whuber that the sign doesn't really matter mathematically. It's just good t... | Are residuals "predicted minus actual" or "actual minus predicted" | The residuals are always actual minus predicted. The models are:
$$y=f(x;\beta)+\varepsilon$$
Hence, the residuals $\hat\varepsilon$, which are estimates of errors $\varepsilon$:
$$\hat\varepsilon=y-\ | Are residuals "predicted minus actual" or "actual minus predicted"
The residuals are always actual minus predicted. The models are:
$$y=f(x;\beta)+\varepsilon$$
Hence, the residuals $\hat\varepsilon$, which are estimates of errors $\varepsilon$:
$$\hat\varepsilon=y-\hat y\\\hat y=f(x;\hat\beta)$$
I agree with @whuber t... | Are residuals "predicted minus actual" or "actual minus predicted"
The residuals are always actual minus predicted. The models are:
$$y=f(x;\beta)+\varepsilon$$
Hence, the residuals $\hat\varepsilon$, which are estimates of errors $\varepsilon$:
$$\hat\varepsilon=y-\ |
3,805 | Are residuals "predicted minus actual" or "actual minus predicted" | I just came across a compelling reason for one answer to be the correct one.
Regression (and most statistical models of any sort) concern how the conditional distributions of a response depend on explanatory variables. An important element of the characterization of those distributions is some measure usually called "... | Are residuals "predicted minus actual" or "actual minus predicted" | I just came across a compelling reason for one answer to be the correct one.
Regression (and most statistical models of any sort) concern how the conditional distributions of a response depend on expl | Are residuals "predicted minus actual" or "actual minus predicted"
I just came across a compelling reason for one answer to be the correct one.
Regression (and most statistical models of any sort) concern how the conditional distributions of a response depend on explanatory variables. An important element of the chara... | Are residuals "predicted minus actual" or "actual minus predicted"
I just came across a compelling reason for one answer to be the correct one.
Regression (and most statistical models of any sort) concern how the conditional distributions of a response depend on expl |
3,806 | Are residuals "predicted minus actual" or "actual minus predicted" | Green & Tashman (2008, Foresight) report on a small survey on the analogous question for forecast errors. I'll summarize arguments for either convention as reported by them:
Arguments for "actual-predicted"
The statistical convention is $y=\hat{y}+\epsilon$.
At least one respondent from seismology wrote that this is a... | Are residuals "predicted minus actual" or "actual minus predicted" | Green & Tashman (2008, Foresight) report on a small survey on the analogous question for forecast errors. I'll summarize arguments for either convention as reported by them:
Arguments for "actual-pred | Are residuals "predicted minus actual" or "actual minus predicted"
Green & Tashman (2008, Foresight) report on a small survey on the analogous question for forecast errors. I'll summarize arguments for either convention as reported by them:
Arguments for "actual-predicted"
The statistical convention is $y=\hat{y}+\eps... | Are residuals "predicted minus actual" or "actual minus predicted"
Green & Tashman (2008, Foresight) report on a small survey on the analogous question for forecast errors. I'll summarize arguments for either convention as reported by them:
Arguments for "actual-pred |
3,807 | Are residuals "predicted minus actual" or "actual minus predicted" | Different terminology suggests different conventions. The term "residual" implies that it's what's left over after all the explanatory variables have been taken into account, i.e. actual-predicted. "Prediction error" implies that it's how much the prediction deviates from actual, i.e. prediction-actual.
One's conceptio... | Are residuals "predicted minus actual" or "actual minus predicted" | Different terminology suggests different conventions. The term "residual" implies that it's what's left over after all the explanatory variables have been taken into account, i.e. actual-predicted. "P | Are residuals "predicted minus actual" or "actual minus predicted"
Different terminology suggests different conventions. The term "residual" implies that it's what's left over after all the explanatory variables have been taken into account, i.e. actual-predicted. "Prediction error" implies that it's how much the predi... | Are residuals "predicted minus actual" or "actual minus predicted"
Different terminology suggests different conventions. The term "residual" implies that it's what's left over after all the explanatory variables have been taken into account, i.e. actual-predicted. "P |
3,808 | Are residuals "predicted minus actual" or "actual minus predicted" | The answer by @Aksakal is completely correct, but I'll just add one additional element that I find helps me (and my students).
The motto: Statistics is "perfect". As in, I can always provide the perfect prediction (I know some eye-brows are raising right about now...so hear me out).
I'm going to predict my observed v... | Are residuals "predicted minus actual" or "actual minus predicted" | The answer by @Aksakal is completely correct, but I'll just add one additional element that I find helps me (and my students).
The motto: Statistics is "perfect". As in, I can always provide the per | Are residuals "predicted minus actual" or "actual minus predicted"
The answer by @Aksakal is completely correct, but I'll just add one additional element that I find helps me (and my students).
The motto: Statistics is "perfect". As in, I can always provide the perfect prediction (I know some eye-brows are raising ri... | Are residuals "predicted minus actual" or "actual minus predicted"
The answer by @Aksakal is completely correct, but I'll just add one additional element that I find helps me (and my students).
The motto: Statistics is "perfect". As in, I can always provide the per |
3,809 | Are residuals "predicted minus actual" or "actual minus predicted" | $\newcommand{\e}{\varepsilon}$I'm going to use the particular case of least squares linear regression. If we take our model to be $Y = X\beta + \e$ then as @Aksakal points out we naturally end up with $\e = Y - X\beta$ so $\hat \e = Y - \hat Y$. If instead we take $Y = X\beta - \e$ as our model, which we are certainly ... | Are residuals "predicted minus actual" or "actual minus predicted" | $\newcommand{\e}{\varepsilon}$I'm going to use the particular case of least squares linear regression. If we take our model to be $Y = X\beta + \e$ then as @Aksakal points out we naturally end up with | Are residuals "predicted minus actual" or "actual minus predicted"
$\newcommand{\e}{\varepsilon}$I'm going to use the particular case of least squares linear regression. If we take our model to be $Y = X\beta + \e$ then as @Aksakal points out we naturally end up with $\e = Y - X\beta$ so $\hat \e = Y - \hat Y$. If inst... | Are residuals "predicted minus actual" or "actual minus predicted"
$\newcommand{\e}{\varepsilon}$I'm going to use the particular case of least squares linear regression. If we take our model to be $Y = X\beta + \e$ then as @Aksakal points out we naturally end up with |
3,810 | Are residuals "predicted minus actual" or "actual minus predicted" | For practical purposes it's better to calculate residuals as "actual minus predicted": When trying to guess what the physical cause of an outlier data point might be, it gives a better intuitive sense to have an unusually large positive observed value have a large positive residual, and this is precisely what you get w... | Are residuals "predicted minus actual" or "actual minus predicted" | For practical purposes it's better to calculate residuals as "actual minus predicted": When trying to guess what the physical cause of an outlier data point might be, it gives a better intuitive sense | Are residuals "predicted minus actual" or "actual minus predicted"
For practical purposes it's better to calculate residuals as "actual minus predicted": When trying to guess what the physical cause of an outlier data point might be, it gives a better intuitive sense to have an unusually large positive observed value h... | Are residuals "predicted minus actual" or "actual minus predicted"
For practical purposes it's better to calculate residuals as "actual minus predicted": When trying to guess what the physical cause of an outlier data point might be, it gives a better intuitive sense |
3,811 | Who created the first standard normal table? | Laplace was the first to recognize the need for tabulation, coming up with the approximation:
$$\begin{align}G(x)&=\int_x^\infty e^{-t^2}dt\\[2ex]&=\small \frac1 x- \frac{1}{2x^3}+\frac{1\cdot3}{4x^5} -\frac{1\cdot 3\cdot5}{8x^7}+\frac{1\cdot 3\cdot 5\cdot 7}{16x^9}+\cdots\tag{1}
\end{align}$$
The first modern table of... | Who created the first standard normal table? | Laplace was the first to recognize the need for tabulation, coming up with the approximation:
$$\begin{align}G(x)&=\int_x^\infty e^{-t^2}dt\\[2ex]&=\small \frac1 x- \frac{1}{2x^3}+\frac{1\cdot3}{4x^5} | Who created the first standard normal table?
Laplace was the first to recognize the need for tabulation, coming up with the approximation:
$$\begin{align}G(x)&=\int_x^\infty e^{-t^2}dt\\[2ex]&=\small \frac1 x- \frac{1}{2x^3}+\frac{1\cdot3}{4x^5} -\frac{1\cdot 3\cdot5}{8x^7}+\frac{1\cdot 3\cdot 5\cdot 7}{16x^9}+\cdots\t... | Who created the first standard normal table?
Laplace was the first to recognize the need for tabulation, coming up with the approximation:
$$\begin{align}G(x)&=\int_x^\infty e^{-t^2}dt\\[2ex]&=\small \frac1 x- \frac{1}{2x^3}+\frac{1\cdot3}{4x^5} |
3,812 | Who created the first standard normal table? | According to H.A. David [1] Laplace recognized the need for tables of the normal distribution "as early as 1783" and the first normal table was produced by Kramp in 1799.
Laplace suggested two series approximations, one for the integral from $0$ to $x$ of $e^{-t^2}$ (which is proportional to a normal distribution with... | Who created the first standard normal table? | According to H.A. David [1] Laplace recognized the need for tables of the normal distribution "as early as 1783" and the first normal table was produced by Kramp in 1799.
Laplace suggested two series | Who created the first standard normal table?
According to H.A. David [1] Laplace recognized the need for tables of the normal distribution "as early as 1783" and the first normal table was produced by Kramp in 1799.
Laplace suggested two series approximations, one for the integral from $0$ to $x$ of $e^{-t^2}$ (which ... | Who created the first standard normal table?
According to H.A. David [1] Laplace recognized the need for tables of the normal distribution "as early as 1783" and the first normal table was produced by Kramp in 1799.
Laplace suggested two series |
3,813 | Who created the first standard normal table? | Interesting issue! I think the first idea did not come through the integration of complex formula; rather, the result of applying the asymptotics in combinatorics. Pen and paper method may take several weeks; not so tough for Karl Gauss compared to calculation of pie for his predecessors. I think Gauss's idea was coura... | Who created the first standard normal table? | Interesting issue! I think the first idea did not come through the integration of complex formula; rather, the result of applying the asymptotics in combinatorics. Pen and paper method may take severa | Who created the first standard normal table?
Interesting issue! I think the first idea did not come through the integration of complex formula; rather, the result of applying the asymptotics in combinatorics. Pen and paper method may take several weeks; not so tough for Karl Gauss compared to calculation of pie for his... | Who created the first standard normal table?
Interesting issue! I think the first idea did not come through the integration of complex formula; rather, the result of applying the asymptotics in combinatorics. Pen and paper method may take severa |
3,814 | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)? | It shouldn't matter that much since the test statistic will always be the difference in means (or something equivalent). Small differences can come from the implementation of Monte-Carlo methods. Trying the three packages with your data with a one-sided test for two independent variables:
DV <- c(x1, y1)
IV <- factor(r... | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)? | It shouldn't matter that much since the test statistic will always be the difference in means (or something equivalent). Small differences can come from the implementation of Monte-Carlo methods. Tryi | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)?
It shouldn't matter that much since the test statistic will always be the difference in means (or something equivalent). Small differences can come from the implementation of Monte-Carlo methods. Trying the three packages with... | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)?
It shouldn't matter that much since the test statistic will always be the difference in means (or something equivalent). Small differences can come from the implementation of Monte-Carlo methods. Tryi |
3,815 | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)? | A few comments are, I believe, in order.
1) I would encourage you to try multiple visual displays of your data, because they can capture things that are lost by (graphs like) histograms, and I also strongly recommend that you plot on side-by-side axes. In this case, I do not believe the histograms do a very good job o... | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)? | A few comments are, I believe, in order.
1) I would encourage you to try multiple visual displays of your data, because they can capture things that are lost by (graphs like) histograms, and I also st | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)?
A few comments are, I believe, in order.
1) I would encourage you to try multiple visual displays of your data, because they can capture things that are lost by (graphs like) histograms, and I also strongly recommend that you ... | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)?
A few comments are, I believe, in order.
1) I would encourage you to try multiple visual displays of your data, because they can capture things that are lost by (graphs like) histograms, and I also st |
3,816 | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)? | My comments are not about implementation of the permutation test but about the more general issues raised by these data and the discussion of it, in particular the post by G. Jay Kerns.
The two distributions actually look quite similar to me EXCEPT for the group of 0s in Y1, which are much different from the other obse... | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)? | My comments are not about implementation of the permutation test but about the more general issues raised by these data and the discussion of it, in particular the post by G. Jay Kerns.
The two distri | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)?
My comments are not about implementation of the permutation test but about the more general issues raised by these data and the discussion of it, in particular the post by G. Jay Kerns.
The two distributions actually look quit... | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)?
My comments are not about implementation of the permutation test but about the more general issues raised by these data and the discussion of it, in particular the post by G. Jay Kerns.
The two distri |
3,817 | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)? | As this question did pop up again, I may add another answer inspired by a recent blog post via R-Bloggers from Robert Kabacoff, the author of Quick-R and R in Action using the lmPerm package.
However, this methods produces sharply contrasting (and very unstable) results to the one produced by the coin package in the an... | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)? | As this question did pop up again, I may add another answer inspired by a recent blog post via R-Bloggers from Robert Kabacoff, the author of Quick-R and R in Action using the lmPerm package.
However, | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)?
As this question did pop up again, I may add another answer inspired by a recent blog post via R-Bloggers from Robert Kabacoff, the author of Quick-R and R in Action using the lmPerm package.
However, this methods produces sha... | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)?
As this question did pop up again, I may add another answer inspired by a recent blog post via R-Bloggers from Robert Kabacoff, the author of Quick-R and R in Action using the lmPerm package.
However, |
3,818 | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)? | Are these scores proportions? If so, you certainly shouldn't be using a gaussian parametric test, and while you could go ahead with a non-parametric approach like a permutation test or bootstrap of the means, I'd suggest that you'll get more statistical power by employing a suitable non-gaussian parametric approach. Sp... | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)? | Are these scores proportions? If so, you certainly shouldn't be using a gaussian parametric test, and while you could go ahead with a non-parametric approach like a permutation test or bootstrap of th | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)?
Are these scores proportions? If so, you certainly shouldn't be using a gaussian parametric test, and while you could go ahead with a non-parametric approach like a permutation test or bootstrap of the means, I'd suggest that ... | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)?
Are these scores proportions? If so, you certainly shouldn't be using a gaussian parametric test, and while you could go ahead with a non-parametric approach like a permutation test or bootstrap of th |
3,819 | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)? | Just adding another approach, ezPerm of ez package:
> # preparing the data
> DV <- c(x1, y1)
> IV <- factor(rep(c("A", "B"), c(length(x1), length(y1))))
> id <- factor(rep(1:length(x1), 2))
> df <- data.frame(id=id,DV=DV,IV=IV)
>
> library(ez)
> ezPerm( data = df, dv = DV, wid = id, within = IV, perms = 1000)
|========... | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)? | Just adding another approach, ezPerm of ez package:
> # preparing the data
> DV <- c(x1, y1)
> IV <- factor(rep(c("A", "B"), c(length(x1), length(y1))))
> id <- factor(rep(1:length(x1), 2))
> df <- da | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)?
Just adding another approach, ezPerm of ez package:
> # preparing the data
> DV <- c(x1, y1)
> IV <- factor(rep(c("A", "B"), c(length(x1), length(y1))))
> id <- factor(rep(1:length(x1), 2))
> df <- data.frame(id=id,DV=DV,IV=IV... | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)?
Just adding another approach, ezPerm of ez package:
> # preparing the data
> DV <- c(x1, y1)
> IV <- factor(rep(c("A", "B"), c(length(x1), length(y1))))
> id <- factor(rep(1:length(x1), 2))
> df <- da |
3,820 | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)? | One more example: MKinfer::perm.t.test(). It's quite fast.
I don't know which one of the above it matches, because neither of you set the seed, so the results will never be well comparable. I use 1000.
> set.seed(1000)
> MKinfer::perm.t.test(x1, y1)
Permutation Welch Two Sample t-test
data: x1 and y1
(Monte-Carl... | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)? | One more example: MKinfer::perm.t.test(). It's quite fast.
I don't know which one of the above it matches, because neither of you set the seed, so the results will never be well comparable. I use 1000 | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)?
One more example: MKinfer::perm.t.test(). It's quite fast.
I don't know which one of the above it matches, because neither of you set the seed, so the results will never be well comparable. I use 1000.
> set.seed(1000)
> MKinf... | Which permutation test implementation in R to use instead of t-tests (paired and non-paired)?
One more example: MKinfer::perm.t.test(). It's quite fast.
I don't know which one of the above it matches, because neither of you set the seed, so the results will never be well comparable. I use 1000 |
3,821 | Is a sample covariance matrix always symmetric and positive definite? | For a sample of vectors $x_i=(x_{i1},\dots,x_{ik})^\top$, with $i=1,\dots,n$, the sample mean vector is
$$
\bar{x}=\frac{1}{n} \sum_{i=1}^n x_i \, ,
$$ and the sample covariance matrix is
$$
Q = \frac{1}{n} \sum_{i=1}^n (x_i-\bar{x})(x_i-\bar{x})^\top \, .
$$
For a nonzero vector $y\in\mathbb{R}^k$, we have
$$
y... | Is a sample covariance matrix always symmetric and positive definite? | For a sample of vectors $x_i=(x_{i1},\dots,x_{ik})^\top$, with $i=1,\dots,n$, the sample mean vector is
$$
\bar{x}=\frac{1}{n} \sum_{i=1}^n x_i \, ,
$$ and the sample covariance matrix is
$$
Q = | Is a sample covariance matrix always symmetric and positive definite?
For a sample of vectors $x_i=(x_{i1},\dots,x_{ik})^\top$, with $i=1,\dots,n$, the sample mean vector is
$$
\bar{x}=\frac{1}{n} \sum_{i=1}^n x_i \, ,
$$ and the sample covariance matrix is
$$
Q = \frac{1}{n} \sum_{i=1}^n (x_i-\bar{x})(x_i-\bar{x}... | Is a sample covariance matrix always symmetric and positive definite?
For a sample of vectors $x_i=(x_{i1},\dots,x_{ik})^\top$, with $i=1,\dots,n$, the sample mean vector is
$$
\bar{x}=\frac{1}{n} \sum_{i=1}^n x_i \, ,
$$ and the sample covariance matrix is
$$
Q = |
3,822 | Is a sample covariance matrix always symmetric and positive definite? | A correct covariance matrix is always symmetric and positive *semi*definite.
The covariance between two variables is defied as $\sigma(x,y) = E [(x-E(x))(y-E(y))]$.
This equation doesn't change if you switch the positions of $x$ and $y$. Hence the matrix has to be symmetric.
It also has to be positive *semi-*definite b... | Is a sample covariance matrix always symmetric and positive definite? | A correct covariance matrix is always symmetric and positive *semi*definite.
The covariance between two variables is defied as $\sigma(x,y) = E [(x-E(x))(y-E(y))]$.
This equation doesn't change if you | Is a sample covariance matrix always symmetric and positive definite?
A correct covariance matrix is always symmetric and positive *semi*definite.
The covariance between two variables is defied as $\sigma(x,y) = E [(x-E(x))(y-E(y))]$.
This equation doesn't change if you switch the positions of $x$ and $y$. Hence the ma... | Is a sample covariance matrix always symmetric and positive definite?
A correct covariance matrix is always symmetric and positive *semi*definite.
The covariance between two variables is defied as $\sigma(x,y) = E [(x-E(x))(y-E(y))]$.
This equation doesn't change if you |
3,823 | Is a sample covariance matrix always symmetric and positive definite? | @Zen's answer plus @whuber's comment to @Konstantin's answer provide a complete proof. Nevertheless, I'll rephrase the proof by trying to place more statistical emphasis.
Indeed, one can say that the sample covariance matrix $S$ is always positive and semi-definite because it can be seen as the variance of a suitable u... | Is a sample covariance matrix always symmetric and positive definite? | @Zen's answer plus @whuber's comment to @Konstantin's answer provide a complete proof. Nevertheless, I'll rephrase the proof by trying to place more statistical emphasis.
Indeed, one can say that the | Is a sample covariance matrix always symmetric and positive definite?
@Zen's answer plus @whuber's comment to @Konstantin's answer provide a complete proof. Nevertheless, I'll rephrase the proof by trying to place more statistical emphasis.
Indeed, one can say that the sample covariance matrix $S$ is always positive an... | Is a sample covariance matrix always symmetric and positive definite?
@Zen's answer plus @whuber's comment to @Konstantin's answer provide a complete proof. Nevertheless, I'll rephrase the proof by trying to place more statistical emphasis.
Indeed, one can say that the |
3,824 | Is a sample covariance matrix always symmetric and positive definite? | Let
$$
X=
\begin{pmatrix}
x_{11} & x_{12} & \cdots & x_{1k} \\
x_{21} & x_{22} & \cdots & x_{2k} \\
\vdots & \vdots & \ddots & \vdots\\
x_{n1} & x_{n2} & \cdots & x_{nk}
\end{pmatrix}
$$
denote the data matrix whose $\left(i,j\right)$-th entry is the $i$-th measurement of the $j$-th variable (with $i \in \{1,\ldots, n\... | Is a sample covariance matrix always symmetric and positive definite? | Let
$$
X=
\begin{pmatrix}
x_{11} & x_{12} & \cdots & x_{1k} \\
x_{21} & x_{22} & \cdots & x_{2k} \\
\vdots & \vdots & \ddots & \vdots\\
x_{n1} & x_{n2} & \cdots & x_{nk}
\end{pmatrix}
$$
denote the da | Is a sample covariance matrix always symmetric and positive definite?
Let
$$
X=
\begin{pmatrix}
x_{11} & x_{12} & \cdots & x_{1k} \\
x_{21} & x_{22} & \cdots & x_{2k} \\
\vdots & \vdots & \ddots & \vdots\\
x_{n1} & x_{n2} & \cdots & x_{nk}
\end{pmatrix}
$$
denote the data matrix whose $\left(i,j\right)$-th entry is the... | Is a sample covariance matrix always symmetric and positive definite?
Let
$$
X=
\begin{pmatrix}
x_{11} & x_{12} & \cdots & x_{1k} \\
x_{21} & x_{22} & \cdots & x_{2k} \\
\vdots & \vdots & \ddots & \vdots\\
x_{n1} & x_{n2} & \cdots & x_{nk}
\end{pmatrix}
$$
denote the da |
3,825 | Is a sample covariance matrix always symmetric and positive definite? | I would add to the nice argument of Zen the following which explains why we often say that the covariance matrix is positive definite if $n-1\geq k$.
If $x_1,x_2,...,x_n$ are a random sample of a continuous probability distribution then $x_1,x_2,...,x_n$ are almost surely (in the probability theory sense) linearly inde... | Is a sample covariance matrix always symmetric and positive definite? | I would add to the nice argument of Zen the following which explains why we often say that the covariance matrix is positive definite if $n-1\geq k$.
If $x_1,x_2,...,x_n$ are a random sample of a cont | Is a sample covariance matrix always symmetric and positive definite?
I would add to the nice argument of Zen the following which explains why we often say that the covariance matrix is positive definite if $n-1\geq k$.
If $x_1,x_2,...,x_n$ are a random sample of a continuous probability distribution then $x_1,x_2,...,... | Is a sample covariance matrix always symmetric and positive definite?
I would add to the nice argument of Zen the following which explains why we often say that the covariance matrix is positive definite if $n-1\geq k$.
If $x_1,x_2,...,x_n$ are a random sample of a cont |
3,826 | Recommended books on experiment design? | for me, the best book around is by George Box:
Statistics for Experimenters: Design, Innovation, and Discovery
of course the book by Maxwell and Delaney is also pretty good:
Designing Experiments and Analyzing Data: A Model Comparison Perspective, Second Edition
I personally prefer the first, but they are both top qua... | Recommended books on experiment design? | for me, the best book around is by George Box:
Statistics for Experimenters: Design, Innovation, and Discovery
of course the book by Maxwell and Delaney is also pretty good:
Designing Experiments and | Recommended books on experiment design?
for me, the best book around is by George Box:
Statistics for Experimenters: Design, Innovation, and Discovery
of course the book by Maxwell and Delaney is also pretty good:
Designing Experiments and Analyzing Data: A Model Comparison Perspective, Second Edition
I personally pre... | Recommended books on experiment design?
for me, the best book around is by George Box:
Statistics for Experimenters: Design, Innovation, and Discovery
of course the book by Maxwell and Delaney is also pretty good:
Designing Experiments and |
3,827 | Recommended books on experiment design? | Montgomery's Design and Analysis of Experiments is a classic and highly regarded text:
If you are interested in experimental design in a particular field (eg. clinical trials) other more specialised texts may be appropriate. | Recommended books on experiment design? | Montgomery's Design and Analysis of Experiments is a classic and highly regarded text:
If you are interested in experimental design in a particular field (eg. clinical trials) other more specialised t | Recommended books on experiment design?
Montgomery's Design and Analysis of Experiments is a classic and highly regarded text:
If you are interested in experimental design in a particular field (eg. clinical trials) other more specialised texts may be appropriate. | Recommended books on experiment design?
Montgomery's Design and Analysis of Experiments is a classic and highly regarded text:
If you are interested in experimental design in a particular field (eg. clinical trials) other more specialised t |
3,828 | Recommended books on experiment design? | Ronald Fisher's The Design of Experiments (link is Wikipedia rather than Amazon since it is long out of print) is interesting for historical context. The book is often credited as founding the whole field, and certainly did a lot to promote things like blocking, randomisation and factorial design, though things have mo... | Recommended books on experiment design? | Ronald Fisher's The Design of Experiments (link is Wikipedia rather than Amazon since it is long out of print) is interesting for historical context. The book is often credited as founding the whole f | Recommended books on experiment design?
Ronald Fisher's The Design of Experiments (link is Wikipedia rather than Amazon since it is long out of print) is interesting for historical context. The book is often credited as founding the whole field, and certainly did a lot to promote things like blocking, randomisation and... | Recommended books on experiment design?
Ronald Fisher's The Design of Experiments (link is Wikipedia rather than Amazon since it is long out of print) is interesting for historical context. The book is often credited as founding the whole f |
3,829 | Recommended books on experiment design? | I am surprise no one mentioned: Statistical Design by George Casella
Google Books Link | Recommended books on experiment design? | I am surprise no one mentioned: Statistical Design by George Casella
Google Books Link | Recommended books on experiment design?
I am surprise no one mentioned: Statistical Design by George Casella
Google Books Link | Recommended books on experiment design?
I am surprise no one mentioned: Statistical Design by George Casella
Google Books Link |
3,830 | Recommended books on experiment design? | There are many excellent books on design of experiments. These procedures apply generally and I do not think there are special designs specific to bakery applications. Here are a few of my favorites.
Statistics for Experimenters: Design, Innovation, and Discovery , 2nd Edition [Hardcover] George E. P. Box (Author) J... | Recommended books on experiment design? | There are many excellent books on design of experiments. These procedures apply generally and I do not think there are special designs specific to bakery applications. Here are a few of my favorites | Recommended books on experiment design?
There are many excellent books on design of experiments. These procedures apply generally and I do not think there are special designs specific to bakery applications. Here are a few of my favorites.
Statistics for Experimenters: Design, Innovation, and Discovery , 2nd Edition... | Recommended books on experiment design?
There are many excellent books on design of experiments. These procedures apply generally and I do not think there are special designs specific to bakery applications. Here are a few of my favorites |
3,831 | Recommended books on experiment design? | Not published yet, but I'm impatient for Design and analysis of experiments with R
There are not enough books on DoE with R. I'm very reluctant to proprietary software, and R documentation is not always the best | Recommended books on experiment design? | Not published yet, but I'm impatient for Design and analysis of experiments with R
There are not enough books on DoE with R. I'm very reluctant to proprietary software, and R documentation is not alwa | Recommended books on experiment design?
Not published yet, but I'm impatient for Design and analysis of experiments with R
There are not enough books on DoE with R. I'm very reluctant to proprietary software, and R documentation is not always the best | Recommended books on experiment design?
Not published yet, but I'm impatient for Design and analysis of experiments with R
There are not enough books on DoE with R. I'm very reluctant to proprietary software, and R documentation is not alwa |
3,832 | Recommended books on experiment design? | Experiments: Planning, Analysis and Optimization by Wu & Hamada.
I'm only a couple of chapters in, so not yet in a position to recommend confidently, but so far it looks like a good graduate text, reasonably detailed, comprehensive and up-to-date. Has more of a "no nonsense" feel than the Montgomery. | Recommended books on experiment design? | Experiments: Planning, Analysis and Optimization by Wu & Hamada.
I'm only a couple of chapters in, so not yet in a position to recommend confidently, but so far it looks like a good graduate text, rea | Recommended books on experiment design?
Experiments: Planning, Analysis and Optimization by Wu & Hamada.
I'm only a couple of chapters in, so not yet in a position to recommend confidently, but so far it looks like a good graduate text, reasonably detailed, comprehensive and up-to-date. Has more of a "no nonsense" feel... | Recommended books on experiment design?
Experiments: Planning, Analysis and Optimization by Wu & Hamada.
I'm only a couple of chapters in, so not yet in a position to recommend confidently, but so far it looks like a good graduate text, rea |
3,833 | Recommended books on experiment design? | Experimental Design for the Life Sciences, by Ruxton & Colegrave. Aimed primarily at undergraduates. | Recommended books on experiment design? | Experimental Design for the Life Sciences, by Ruxton & Colegrave. Aimed primarily at undergraduates. | Recommended books on experiment design?
Experimental Design for the Life Sciences, by Ruxton & Colegrave. Aimed primarily at undergraduates. | Recommended books on experiment design?
Experimental Design for the Life Sciences, by Ruxton & Colegrave. Aimed primarily at undergraduates. |
3,834 | Recommended books on experiment design? | If you're interested in pharmaceutical trials, two books I recommend:
Statistical Issues in Drug Development by Stephen Senn (Amazon link)
Cross-over Trials in Clinical Research by Stephen Senn (Amazon link) | Recommended books on experiment design? | If you're interested in pharmaceutical trials, two books I recommend:
Statistical Issues in Drug Development by Stephen Senn (Amazon link)
Cross-over Trials in Clinical Research by Stephen Senn (Amaz | Recommended books on experiment design?
If you're interested in pharmaceutical trials, two books I recommend:
Statistical Issues in Drug Development by Stephen Senn (Amazon link)
Cross-over Trials in Clinical Research by Stephen Senn (Amazon link) | Recommended books on experiment design?
If you're interested in pharmaceutical trials, two books I recommend:
Statistical Issues in Drug Development by Stephen Senn (Amazon link)
Cross-over Trials in Clinical Research by Stephen Senn (Amaz |
3,835 | Recommended books on experiment design? | Not really a book but a gentle introduction on DoE in R: An R companion to Experimental Design. | Recommended books on experiment design? | Not really a book but a gentle introduction on DoE in R: An R companion to Experimental Design. | Recommended books on experiment design?
Not really a book but a gentle introduction on DoE in R: An R companion to Experimental Design. | Recommended books on experiment design?
Not really a book but a gentle introduction on DoE in R: An R companion to Experimental Design. |
3,836 | Recommended books on experiment design? | If your field is biology/ecology, a nice and well written text is "Experimental Design and Data Analysis for Biologists" of Quinn and Keough (amazon
the work done by Underwood is also very interesting to read:
Experiments in Ecology: Their Logical Design and Interpretation Using Analysis of Variance (amazon) | Recommended books on experiment design? | If your field is biology/ecology, a nice and well written text is "Experimental Design and Data Analysis for Biologists" of Quinn and Keough (amazon
the work done by Underwood is also very interestin | Recommended books on experiment design?
If your field is biology/ecology, a nice and well written text is "Experimental Design and Data Analysis for Biologists" of Quinn and Keough (amazon
the work done by Underwood is also very interesting to read:
Experiments in Ecology: Their Logical Design and Interpretation Using... | Recommended books on experiment design?
If your field is biology/ecology, a nice and well written text is "Experimental Design and Data Analysis for Biologists" of Quinn and Keough (amazon
the work done by Underwood is also very interestin |
3,837 | Recommended books on experiment design? | The Design of Experiments: Statistical Principles for Practical Applications by Roger Mead. Examples are drawn from agriculture and biology, so probably most appropriate if you're interested in one of those fields. Rather expensive for a 600-page paperback but you can probably find it second-hand. | Recommended books on experiment design? | The Design of Experiments: Statistical Principles for Practical Applications by Roger Mead. Examples are drawn from agriculture and biology, so probably most appropriate if you're interested in one of | Recommended books on experiment design?
The Design of Experiments: Statistical Principles for Practical Applications by Roger Mead. Examples are drawn from agriculture and biology, so probably most appropriate if you're interested in one of those fields. Rather expensive for a 600-page paperback but you can probably fi... | Recommended books on experiment design?
The Design of Experiments: Statistical Principles for Practical Applications by Roger Mead. Examples are drawn from agriculture and biology, so probably most appropriate if you're interested in one of |
3,838 | Recommended books on experiment design? | Experimental Design in Biotechnology by Perry D. Haaland, ed Marcel Dekker. | Recommended books on experiment design? | Experimental Design in Biotechnology by Perry D. Haaland, ed Marcel Dekker. | Recommended books on experiment design?
Experimental Design in Biotechnology by Perry D. Haaland, ed Marcel Dekker. | Recommended books on experiment design?
Experimental Design in Biotechnology by Perry D. Haaland, ed Marcel Dekker. |
3,839 | Recommended books on experiment design? | If you're in the social sciences:
Using Randomization in Development Economics Research: A Toolkit | Recommended books on experiment design? | If you're in the social sciences:
Using Randomization in Development Economics Research: A Toolkit | Recommended books on experiment design?
If you're in the social sciences:
Using Randomization in Development Economics Research: A Toolkit | Recommended books on experiment design?
If you're in the social sciences:
Using Randomization in Development Economics Research: A Toolkit |
3,840 | Recommended books on experiment design? | I have recently reviewed a large collection of DoE books (17), with the following requirements:
Not a cookbook approach but geared towards understanding (hard requirement)
Decently in-depth (hard requirement)
Written with an understanding of the New Causal Revolution (nice-to-have)
Uses Hasse diagrams to simplify unde... | Recommended books on experiment design? | I have recently reviewed a large collection of DoE books (17), with the following requirements:
Not a cookbook approach but geared towards understanding (hard requirement)
Decently in-depth (hard req | Recommended books on experiment design?
I have recently reviewed a large collection of DoE books (17), with the following requirements:
Not a cookbook approach but geared towards understanding (hard requirement)
Decently in-depth (hard requirement)
Written with an understanding of the New Causal Revolution (nice-to-ha... | Recommended books on experiment design?
I have recently reviewed a large collection of DoE books (17), with the following requirements:
Not a cookbook approach but geared towards understanding (hard requirement)
Decently in-depth (hard req |
3,841 | Recommended books on experiment design? | This book gives you a statistical perspective on experimental design:
Casella, G. (2008). Statistical Design. Springer. | Recommended books on experiment design? | This book gives you a statistical perspective on experimental design:
Casella, G. (2008). Statistical Design. Springer. | Recommended books on experiment design?
This book gives you a statistical perspective on experimental design:
Casella, G. (2008). Statistical Design. Springer. | Recommended books on experiment design?
This book gives you a statistical perspective on experimental design:
Casella, G. (2008). Statistical Design. Springer. |
3,842 | Recommended books on experiment design? | Hands on DOE book
John Lawson has written two books.
Design and Analysis of Experiments with SAS
Design and Analysis of Experiments with R
One is for SAS users and another one for R users. Both the version are same in content and context, the only difference is the software used in the book. Second one which is for ... | Recommended books on experiment design? | Hands on DOE book
John Lawson has written two books.
Design and Analysis of Experiments with SAS
Design and Analysis of Experiments with R
One is for SAS users and another one for R users. Both the | Recommended books on experiment design?
Hands on DOE book
John Lawson has written two books.
Design and Analysis of Experiments with SAS
Design and Analysis of Experiments with R
One is for SAS users and another one for R users. Both the version are same in content and context, the only difference is the software us... | Recommended books on experiment design?
Hands on DOE book
John Lawson has written two books.
Design and Analysis of Experiments with SAS
Design and Analysis of Experiments with R
One is for SAS users and another one for R users. Both the |
3,843 | Recommended books on experiment design? | A contemporary reference that I've found really useful is
"Randomization in Clinical Trials" by Rosenberger and Lachin
While the focus is on randomized trials and in-human studies, it covers many topics not previously covered in a nice, codified reference (group sequential designs, covariate adaptive designs, causality... | Recommended books on experiment design? | A contemporary reference that I've found really useful is
"Randomization in Clinical Trials" by Rosenberger and Lachin
While the focus is on randomized trials and in-human studies, it covers many topi | Recommended books on experiment design?
A contemporary reference that I've found really useful is
"Randomization in Clinical Trials" by Rosenberger and Lachin
While the focus is on randomized trials and in-human studies, it covers many topics not previously covered in a nice, codified reference (group sequential design... | Recommended books on experiment design?
A contemporary reference that I've found really useful is
"Randomization in Clinical Trials" by Rosenberger and Lachin
While the focus is on randomized trials and in-human studies, it covers many topi |
3,844 | Is every covariance matrix positive definite? | No.
Consider three variables, $X$, $Y$ and $Z = X+Y$. Their covariance matrix, $M$, is not positive definite, since there's a vector $z$ ($= (1, 1, -1)'$) for which $z'Mz$ is not positive.
Population covariance matrices are positive semi-definite.
(See property 2 here.)
The same should generally apply to covariance ma... | Is every covariance matrix positive definite? | No.
Consider three variables, $X$, $Y$ and $Z = X+Y$. Their covariance matrix, $M$, is not positive definite, since there's a vector $z$ ($= (1, 1, -1)'$) for which $z'Mz$ is not positive.
Population | Is every covariance matrix positive definite?
No.
Consider three variables, $X$, $Y$ and $Z = X+Y$. Their covariance matrix, $M$, is not positive definite, since there's a vector $z$ ($= (1, 1, -1)'$) for which $z'Mz$ is not positive.
Population covariance matrices are positive semi-definite.
(See property 2 here.)
Th... | Is every covariance matrix positive definite?
No.
Consider three variables, $X$, $Y$ and $Z = X+Y$. Their covariance matrix, $M$, is not positive definite, since there's a vector $z$ ($= (1, 1, -1)'$) for which $z'Mz$ is not positive.
Population |
3,845 | Is every covariance matrix positive definite? | Well, to understand why the covariance matrix of a population is always positive semi-definite, notice that:
$$
\sum_{i,j =1}^{n} y_i \cdot y_j \cdot Cov(X_i, X_j) = Var(\sum_{i=1}^n y_iX_i) \geq 0
$$
where $y_i$ are some real numbers, and $X_i$ are some real valued random variables.
This also explains why in the examp... | Is every covariance matrix positive definite? | Well, to understand why the covariance matrix of a population is always positive semi-definite, notice that:
$$
\sum_{i,j =1}^{n} y_i \cdot y_j \cdot Cov(X_i, X_j) = Var(\sum_{i=1}^n y_iX_i) \geq 0
$$ | Is every covariance matrix positive definite?
Well, to understand why the covariance matrix of a population is always positive semi-definite, notice that:
$$
\sum_{i,j =1}^{n} y_i \cdot y_j \cdot Cov(X_i, X_j) = Var(\sum_{i=1}^n y_iX_i) \geq 0
$$
where $y_i$ are some real numbers, and $X_i$ are some real valued random ... | Is every covariance matrix positive definite?
Well, to understand why the covariance matrix of a population is always positive semi-definite, notice that:
$$
\sum_{i,j =1}^{n} y_i \cdot y_j \cdot Cov(X_i, X_j) = Var(\sum_{i=1}^n y_iX_i) \geq 0
$$ |
3,846 | Is every covariance matrix positive definite? | As the other answer note, the covariance matrix is positive semi-definite (which I prefer to call non-negative definite), but not necessarily positive definite. We can show that the covariance matrix is positive semi-definite from first principles using its definition. To do this, suppose we consider a random vector ... | Is every covariance matrix positive definite? | As the other answer note, the covariance matrix is positive semi-definite (which I prefer to call non-negative definite), but not necessarily positive definite. We can show that the covariance matrix | Is every covariance matrix positive definite?
As the other answer note, the covariance matrix is positive semi-definite (which I prefer to call non-negative definite), but not necessarily positive definite. We can show that the covariance matrix is positive semi-definite from first principles using its definition. To... | Is every covariance matrix positive definite?
As the other answer note, the covariance matrix is positive semi-definite (which I prefer to call non-negative definite), but not necessarily positive definite. We can show that the covariance matrix |
3,847 | Is every covariance matrix positive definite? | As the other answers already make clear, a covariance matrix is not necessarily positive definite, but only positive semi-definite.
However, a covariance matrix is generally positive definite unless the space spanned by the variables is actually a linear subspace of lower dimension. This is exactly why in the example w... | Is every covariance matrix positive definite? | As the other answers already make clear, a covariance matrix is not necessarily positive definite, but only positive semi-definite.
However, a covariance matrix is generally positive definite unless t | Is every covariance matrix positive definite?
As the other answers already make clear, a covariance matrix is not necessarily positive definite, but only positive semi-definite.
However, a covariance matrix is generally positive definite unless the space spanned by the variables is actually a linear subspace of lower d... | Is every covariance matrix positive definite?
As the other answers already make clear, a covariance matrix is not necessarily positive definite, but only positive semi-definite.
However, a covariance matrix is generally positive definite unless t |
3,848 | Is every covariance matrix positive definite? | $$\begin{array}{l}theory:\left\{ {{{\bf{\Sigma }}_{\bf{X}}}{\rm{ is positive semi - definite}}} \right.\\proof::\\set:\left\{ {{\bf{a}} = {\rm{vector }}\left( {p \times 1} \right){\rm{ }}\left( {{\mathop{\rm const}\nolimits} } \right) \ne \vec 0} \right.\\{{\bf{a}}^T}\Sigma {\bf{a}} = {\left[ {\begin{array}{*{20}{c}}{{... | Is every covariance matrix positive definite? | $$\begin{array}{l}theory:\left\{ {{{\bf{\Sigma }}_{\bf{X}}}{\rm{ is positive semi - definite}}} \right.\\proof::\\set:\left\{ {{\bf{a}} = {\rm{vector }}\left( {p \times 1} \right){\rm{ }}\left( {{\mat | Is every covariance matrix positive definite?
$$\begin{array}{l}theory:\left\{ {{{\bf{\Sigma }}_{\bf{X}}}{\rm{ is positive semi - definite}}} \right.\\proof::\\set:\left\{ {{\bf{a}} = {\rm{vector }}\left( {p \times 1} \right){\rm{ }}\left( {{\mathop{\rm const}\nolimits} } \right) \ne \vec 0} \right.\\{{\bf{a}}^T}\Sigma... | Is every covariance matrix positive definite?
$$\begin{array}{l}theory:\left\{ {{{\bf{\Sigma }}_{\bf{X}}}{\rm{ is positive semi - definite}}} \right.\\proof::\\set:\left\{ {{\bf{a}} = {\rm{vector }}\left( {p \times 1} \right){\rm{ }}\left( {{\mat |
3,849 | How to calculate pseudo-$R^2$ from R's logistic regression? | Don't forget the rms package, by Frank Harrell. You'll find everything you need for fitting and validating GLMs.
Here is a toy example (with only one predictor):
set.seed(101)
n <- 200
x <- rnorm(n)
a <- 1
b <- -2
p <- exp(a+b*x)/(1+exp(a+b*x))
y <- factor(ifelse(runif(n)<p, 1, 0), levels=0:1)
mod1 <- glm(y ~ x, famil... | How to calculate pseudo-$R^2$ from R's logistic regression? | Don't forget the rms package, by Frank Harrell. You'll find everything you need for fitting and validating GLMs.
Here is a toy example (with only one predictor):
set.seed(101)
n <- 200
x <- rnorm(n)
| How to calculate pseudo-$R^2$ from R's logistic regression?
Don't forget the rms package, by Frank Harrell. You'll find everything you need for fitting and validating GLMs.
Here is a toy example (with only one predictor):
set.seed(101)
n <- 200
x <- rnorm(n)
a <- 1
b <- -2
p <- exp(a+b*x)/(1+exp(a+b*x))
y <- factor(if... | How to calculate pseudo-$R^2$ from R's logistic regression?
Don't forget the rms package, by Frank Harrell. You'll find everything you need for fitting and validating GLMs.
Here is a toy example (with only one predictor):
set.seed(101)
n <- 200
x <- rnorm(n)
|
3,850 | How to calculate pseudo-$R^2$ from R's logistic regression? | To easily get a McFadden's pseudo $R^2$ for a fitted model in R, use the "pscl" package by Simon Jackman and use the pR2 command. http://cran.r-project.org/web/packages/pscl/index.html | How to calculate pseudo-$R^2$ from R's logistic regression? | To easily get a McFadden's pseudo $R^2$ for a fitted model in R, use the "pscl" package by Simon Jackman and use the pR2 command. http://cran.r-project.org/web/packages/pscl/index.html | How to calculate pseudo-$R^2$ from R's logistic regression?
To easily get a McFadden's pseudo $R^2$ for a fitted model in R, use the "pscl" package by Simon Jackman and use the pR2 command. http://cran.r-project.org/web/packages/pscl/index.html | How to calculate pseudo-$R^2$ from R's logistic regression?
To easily get a McFadden's pseudo $R^2$ for a fitted model in R, use the "pscl" package by Simon Jackman and use the pR2 command. http://cran.r-project.org/web/packages/pscl/index.html |
3,851 | How to calculate pseudo-$R^2$ from R's logistic regression? | Before calculating the pseudo-$R^2$ for your logistic regression, I want to ask you, do you think McFadden’s or McKelvey-Zavoina’s pseudo-$R^2$ measures good enough? The paper has been published. Surrogate R-squared measure
Cannot find a suitable R-squared measure for binary or ordinal data regression models? Here come... | How to calculate pseudo-$R^2$ from R's logistic regression? | Before calculating the pseudo-$R^2$ for your logistic regression, I want to ask you, do you think McFadden’s or McKelvey-Zavoina’s pseudo-$R^2$ measures good enough? The paper has been published. Surr | How to calculate pseudo-$R^2$ from R's logistic regression?
Before calculating the pseudo-$R^2$ for your logistic regression, I want to ask you, do you think McFadden’s or McKelvey-Zavoina’s pseudo-$R^2$ measures good enough? The paper has been published. Surrogate R-squared measure
Cannot find a suitable R-squared mea... | How to calculate pseudo-$R^2$ from R's logistic regression?
Before calculating the pseudo-$R^2$ for your logistic regression, I want to ask you, do you think McFadden’s or McKelvey-Zavoina’s pseudo-$R^2$ measures good enough? The paper has been published. Surr |
3,852 | How to calculate pseudo-$R^2$ from R's logistic regression? | if deviance were proportional to log likelihood, and one uses the definition (see for example McFadden's here)
pseudo R^2 = 1 - L(model) / L(intercept)
then the pseudo-$R^2$ above would be $1 - \frac{198.63}{958.66}$ = 0.7928
The question is: is reported deviance proportional to log likelihood? | How to calculate pseudo-$R^2$ from R's logistic regression? | if deviance were proportional to log likelihood, and one uses the definition (see for example McFadden's here)
pseudo R^2 = 1 - L(model) / L(intercept)
then the pseudo-$R^2$ above would be $1 - \frac | How to calculate pseudo-$R^2$ from R's logistic regression?
if deviance were proportional to log likelihood, and one uses the definition (see for example McFadden's here)
pseudo R^2 = 1 - L(model) / L(intercept)
then the pseudo-$R^2$ above would be $1 - \frac{198.63}{958.66}$ = 0.7928
The question is: is reported devi... | How to calculate pseudo-$R^2$ from R's logistic regression?
if deviance were proportional to log likelihood, and one uses the definition (see for example McFadden's here)
pseudo R^2 = 1 - L(model) / L(intercept)
then the pseudo-$R^2$ above would be $1 - \frac |
3,853 | How to calculate pseudo-$R^2$ from R's logistic regression? | If its out of sample, then I believe the $R^2$ must be computed with the according log-likelihoods as $R^2=1-\frac{ll_{full}}{ll_{constant}}$, where $ll_{full}$ is the log-likelihood of the test data with the predictive model calibrated on the training set, and $ll_{constant}$ is the log-likelihood of the test data wi... | How to calculate pseudo-$R^2$ from R's logistic regression? | If its out of sample, then I believe the $R^2$ must be computed with the according log-likelihoods as $R^2=1-\frac{ll_{full}}{ll_{constant}}$, where $ll_{full}$ is the log-likelihood of the test data | How to calculate pseudo-$R^2$ from R's logistic regression?
If its out of sample, then I believe the $R^2$ must be computed with the according log-likelihoods as $R^2=1-\frac{ll_{full}}{ll_{constant}}$, where $ll_{full}$ is the log-likelihood of the test data with the predictive model calibrated on the training set, a... | How to calculate pseudo-$R^2$ from R's logistic regression?
If its out of sample, then I believe the $R^2$ must be computed with the according log-likelihoods as $R^2=1-\frac{ll_{full}}{ll_{constant}}$, where $ll_{full}$ is the log-likelihood of the test data |
3,854 | Comparing SVM and logistic regression | Linear SVMs and logistic regression generally perform comparably in practice. Use SVM with a nonlinear kernel if you have reason to believe your data won't be linearly separable (or you need to be more robust to outliers than LR will normally tolerate). Otherwise, just try logistic regression first and see how you do w... | Comparing SVM and logistic regression | Linear SVMs and logistic regression generally perform comparably in practice. Use SVM with a nonlinear kernel if you have reason to believe your data won't be linearly separable (or you need to be mor | Comparing SVM and logistic regression
Linear SVMs and logistic regression generally perform comparably in practice. Use SVM with a nonlinear kernel if you have reason to believe your data won't be linearly separable (or you need to be more robust to outliers than LR will normally tolerate). Otherwise, just try logistic... | Comparing SVM and logistic regression
Linear SVMs and logistic regression generally perform comparably in practice. Use SVM with a nonlinear kernel if you have reason to believe your data won't be linearly separable (or you need to be mor |
3,855 | Comparing SVM and logistic regression | Image signifies the difference between SVM and Logistic Regression and where to use which method
this picture comes from the coursera course : "machine learning" by Andrew NG. It can be found in week 7 at the end of: "Support vector machines - using an SVM" | Comparing SVM and logistic regression | Image signifies the difference between SVM and Logistic Regression and where to use which method
this picture comes from the coursera course : "machine learning" by Andrew NG. It can be found in week | Comparing SVM and logistic regression
Image signifies the difference between SVM and Logistic Regression and where to use which method
this picture comes from the coursera course : "machine learning" by Andrew NG. It can be found in week 7 at the end of: "Support vector machines - using an SVM" | Comparing SVM and logistic regression
Image signifies the difference between SVM and Logistic Regression and where to use which method
this picture comes from the coursera course : "machine learning" by Andrew NG. It can be found in week |
3,856 | Comparing SVM and logistic regression | LR gives calibrated probabilities that can be interpreted as
confidence in a decision.
LR gives us an unconstrained, smooth objective.
LR can be (straightforwardly) used within Bayesian models.
SVMs don’t penalize examples for which the correct decision is
made with sufficient confidence. This may be good for
generaliz... | Comparing SVM and logistic regression | LR gives calibrated probabilities that can be interpreted as
confidence in a decision.
LR gives us an unconstrained, smooth objective.
LR can be (straightforwardly) used within Bayesian models.
SVMs d | Comparing SVM and logistic regression
LR gives calibrated probabilities that can be interpreted as
confidence in a decision.
LR gives us an unconstrained, smooth objective.
LR can be (straightforwardly) used within Bayesian models.
SVMs don’t penalize examples for which the correct decision is
made with sufficient conf... | Comparing SVM and logistic regression
LR gives calibrated probabilities that can be interpreted as
confidence in a decision.
LR gives us an unconstrained, smooth objective.
LR can be (straightforwardly) used within Bayesian models.
SVMs d |
3,857 | Comparing SVM and logistic regression | I think another advantage of LR is that it's actually optimising the weights of an interpretable function (e.g. Y = B0 + B1X1 +B2X2, where X1 and X2 are your predictor variables/features). This means that you could use the model with pen, paper and a basic scientific calculator and get a probability output if you wante... | Comparing SVM and logistic regression | I think another advantage of LR is that it's actually optimising the weights of an interpretable function (e.g. Y = B0 + B1X1 +B2X2, where X1 and X2 are your predictor variables/features). This means | Comparing SVM and logistic regression
I think another advantage of LR is that it's actually optimising the weights of an interpretable function (e.g. Y = B0 + B1X1 +B2X2, where X1 and X2 are your predictor variables/features). This means that you could use the model with pen, paper and a basic scientific calculator and... | Comparing SVM and logistic regression
I think another advantage of LR is that it's actually optimising the weights of an interpretable function (e.g. Y = B0 + B1X1 +B2X2, where X1 and X2 are your predictor variables/features). This means |
3,858 | Best practice when analysing pre-post treatment-control designs | There is a huge literature around this topic (change/gain scores), and I think the best references come from the biomedical domain, e.g.
Senn, S (2007). Statistical issues in
drug development. Wiley (chap. 7 pp.
96-112)
In biomedical research, interesting work has also been done in the study of cross-over trials (esp... | Best practice when analysing pre-post treatment-control designs | There is a huge literature around this topic (change/gain scores), and I think the best references come from the biomedical domain, e.g.
Senn, S (2007). Statistical issues in
drug development. Wiley | Best practice when analysing pre-post treatment-control designs
There is a huge literature around this topic (change/gain scores), and I think the best references come from the biomedical domain, e.g.
Senn, S (2007). Statistical issues in
drug development. Wiley (chap. 7 pp.
96-112)
In biomedical research, interestin... | Best practice when analysing pre-post treatment-control designs
There is a huge literature around this topic (change/gain scores), and I think the best references come from the biomedical domain, e.g.
Senn, S (2007). Statistical issues in
drug development. Wiley |
3,859 | Best practice when analysing pre-post treatment-control designs | Daniel B. Wright discusses this in section 5 of his article Making Friends with your Data.
He suggests (p.130):
The only procedure that
is always correct in this situation is
a scatterplot comparing the scores at
time 2 with those at time 1 for the
different groups. In most cases you
should analyse the data ... | Best practice when analysing pre-post treatment-control designs | Daniel B. Wright discusses this in section 5 of his article Making Friends with your Data.
He suggests (p.130):
The only procedure that
is always correct in this situation is
a scatterplot compar | Best practice when analysing pre-post treatment-control designs
Daniel B. Wright discusses this in section 5 of his article Making Friends with your Data.
He suggests (p.130):
The only procedure that
is always correct in this situation is
a scatterplot comparing the scores at
time 2 with those at time 1 for the
... | Best practice when analysing pre-post treatment-control designs
Daniel B. Wright discusses this in section 5 of his article Making Friends with your Data.
He suggests (p.130):
The only procedure that
is always correct in this situation is
a scatterplot compar |
3,860 | Best practice when analysing pre-post treatment-control designs | The most common strategies would be:
Repeated measures ANOVA with one within-subject factor (pre vs. post-test) and one between-subject factor (treatment vs. control).
ANCOVA on the post-treatment scores, with pre-treatment score as a covariate and treatment as an independent variable. Intuitively, the idea is that a ... | Best practice when analysing pre-post treatment-control designs | The most common strategies would be:
Repeated measures ANOVA with one within-subject factor (pre vs. post-test) and one between-subject factor (treatment vs. control).
ANCOVA on the post-treatment sc | Best practice when analysing pre-post treatment-control designs
The most common strategies would be:
Repeated measures ANOVA with one within-subject factor (pre vs. post-test) and one between-subject factor (treatment vs. control).
ANCOVA on the post-treatment scores, with pre-treatment score as a covariate and treatm... | Best practice when analysing pre-post treatment-control designs
The most common strategies would be:
Repeated measures ANOVA with one within-subject factor (pre vs. post-test) and one between-subject factor (treatment vs. control).
ANCOVA on the post-treatment sc |
3,861 | Best practice when analysing pre-post treatment-control designs | ANCOVA and repeated measures/mixed model for interaction term are testing two different hypothesis.
Refer to this article: ariticle 1 and this article: article 2 | Best practice when analysing pre-post treatment-control designs | ANCOVA and repeated measures/mixed model for interaction term are testing two different hypothesis.
Refer to this article: ariticle 1 and this article: article 2 | Best practice when analysing pre-post treatment-control designs
ANCOVA and repeated measures/mixed model for interaction term are testing two different hypothesis.
Refer to this article: ariticle 1 and this article: article 2 | Best practice when analysing pre-post treatment-control designs
ANCOVA and repeated measures/mixed model for interaction term are testing two different hypothesis.
Refer to this article: ariticle 1 and this article: article 2 |
3,862 | Best practice when analysing pre-post treatment-control designs | Since you have two means (either of a specific item, or of the sum of the inventory), there's no reason to consider an ANOVA. A paired t-test is probably appropriate; this may help you choose which t-test you need.
Do you want to look at item-specific results, or at overall scores? If you want to do an item analysis, t... | Best practice when analysing pre-post treatment-control designs | Since you have two means (either of a specific item, or of the sum of the inventory), there's no reason to consider an ANOVA. A paired t-test is probably appropriate; this may help you choose which t- | Best practice when analysing pre-post treatment-control designs
Since you have two means (either of a specific item, or of the sum of the inventory), there's no reason to consider an ANOVA. A paired t-test is probably appropriate; this may help you choose which t-test you need.
Do you want to look at item-specific resu... | Best practice when analysing pre-post treatment-control designs
Since you have two means (either of a specific item, or of the sum of the inventory), there's no reason to consider an ANOVA. A paired t-test is probably appropriate; this may help you choose which t- |
3,863 | Can someone explain the concept of 'exchangeability'? | Exchangeability is meant to capture symmetry in a problem, symmetry in a sense that does not require independence. Formally, a sequence is exchangeable if its joint probability distribution is a symmetric function of its $n$ arguments. Intuitively it means we can swap around, or reorder, variables in the sequence with... | Can someone explain the concept of 'exchangeability'? | Exchangeability is meant to capture symmetry in a problem, symmetry in a sense that does not require independence. Formally, a sequence is exchangeable if its joint probability distribution is a symme | Can someone explain the concept of 'exchangeability'?
Exchangeability is meant to capture symmetry in a problem, symmetry in a sense that does not require independence. Formally, a sequence is exchangeable if its joint probability distribution is a symmetric function of its $n$ arguments. Intuitively it means we can s... | Can someone explain the concept of 'exchangeability'?
Exchangeability is meant to capture symmetry in a problem, symmetry in a sense that does not require independence. Formally, a sequence is exchangeable if its joint probability distribution is a symme |
3,864 | Under what conditions should Likert scales be used as ordinal or interval data? | Maybe too late but I add my answer anyway...
It depends on what you intend to do with your data: If you are interested in showing that scores differ when considering different group of participants (gender, country, etc.), you may treat your scores as numeric values, provided they fulfill usual assumptions about varian... | Under what conditions should Likert scales be used as ordinal or interval data? | Maybe too late but I add my answer anyway...
It depends on what you intend to do with your data: If you are interested in showing that scores differ when considering different group of participants (g | Under what conditions should Likert scales be used as ordinal or interval data?
Maybe too late but I add my answer anyway...
It depends on what you intend to do with your data: If you are interested in showing that scores differ when considering different group of participants (gender, country, etc.), you may treat you... | Under what conditions should Likert scales be used as ordinal or interval data?
Maybe too late but I add my answer anyway...
It depends on what you intend to do with your data: If you are interested in showing that scores differ when considering different group of participants (g |
3,865 | Under what conditions should Likert scales be used as ordinal or interval data? | The simple answer is that Likert scales are always ordinal. The intervals between positions on the scale are monotonic but never so well-defined as to be numerically uniform increments.
That said, the distinction between ordinal and interval is based on the specific demands of the analysis being performed. Under specia... | Under what conditions should Likert scales be used as ordinal or interval data? | The simple answer is that Likert scales are always ordinal. The intervals between positions on the scale are monotonic but never so well-defined as to be numerically uniform increments.
That said, the | Under what conditions should Likert scales be used as ordinal or interval data?
The simple answer is that Likert scales are always ordinal. The intervals between positions on the scale are monotonic but never so well-defined as to be numerically uniform increments.
That said, the distinction between ordinal and interva... | Under what conditions should Likert scales be used as ordinal or interval data?
The simple answer is that Likert scales are always ordinal. The intervals between positions on the scale are monotonic but never so well-defined as to be numerically uniform increments.
That said, the |
3,866 | Under what conditions should Likert scales be used as ordinal or interval data? | In addition to what has already been said above about summated scales, I'd also mention that the issue can change when analysing data at the group-level. For example, if you were examining
life satisfaction of states or countries,
job satisfaction of organisations or departments,
student satisfaction in subjects.
In ... | Under what conditions should Likert scales be used as ordinal or interval data? | In addition to what has already been said above about summated scales, I'd also mention that the issue can change when analysing data at the group-level. For example, if you were examining
life satis | Under what conditions should Likert scales be used as ordinal or interval data?
In addition to what has already been said above about summated scales, I'd also mention that the issue can change when analysing data at the group-level. For example, if you were examining
life satisfaction of states or countries,
job sati... | Under what conditions should Likert scales be used as ordinal or interval data?
In addition to what has already been said above about summated scales, I'd also mention that the issue can change when analysing data at the group-level. For example, if you were examining
life satis |
3,867 | Under what conditions should Likert scales be used as ordinal or interval data? | likert scale always in ordinal form
: A method of ascribing quantitativevalue to qualitative data, to make it amenable to statistical analysis. A numerical value is assigned to each potential choice and a mean figure for all the responses is computed at the end of the evaluation or survey. | Under what conditions should Likert scales be used as ordinal or interval data? | likert scale always in ordinal form
: A method of ascribing quantitativevalue to qualitative data, to make it amenable to statistical analysis. A numerical value is assigned to each potential choice a | Under what conditions should Likert scales be used as ordinal or interval data?
likert scale always in ordinal form
: A method of ascribing quantitativevalue to qualitative data, to make it amenable to statistical analysis. A numerical value is assigned to each potential choice and a mean figure for all the responses i... | Under what conditions should Likert scales be used as ordinal or interval data?
likert scale always in ordinal form
: A method of ascribing quantitativevalue to qualitative data, to make it amenable to statistical analysis. A numerical value is assigned to each potential choice a |
3,868 | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoherent mishmash"? | I believe the papers, articles, posts e.t.c. that you diligently gathered, contain enough information and analysis as to where and why the two approaches differ. But being different does not mean being incompatible.
The problem with the "hybrid" is that it is a hybrid and not a synthesis, and this is why it is treated ... | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoh | I believe the papers, articles, posts e.t.c. that you diligently gathered, contain enough information and analysis as to where and why the two approaches differ. But being different does not mean bein | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoherent mishmash"?
I believe the papers, articles, posts e.t.c. that you diligently gathered, contain enough information and analysis as to where and why the two approaches differ. But being different does not mean being i... | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoh
I believe the papers, articles, posts e.t.c. that you diligently gathered, contain enough information and analysis as to where and why the two approaches differ. But being different does not mean bein |
3,869 | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoherent mishmash"? | My own take on my question is that there is nothing particularly incoherent in the hybrid (i.e. accepted) approach. But as I was not sure if I am maybe failing to comprehend the validity of the arguments presented in the anti-hybrid papers, I was happy to find the discussion published together with this paper:
Hubbard... | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoh | My own take on my question is that there is nothing particularly incoherent in the hybrid (i.e. accepted) approach. But as I was not sure if I am maybe failing to comprehend the validity of the argume | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoherent mishmash"?
My own take on my question is that there is nothing particularly incoherent in the hybrid (i.e. accepted) approach. But as I was not sure if I am maybe failing to comprehend the validity of the arguments... | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoh
My own take on my question is that there is nothing particularly incoherent in the hybrid (i.e. accepted) approach. But as I was not sure if I am maybe failing to comprehend the validity of the argume |
3,870 | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoherent mishmash"? | I fear that a real response to this excellent question would require a full-length paper. However, here are a couple of points that are not present in either the question or the current answers.
The error rate 'belongs' to the procedure but the evidence 'belongs' to the experimental results. Thus it is possible with m... | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoh | I fear that a real response to this excellent question would require a full-length paper. However, here are a couple of points that are not present in either the question or the current answers.
The | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoherent mishmash"?
I fear that a real response to this excellent question would require a full-length paper. However, here are a couple of points that are not present in either the question or the current answers.
The err... | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoh
I fear that a real response to this excellent question would require a full-length paper. However, here are a couple of points that are not present in either the question or the current answers.
The |
3,871 | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoherent mishmash"? | An often seen (and supposedly accepted) union (or better: "hybrid") between the two approaches is as follows:
Set a prespecified level $\alpha$ (0.05 say)
Then test your hypothesis, e.g. $H_o: \mu = 0$ vs. $H_1: \mu \ne 0$
State the p value and formulate your decision based on the level $\alpha$:
If the resulting p v... | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoh | An often seen (and supposedly accepted) union (or better: "hybrid") between the two approaches is as follows:
Set a prespecified level $\alpha$ (0.05 say)
Then test your hypothesis, e.g. $H_o: \mu = | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoherent mishmash"?
An often seen (and supposedly accepted) union (or better: "hybrid") between the two approaches is as follows:
Set a prespecified level $\alpha$ (0.05 say)
Then test your hypothesis, e.g. $H_o: \mu = 0$... | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoh
An often seen (and supposedly accepted) union (or better: "hybrid") between the two approaches is as follows:
Set a prespecified level $\alpha$ (0.05 say)
Then test your hypothesis, e.g. $H_o: \mu = |
3,872 | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoherent mishmash"? | accepting that both F and N-P are valid and meaningful approaches,
what is so bad about their hybrid?
Short answer: the use of a nil (no difference, no correlation) null hypothesis irregardless of the context. Everything else is a "misuse" by people who have created myths for themselves about what the process can ac... | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoh | accepting that both F and N-P are valid and meaningful approaches,
what is so bad about their hybrid?
Short answer: the use of a nil (no difference, no correlation) null hypothesis irregardless of | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoherent mishmash"?
accepting that both F and N-P are valid and meaningful approaches,
what is so bad about their hybrid?
Short answer: the use of a nil (no difference, no correlation) null hypothesis irregardless of the... | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoh
accepting that both F and N-P are valid and meaningful approaches,
what is so bad about their hybrid?
Short answer: the use of a nil (no difference, no correlation) null hypothesis irregardless of |
3,873 | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoherent mishmash"? | I see that those with more expertise than myself have provided answers, but I think my answer has the potential to add something additional, so I'll offer this as one other layman's perspective.
Is the hybrid approach incoherent? I'd say it depends on whether or not the researcher ends up acting inconsistently with th... | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoh | I see that those with more expertise than myself have provided answers, but I think my answer has the potential to add something additional, so I'll offer this as one other layman's perspective.
Is th | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoherent mishmash"?
I see that those with more expertise than myself have provided answers, but I think my answer has the potential to add something additional, so I'll offer this as one other layman's perspective.
Is the h... | Is the "hybrid" between Fisher and Neyman-Pearson approaches to statistical testing really an "incoh
I see that those with more expertise than myself have provided answers, but I think my answer has the potential to add something additional, so I'll offer this as one other layman's perspective.
Is th |
3,874 | Logistic regression in R resulted in perfect separation (Hauck-Donner phenomenon). Now what? [duplicate] | With such a large design space ($\mathbb{R}^{50}$!) it is possible to get perfect separation without having separation in any of the variable taken individually. I would even second David J. Harris's comment in saying that this is likely.
You can easily test whether your classes are perfectly separated in your design... | Logistic regression in R resulted in perfect separation (Hauck-Donner phenomenon). Now what? [duplic | With such a large design space ($\mathbb{R}^{50}$!) it is possible to get perfect separation without having separation in any of the variable taken individually. I would even second David J. Harris's | Logistic regression in R resulted in perfect separation (Hauck-Donner phenomenon). Now what? [duplicate]
With such a large design space ($\mathbb{R}^{50}$!) it is possible to get perfect separation without having separation in any of the variable taken individually. I would even second David J. Harris's comment in say... | Logistic regression in R resulted in perfect separation (Hauck-Donner phenomenon). Now what? [duplic
With such a large design space ($\mathbb{R}^{50}$!) it is possible to get perfect separation without having separation in any of the variable taken individually. I would even second David J. Harris's |
3,875 | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so from the statistics viewpoint? | It is decidedly out of the ordinary.
The reason is that counts like these tend to have Poisson distributions. This implies their inherent variance equals the count. For counts near $100,$ that variance of $100$ means the standard deviations are nearly $10.$ Unless there is extreme serial correlation of the results (w... | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so f | It is decidedly out of the ordinary.
The reason is that counts like these tend to have Poisson distributions. This implies their inherent variance equals the count. For counts near $100,$ that varia | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so from the statistics viewpoint?
It is decidedly out of the ordinary.
The reason is that counts like these tend to have Poisson distributions. This implies their inherent variance equals the count. For counts near $100,$ ... | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so f
It is decidedly out of the ordinary.
The reason is that counts like these tend to have Poisson distributions. This implies their inherent variance equals the count. For counts near $100,$ that varia |
3,876 | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so from the statistics viewpoint? | The Krasnodar Krai case is not the only one. Below is a plot for the data from 36 regions (I selected the best examples out of 84) where we either see
a similar underdispersion
or at least the numbers seem to be reaching a plateau around a 'nice' number (I have drawn lines at 10, 25, 50 and 100, where several regions... | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so f | The Krasnodar Krai case is not the only one. Below is a plot for the data from 36 regions (I selected the best examples out of 84) where we either see
a similar underdispersion
or at least the numbe | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so from the statistics viewpoint?
The Krasnodar Krai case is not the only one. Below is a plot for the data from 36 regions (I selected the best examples out of 84) where we either see
a similar underdispersion
or at least... | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so f
The Krasnodar Krai case is not the only one. Below is a plot for the data from 36 regions (I selected the best examples out of 84) where we either see
a similar underdispersion
or at least the numbe |
3,877 | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so from the statistics viewpoint? | I will just mention one aspect that I haven't seen mentioned in the other answers. The problem with any analysis that states that this is significantly out of the ordinary is that it doesn't take into account that the data have been selected based on looking strange. At least I'd assume that the thread opener has not o... | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so f | I will just mention one aspect that I haven't seen mentioned in the other answers. The problem with any analysis that states that this is significantly out of the ordinary is that it doesn't take into | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so from the statistics viewpoint?
I will just mention one aspect that I haven't seen mentioned in the other answers. The problem with any analysis that states that this is significantly out of the ordinary is that it doesn't... | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so f
I will just mention one aspect that I haven't seen mentioned in the other answers. The problem with any analysis that states that this is significantly out of the ordinary is that it doesn't take into |
3,878 | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so from the statistics viewpoint? | Krasnodar
The data for a region is clearly not realistic in terms of its dispersion. Here's a data on Krasnodar town. The sample average is 34 in May, and the dispersion is 8.7.
This is more than Poisson distribution would suggest, where the dispersion is the square root of average, i.e. 5.9. This is overdispersed but... | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so f | Krasnodar
The data for a region is clearly not realistic in terms of its dispersion. Here's a data on Krasnodar town. The sample average is 34 in May, and the dispersion is 8.7.
This is more than Poi | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so from the statistics viewpoint?
Krasnodar
The data for a region is clearly not realistic in terms of its dispersion. Here's a data on Krasnodar town. The sample average is 34 in May, and the dispersion is 8.7.
This is mor... | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so f
Krasnodar
The data for a region is clearly not realistic in terms of its dispersion. Here's a data on Krasnodar town. The sample average is 34 in May, and the dispersion is 8.7.
This is more than Poi |
3,879 | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so from the statistics viewpoint? | So I think these are the data:
month day new delta tens ones
4 29 63 NA 6 3
4 30 66 3 6 6
5 1 65 -1 6 5
5 2 79 14 7 9
5 3 82 3 8 2
5 4 96 14 9 6
5 5 97 1 9 7
5 6 97 0 9 7
5... | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so f | So I think these are the data:
month day new delta tens ones
4 29 63 NA 6 3
4 30 66 3 6 6
5 1 65 -1 6 5
5 2 79 14 7 9
5 3 | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so from the statistics viewpoint?
So I think these are the data:
month day new delta tens ones
4 29 63 NA 6 3
4 30 66 3 6 6
5 1 65 -1 6 5
5 2 79 14 7 9
... | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so f
So I think these are the data:
month day new delta tens ones
4 29 63 NA 6 3
4 30 66 3 6 6
5 1 65 -1 6 5
5 2 79 14 7 9
5 3 |
3,880 | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so from the statistics viewpoint? | Interesting points from everyone. Let me contradict some.
1) Why Poisson? Cases generation process is intristically interdependent as a pandemic interaction between ill and healthy, so case occurence in a time interval maybe affected by the previous interval occurences. The dependency may be complicated but strong.
UD... | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so f | Interesting points from everyone. Let me contradict some.
1) Why Poisson? Cases generation process is intristically interdependent as a pandemic interaction between ill and healthy, so case occurence | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so from the statistics viewpoint?
Interesting points from everyone. Let me contradict some.
1) Why Poisson? Cases generation process is intristically interdependent as a pandemic interaction between ill and healthy, so case... | A chart of daily cases of COVID-19 in a Russian region looks suspiciously level to me - is this so f
Interesting points from everyone. Let me contradict some.
1) Why Poisson? Cases generation process is intristically interdependent as a pandemic interaction between ill and healthy, so case occurence |
3,881 | Why is the regularization term *added* to the cost function (instead of multiplied etc.)? | It has quite a nice intuition in the Bayesian framework. Consider that the regularized cost function $J$ has a similar role as the probability of a parameter configuration $\theta$ given the observations $X, y$. Applying the Bayes theorem, we get:
$$P(\theta|X,y) = \frac{P(X,y|\theta)P(\theta)}{P(X,y)}.$$
Taking the lo... | Why is the regularization term *added* to the cost function (instead of multiplied etc.)? | It has quite a nice intuition in the Bayesian framework. Consider that the regularized cost function $J$ has a similar role as the probability of a parameter configuration $\theta$ given the observati | Why is the regularization term *added* to the cost function (instead of multiplied etc.)?
It has quite a nice intuition in the Bayesian framework. Consider that the regularized cost function $J$ has a similar role as the probability of a parameter configuration $\theta$ given the observations $X, y$. Applying the Bayes... | Why is the regularization term *added* to the cost function (instead of multiplied etc.)?
It has quite a nice intuition in the Bayesian framework. Consider that the regularized cost function $J$ has a similar role as the probability of a parameter configuration $\theta$ given the observati |
3,882 | Why is the regularization term *added* to the cost function (instead of multiplied etc.)? | Jan and Cagdas give a good Bayesian reason, interpreting the regularizer as a prior. Here are some non-Bayesian ones:
If your unregularized objective is convex, and you add a convex regularizer, then your total objective will still be convex. This won't be true if you multiply it, or most other methods of combining. C... | Why is the regularization term *added* to the cost function (instead of multiplied etc.)? | Jan and Cagdas give a good Bayesian reason, interpreting the regularizer as a prior. Here are some non-Bayesian ones:
If your unregularized objective is convex, and you add a convex regularizer, then | Why is the regularization term *added* to the cost function (instead of multiplied etc.)?
Jan and Cagdas give a good Bayesian reason, interpreting the regularizer as a prior. Here are some non-Bayesian ones:
If your unregularized objective is convex, and you add a convex regularizer, then your total objective will sti... | Why is the regularization term *added* to the cost function (instead of multiplied etc.)?
Jan and Cagdas give a good Bayesian reason, interpreting the regularizer as a prior. Here are some non-Bayesian ones:
If your unregularized objective is convex, and you add a convex regularizer, then |
3,883 | Why is the regularization term *added* to the cost function (instead of multiplied etc.)? | You want to minimize both terms in the objective function. Therefore, you need to decouple the terms. If you multiply the terms you can have one term large and the other very low. So, you still end up with a low value of the objective function, but with an undesirable result.
You may end up with a model that has most ... | Why is the regularization term *added* to the cost function (instead of multiplied etc.)? | You want to minimize both terms in the objective function. Therefore, you need to decouple the terms. If you multiply the terms you can have one term large and the other very low. So, you still end up | Why is the regularization term *added* to the cost function (instead of multiplied etc.)?
You want to minimize both terms in the objective function. Therefore, you need to decouple the terms. If you multiply the terms you can have one term large and the other very low. So, you still end up with a low value of the objec... | Why is the regularization term *added* to the cost function (instead of multiplied etc.)?
You want to minimize both terms in the objective function. Therefore, you need to decouple the terms. If you multiply the terms you can have one term large and the other very low. So, you still end up |
3,884 | Why is the regularization term *added* to the cost function (instead of multiplied etc.)? | You can try other binary operations ($\max,\min,\times$) and see how they compare.
The problem with $\min$ and $\times$ is that if the error is $0$, then the regularized penalty will end up being $0$. This allows the model to overfit.
The problem with $\max$ is that you end up minimizing the "harder" of the two penalti... | Why is the regularization term *added* to the cost function (instead of multiplied etc.)? | You can try other binary operations ($\max,\min,\times$) and see how they compare.
The problem with $\min$ and $\times$ is that if the error is $0$, then the regularized penalty will end up being $0$. | Why is the regularization term *added* to the cost function (instead of multiplied etc.)?
You can try other binary operations ($\max,\min,\times$) and see how they compare.
The problem with $\min$ and $\times$ is that if the error is $0$, then the regularized penalty will end up being $0$. This allows the model to over... | Why is the regularization term *added* to the cost function (instead of multiplied etc.)?
You can try other binary operations ($\max,\min,\times$) and see how they compare.
The problem with $\min$ and $\times$ is that if the error is $0$, then the regularized penalty will end up being $0$. |
3,885 | Why is the regularization term *added* to the cost function (instead of multiplied etc.)? | I think you have a valid question. To give you a proper answer you will have to understand the probabilistic nature of the problem.
In general the problem we are trying to solve is the following: Given data $D$ what is the distribution of hypotheses that explains this data. When we say hypothesis we mean a PDF (at leas... | Why is the regularization term *added* to the cost function (instead of multiplied etc.)? | I think you have a valid question. To give you a proper answer you will have to understand the probabilistic nature of the problem.
In general the problem we are trying to solve is the following: Give | Why is the regularization term *added* to the cost function (instead of multiplied etc.)?
I think you have a valid question. To give you a proper answer you will have to understand the probabilistic nature of the problem.
In general the problem we are trying to solve is the following: Given data $D$ what is the distrib... | Why is the regularization term *added* to the cost function (instead of multiplied etc.)?
I think you have a valid question. To give you a proper answer you will have to understand the probabilistic nature of the problem.
In general the problem we are trying to solve is the following: Give |
3,886 | Why is the regularization term *added* to the cost function (instead of multiplied etc.)? | Ridge is a very convenient formulation. In contrast to the probabilistic answers, this answers does not give any interpretation of the estimate but instead explains why ridge is an old and obvious formulation.
In linear regression, the normal equations give
$\hat{\theta} = (X^TX)^{-1} X^T y$
But, the matrix $X^TX$ is s... | Why is the regularization term *added* to the cost function (instead of multiplied etc.)? | Ridge is a very convenient formulation. In contrast to the probabilistic answers, this answers does not give any interpretation of the estimate but instead explains why ridge is an old and obvious for | Why is the regularization term *added* to the cost function (instead of multiplied etc.)?
Ridge is a very convenient formulation. In contrast to the probabilistic answers, this answers does not give any interpretation of the estimate but instead explains why ridge is an old and obvious formulation.
In linear regression... | Why is the regularization term *added* to the cost function (instead of multiplied etc.)?
Ridge is a very convenient formulation. In contrast to the probabilistic answers, this answers does not give any interpretation of the estimate but instead explains why ridge is an old and obvious for |
3,887 | Why is the regularization term *added* to the cost function (instead of multiplied etc.)? | I think there is a more intuitive reason as to why we can't multiply by the regularisation term.
Lets take our penalty function to the regular penalty function multiplied by a regularisation term like you suggest.
$$J(θ)=(\frac{1}{2}(y−θX^T)(y−θX^T)^T)α‖θ‖^2_2$$
Here we create a global minimum of the penalty function w... | Why is the regularization term *added* to the cost function (instead of multiplied etc.)? | I think there is a more intuitive reason as to why we can't multiply by the regularisation term.
Lets take our penalty function to the regular penalty function multiplied by a regularisation term like | Why is the regularization term *added* to the cost function (instead of multiplied etc.)?
I think there is a more intuitive reason as to why we can't multiply by the regularisation term.
Lets take our penalty function to the regular penalty function multiplied by a regularisation term like you suggest.
$$J(θ)=(\frac{1}... | Why is the regularization term *added* to the cost function (instead of multiplied etc.)?
I think there is a more intuitive reason as to why we can't multiply by the regularisation term.
Lets take our penalty function to the regular penalty function multiplied by a regularisation term like |
3,888 | Software needed to scrape data from graph [closed] | Check out the digitize package for R. Its designed to solve exactly this sort of problem. | Software needed to scrape data from graph [closed] | Check out the digitize package for R. Its designed to solve exactly this sort of problem. | Software needed to scrape data from graph [closed]
Check out the digitize package for R. Its designed to solve exactly this sort of problem. | Software needed to scrape data from graph [closed]
Check out the digitize package for R. Its designed to solve exactly this sort of problem. |
3,889 | Software needed to scrape data from graph [closed] | graph digitizing software
There are many different options, but all basically use the same workflow:
upload an image
set the x and y scales by indicating the values at two points on each axis
indicate if the scale is linear, log, etc,
click on the points.
Some of the programs automatically recognize lines or poi... | Software needed to scrape data from graph [closed] | graph digitizing software
There are many different options, but all basically use the same workflow:
upload an image
set the x and y scales by indicating the values at two points on each axis
indic | Software needed to scrape data from graph [closed]
graph digitizing software
There are many different options, but all basically use the same workflow:
upload an image
set the x and y scales by indicating the values at two points on each axis
indicate if the scale is linear, log, etc,
click on the points.
Some o... | Software needed to scrape data from graph [closed]
graph digitizing software
There are many different options, but all basically use the same workflow:
upload an image
set the x and y scales by indicating the values at two points on each axis
indic |
3,890 | Software needed to scrape data from graph [closed] | Other answerers assume that you deal with raster image of a graph. But nowadays the good practice is to publish graphs in vector form. In this case you can achieve much higher exactness of the recovered data and even estimate the recovery error if you work with the code of the vector graph directly, without converting ... | Software needed to scrape data from graph [closed] | Other answerers assume that you deal with raster image of a graph. But nowadays the good practice is to publish graphs in vector form. In this case you can achieve much higher exactness of the recover | Software needed to scrape data from graph [closed]
Other answerers assume that you deal with raster image of a graph. But nowadays the good practice is to publish graphs in vector form. In this case you can achieve much higher exactness of the recovered data and even estimate the recovery error if you work with the cod... | Software needed to scrape data from graph [closed]
Other answerers assume that you deal with raster image of a graph. But nowadays the good practice is to publish graphs in vector form. In this case you can achieve much higher exactness of the recover |
3,891 | Software needed to scrape data from graph [closed] | I haven't used it, but UWA CogSci lab recommend DataThief (shareware). | Software needed to scrape data from graph [closed] | I haven't used it, but UWA CogSci lab recommend DataThief (shareware). | Software needed to scrape data from graph [closed]
I haven't used it, but UWA CogSci lab recommend DataThief (shareware). | Software needed to scrape data from graph [closed]
I haven't used it, but UWA CogSci lab recommend DataThief (shareware). |
3,892 | Software needed to scrape data from graph [closed] | Check out engauge. Its free and open source
http://digitizer.sourceforge.net/ | Software needed to scrape data from graph [closed] | Check out engauge. Its free and open source
http://digitizer.sourceforge.net/ | Software needed to scrape data from graph [closed]
Check out engauge. Its free and open source
http://digitizer.sourceforge.net/ | Software needed to scrape data from graph [closed]
Check out engauge. Its free and open source
http://digitizer.sourceforge.net/ |
3,893 | Software needed to scrape data from graph [closed] | Un-Scan-It
http://www.silkscientific.com/graph-digitizer.htm | Software needed to scrape data from graph [closed] | Un-Scan-It
http://www.silkscientific.com/graph-digitizer.htm | Software needed to scrape data from graph [closed]
Un-Scan-It
http://www.silkscientific.com/graph-digitizer.htm | Software needed to scrape data from graph [closed]
Un-Scan-It
http://www.silkscientific.com/graph-digitizer.htm |
3,894 | Software needed to scrape data from graph [closed] | Try scanit: http://amsterchem.com/scanit.html
It is free of charge, runs on Windows | Software needed to scrape data from graph [closed] | Try scanit: http://amsterchem.com/scanit.html
It is free of charge, runs on Windows | Software needed to scrape data from graph [closed]
Try scanit: http://amsterchem.com/scanit.html
It is free of charge, runs on Windows | Software needed to scrape data from graph [closed]
Try scanit: http://amsterchem.com/scanit.html
It is free of charge, runs on Windows |
3,895 | Software needed to scrape data from graph [closed] | You can also try im2graph (http://www.im2graph.co.il) to convert graphs to data. Works in Linux and Windows. | Software needed to scrape data from graph [closed] | You can also try im2graph (http://www.im2graph.co.il) to convert graphs to data. Works in Linux and Windows. | Software needed to scrape data from graph [closed]
You can also try im2graph (http://www.im2graph.co.il) to convert graphs to data. Works in Linux and Windows. | Software needed to scrape data from graph [closed]
You can also try im2graph (http://www.im2graph.co.il) to convert graphs to data. Works in Linux and Windows. |
3,896 | Software needed to scrape data from graph [closed] | 'g3data' is a software which can be used to serve your purpose. It's a free software and I have used it. You can download it from here: http://www.frantz.fi/software/g3data.php | Software needed to scrape data from graph [closed] | 'g3data' is a software which can be used to serve your purpose. It's a free software and I have used it. You can download it from here: http://www.frantz.fi/software/g3data.php | Software needed to scrape data from graph [closed]
'g3data' is a software which can be used to serve your purpose. It's a free software and I have used it. You can download it from here: http://www.frantz.fi/software/g3data.php | Software needed to scrape data from graph [closed]
'g3data' is a software which can be used to serve your purpose. It's a free software and I have used it. You can download it from here: http://www.frantz.fi/software/g3data.php |
3,897 | Software needed to scrape data from graph [closed] | I had to do this so many times in my career I eventually put together a javascript program which is available here:
http://kdusling.github.io/projects/DataGrab/index.html
Sorry, but you will still need to click on every single point. Though you can use the arrow keys which does save some wrist strain. | Software needed to scrape data from graph [closed] | I had to do this so many times in my career I eventually put together a javascript program which is available here:
http://kdusling.github.io/projects/DataGrab/index.html
Sorry, but you will still nee | Software needed to scrape data from graph [closed]
I had to do this so many times in my career I eventually put together a javascript program which is available here:
http://kdusling.github.io/projects/DataGrab/index.html
Sorry, but you will still need to click on every single point. Though you can use the arrow keys w... | Software needed to scrape data from graph [closed]
I had to do this so many times in my career I eventually put together a javascript program which is available here:
http://kdusling.github.io/projects/DataGrab/index.html
Sorry, but you will still nee |
3,898 | Software needed to scrape data from graph [closed] | STIPlotDigitizer has been newly released.
http://stiwww.com/product/software-techniques-plot-digitizer | Software needed to scrape data from graph [closed] | STIPlotDigitizer has been newly released.
http://stiwww.com/product/software-techniques-plot-digitizer | Software needed to scrape data from graph [closed]
STIPlotDigitizer has been newly released.
http://stiwww.com/product/software-techniques-plot-digitizer | Software needed to scrape data from graph [closed]
STIPlotDigitizer has been newly released.
http://stiwww.com/product/software-techniques-plot-digitizer |
3,899 | Software needed to scrape data from graph [closed] | For R users, the package grImport (on CRAN) can import vector graphics and convert them into objects that R can interpret. It assumes that one can convert PDF (or other vector format of interest) to PostScript format. This can be done for example with Inkscape: import (File > Import) your PDF page with your figure into... | Software needed to scrape data from graph [closed] | For R users, the package grImport (on CRAN) can import vector graphics and convert them into objects that R can interpret. It assumes that one can convert PDF (or other vector format of interest) to P | Software needed to scrape data from graph [closed]
For R users, the package grImport (on CRAN) can import vector graphics and convert them into objects that R can interpret. It assumes that one can convert PDF (or other vector format of interest) to PostScript format. This can be done for example with Inkscape: import ... | Software needed to scrape data from graph [closed]
For R users, the package grImport (on CRAN) can import vector graphics and convert them into objects that R can interpret. It assumes that one can convert PDF (or other vector format of interest) to P |
3,900 | Why do we use Kullback-Leibler divergence rather than cross entropy in the t-SNE objective function? | KL divergence is a natural way to measure the difference between two probability distributions. The entropy $H(p)$ of a distribution $p$ gives the minimum possible number of bits per message that would be needed (on average) to losslessly encode events drawn from $p$. Achieving this bound would require using an optimal... | Why do we use Kullback-Leibler divergence rather than cross entropy in the t-SNE objective function? | KL divergence is a natural way to measure the difference between two probability distributions. The entropy $H(p)$ of a distribution $p$ gives the minimum possible number of bits per message that woul | Why do we use Kullback-Leibler divergence rather than cross entropy in the t-SNE objective function?
KL divergence is a natural way to measure the difference between two probability distributions. The entropy $H(p)$ of a distribution $p$ gives the minimum possible number of bits per message that would be needed (on ave... | Why do we use Kullback-Leibler divergence rather than cross entropy in the t-SNE objective function?
KL divergence is a natural way to measure the difference between two probability distributions. The entropy $H(p)$ of a distribution $p$ gives the minimum possible number of bits per message that woul |
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