idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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35,401 | Does the first principal component differ from simply computing the mean of all variables? | Some purely geometric meditation on the question. How can we graphically compare "mean as the construct" with "PC1 as the construct"?
Let us have two variables $X$ and $Y$ with this covariance matrix
and we have computed the variable which is the sum $S$ or the mean $M$ of $X$ and $Y$. We also performed PCA of the $X,... | Does the first principal component differ from simply computing the mean of all variables? | Some purely geometric meditation on the question. How can we graphically compare "mean as the construct" with "PC1 as the construct"?
Let us have two variables $X$ and $Y$ with this covariance matrix
| Does the first principal component differ from simply computing the mean of all variables?
Some purely geometric meditation on the question. How can we graphically compare "mean as the construct" with "PC1 as the construct"?
Let us have two variables $X$ and $Y$ with this covariance matrix
and we have computed the var... | Does the first principal component differ from simply computing the mean of all variables?
Some purely geometric meditation on the question. How can we graphically compare "mean as the construct" with "PC1 as the construct"?
Let us have two variables $X$ and $Y$ with this covariance matrix
|
35,402 | How to train convolutional neural networks with multi-channel images? | You should work with each image as a volume of dimensions 224x224x5. You still do 2D convolution over the first 2 dimensions as usual, but keep the entire 3rd dimension. For instance, if you use a 7x7 convolution window, each filter will produce a 224x224x1 volume as output (with stride = 1 and zero padding), and the c... | How to train convolutional neural networks with multi-channel images? | You should work with each image as a volume of dimensions 224x224x5. You still do 2D convolution over the first 2 dimensions as usual, but keep the entire 3rd dimension. For instance, if you use a 7x7 | How to train convolutional neural networks with multi-channel images?
You should work with each image as a volume of dimensions 224x224x5. You still do 2D convolution over the first 2 dimensions as usual, but keep the entire 3rd dimension. For instance, if you use a 7x7 convolution window, each filter will produce a 22... | How to train convolutional neural networks with multi-channel images?
You should work with each image as a volume of dimensions 224x224x5. You still do 2D convolution over the first 2 dimensions as usual, but keep the entire 3rd dimension. For instance, if you use a 7x7 |
35,403 | How to train convolutional neural networks with multi-channel images? | Regarding your second question:
What is the best way to train a CNN architecture using this data when mm is small (less than 2000)?
There are some common ways to artificially increase the training set size, e.g. adding jitter or doing some transformation such as rotations. | How to train convolutional neural networks with multi-channel images? | Regarding your second question:
What is the best way to train a CNN architecture using this data when mm is small (less than 2000)?
There are some common ways to artificially increase the training | How to train convolutional neural networks with multi-channel images?
Regarding your second question:
What is the best way to train a CNN architecture using this data when mm is small (less than 2000)?
There are some common ways to artificially increase the training set size, e.g. adding jitter or doing some transfo... | How to train convolutional neural networks with multi-channel images?
Regarding your second question:
What is the best way to train a CNN architecture using this data when mm is small (less than 2000)?
There are some common ways to artificially increase the training |
35,404 | Is each of the PCA or PLS components just one of the original variables? | The possible confusion here, as @amoeba points out in a comment, is the difference between variable selection and dimensionality reduction.
Both PCA and PLS are intended to reduce the dimensionality of the problem. If you have measured 8 variables on each of your cases (and you have more than 8 cases) then the original... | Is each of the PCA or PLS components just one of the original variables? | The possible confusion here, as @amoeba points out in a comment, is the difference between variable selection and dimensionality reduction.
Both PCA and PLS are intended to reduce the dimensionality o | Is each of the PCA or PLS components just one of the original variables?
The possible confusion here, as @amoeba points out in a comment, is the difference between variable selection and dimensionality reduction.
Both PCA and PLS are intended to reduce the dimensionality of the problem. If you have measured 8 variables... | Is each of the PCA or PLS components just one of the original variables?
The possible confusion here, as @amoeba points out in a comment, is the difference between variable selection and dimensionality reduction.
Both PCA and PLS are intended to reduce the dimensionality o |
35,405 | Why do we use the chi-squared test to test independence of 2 categorical variables? | Instead of asking why the chi-squared test assesses independence, think about how you would test the association of two categorical variables against the null hypothesis of independence. For the sake of simplicity, consider two variables / properties A and B, each with two levels, "yes" and "no". A set of N units eac... | Why do we use the chi-squared test to test independence of 2 categorical variables? | Instead of asking why the chi-squared test assesses independence, think about how you would test the association of two categorical variables against the null hypothesis of independence. For the sake | Why do we use the chi-squared test to test independence of 2 categorical variables?
Instead of asking why the chi-squared test assesses independence, think about how you would test the association of two categorical variables against the null hypothesis of independence. For the sake of simplicity, consider two variabl... | Why do we use the chi-squared test to test independence of 2 categorical variables?
Instead of asking why the chi-squared test assesses independence, think about how you would test the association of two categorical variables against the null hypothesis of independence. For the sake |
35,406 | Why do we use the chi-squared test to test independence of 2 categorical variables? | $\chi_1^2$ is the distribution of a random variable $X^2$, where $X \sim N(0,1)$.
In the test of independence of two categorical variables, the actual counts are subtracted from the expected counts, and normalized by dividing by the expected counts. Squaring is extremely useful, because we are not interested in the di... | Why do we use the chi-squared test to test independence of 2 categorical variables? | $\chi_1^2$ is the distribution of a random variable $X^2$, where $X \sim N(0,1)$.
In the test of independence of two categorical variables, the actual counts are subtracted from the expected counts, | Why do we use the chi-squared test to test independence of 2 categorical variables?
$\chi_1^2$ is the distribution of a random variable $X^2$, where $X \sim N(0,1)$.
In the test of independence of two categorical variables, the actual counts are subtracted from the expected counts, and normalized by dividing by the ex... | Why do we use the chi-squared test to test independence of 2 categorical variables?
$\chi_1^2$ is the distribution of a random variable $X^2$, where $X \sim N(0,1)$.
In the test of independence of two categorical variables, the actual counts are subtracted from the expected counts, |
35,407 | Why do we use the chi-squared test to test independence of 2 categorical variables? | The threshold of p value is usually set at 0.05, which can be traced back to the beginning of statistics. If you want to be more conservative, you can of course use p<0.01. It just shows how unlikely the null hypothesis of independence is, therefore leading to a reasonable rejection of the null hypothesis.
An example ... | Why do we use the chi-squared test to test independence of 2 categorical variables? | The threshold of p value is usually set at 0.05, which can be traced back to the beginning of statistics. If you want to be more conservative, you can of course use p<0.01. It just shows how unlikely | Why do we use the chi-squared test to test independence of 2 categorical variables?
The threshold of p value is usually set at 0.05, which can be traced back to the beginning of statistics. If you want to be more conservative, you can of course use p<0.01. It just shows how unlikely the null hypothesis of independence ... | Why do we use the chi-squared test to test independence of 2 categorical variables?
The threshold of p value is usually set at 0.05, which can be traced back to the beginning of statistics. If you want to be more conservative, you can of course use p<0.01. It just shows how unlikely |
35,408 | Resources to get started with deep reinforcement learning | A nice introduction deep reinforcement learning by Lex Fridman (2019-01): https://youtu.be/zR11FLZ-O9M
2 complimentary, easy-to-read blog posts to get started on deep reinforcement learning: the first one focuses on policy gradients, the second one focuses on deep Q-learning.
Deep Reinforcement Learning: Pong from Pi... | Resources to get started with deep reinforcement learning | A nice introduction deep reinforcement learning by Lex Fridman (2019-01): https://youtu.be/zR11FLZ-O9M
2 complimentary, easy-to-read blog posts to get started on deep reinforcement learning: the firs | Resources to get started with deep reinforcement learning
A nice introduction deep reinforcement learning by Lex Fridman (2019-01): https://youtu.be/zR11FLZ-O9M
2 complimentary, easy-to-read blog posts to get started on deep reinforcement learning: the first one focuses on policy gradients, the second one focuses on d... | Resources to get started with deep reinforcement learning
A nice introduction deep reinforcement learning by Lex Fridman (2019-01): https://youtu.be/zR11FLZ-O9M
2 complimentary, easy-to-read blog posts to get started on deep reinforcement learning: the firs |
35,409 | Resources to get started with deep reinforcement learning | You can see many resources on github already including this recent list of Deep RL papers
Also checkout some implementations such as Deep Q learning
And here is a nice video by David Silver at RLDM videolectures.net deep RL | Resources to get started with deep reinforcement learning | You can see many resources on github already including this recent list of Deep RL papers
Also checkout some implementations such as Deep Q learning
And here is a nice video by David Silver at RLDM v | Resources to get started with deep reinforcement learning
You can see many resources on github already including this recent list of Deep RL papers
Also checkout some implementations such as Deep Q learning
And here is a nice video by David Silver at RLDM videolectures.net deep RL | Resources to get started with deep reinforcement learning
You can see many resources on github already including this recent list of Deep RL papers
Also checkout some implementations such as Deep Q learning
And here is a nice video by David Silver at RLDM v |
35,410 | In TensorFlow's Computational Model, is it possible to implement general machine learning algorithms? | This is a bit of a necropost, but if you are still interested, here is a set of general tensorflow tutorials that explain how to run things in tensorflow. It includes examples of doing linear and nearest neighbor regressions, so it should help with your original question.
https://github.com/aymericdamien/TensorFlow-Exa... | In TensorFlow's Computational Model, is it possible to implement general machine learning algorithms | This is a bit of a necropost, but if you are still interested, here is a set of general tensorflow tutorials that explain how to run things in tensorflow. It includes examples of doing linear and near | In TensorFlow's Computational Model, is it possible to implement general machine learning algorithms?
This is a bit of a necropost, but if you are still interested, here is a set of general tensorflow tutorials that explain how to run things in tensorflow. It includes examples of doing linear and nearest neighbor regre... | In TensorFlow's Computational Model, is it possible to implement general machine learning algorithms
This is a bit of a necropost, but if you are still interested, here is a set of general tensorflow tutorials that explain how to run things in tensorflow. It includes examples of doing linear and near |
35,411 | In TensorFlow's Computational Model, is it possible to implement general machine learning algorithms? | With TensorFlow you can implement any machine learning algorithm that relies on gradient descent and backpropagation (chain rule) or can be restated as such. That includes logistic regression, support vector machines and many others. But I wouldn't know how to implement random forest in TensorFlow. | In TensorFlow's Computational Model, is it possible to implement general machine learning algorithms | With TensorFlow you can implement any machine learning algorithm that relies on gradient descent and backpropagation (chain rule) or can be restated as such. That includes logistic regression, support | In TensorFlow's Computational Model, is it possible to implement general machine learning algorithms?
With TensorFlow you can implement any machine learning algorithm that relies on gradient descent and backpropagation (chain rule) or can be restated as such. That includes logistic regression, support vector machines a... | In TensorFlow's Computational Model, is it possible to implement general machine learning algorithms
With TensorFlow you can implement any machine learning algorithm that relies on gradient descent and backpropagation (chain rule) or can be restated as such. That includes logistic regression, support |
35,412 | In TensorFlow's Computational Model, is it possible to implement general machine learning algorithms? | A few of numpy operations are mirrored in TensorFlow, so if you can implement it in numpy, porting to TensorFlow can be straightforward. For instance, here's an example of K-means clustering: https://stackoverflow.com/questions/33621643/how-would-i-implement-k-means-with-tensorflow | In TensorFlow's Computational Model, is it possible to implement general machine learning algorithms | A few of numpy operations are mirrored in TensorFlow, so if you can implement it in numpy, porting to TensorFlow can be straightforward. For instance, here's an example of K-means clustering: https:// | In TensorFlow's Computational Model, is it possible to implement general machine learning algorithms?
A few of numpy operations are mirrored in TensorFlow, so if you can implement it in numpy, porting to TensorFlow can be straightforward. For instance, here's an example of K-means clustering: https://stackoverflow.com/... | In TensorFlow's Computational Model, is it possible to implement general machine learning algorithms
A few of numpy operations are mirrored in TensorFlow, so if you can implement it in numpy, porting to TensorFlow can be straightforward. For instance, here's an example of K-means clustering: https:// |
35,413 | Correlation coefficient for a uniform distribution on an ellipse | Let $(X,Y)$ be uniformly distributed on the interior of the ellipse
$$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ where $a$ and $b$ are the
semi-axes of the ellipse. Then, $X$ and $Y$ have marginal densities
\begin{align}
f_X(x) &= \frac{2}{\pi a^2}\sqrt{a^2-x^2}\,\,\mathbf 1_{-a,a}(x),\\
f_X(x) &= \frac{2}{\pi b^2}\sqrt{... | Correlation coefficient for a uniform distribution on an ellipse | Let $(X,Y)$ be uniformly distributed on the interior of the ellipse
$$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ where $a$ and $b$ are the
semi-axes of the ellipse. Then, $X$ and $Y$ have marginal densi | Correlation coefficient for a uniform distribution on an ellipse
Let $(X,Y)$ be uniformly distributed on the interior of the ellipse
$$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ where $a$ and $b$ are the
semi-axes of the ellipse. Then, $X$ and $Y$ have marginal densities
\begin{align}
f_X(x) &= \frac{2}{\pi a^2}\sqrt{a^2... | Correlation coefficient for a uniform distribution on an ellipse
Let $(X,Y)$ be uniformly distributed on the interior of the ellipse
$$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ where $a$ and $b$ are the
semi-axes of the ellipse. Then, $X$ and $Y$ have marginal densi |
35,414 | Covariance of Non-Random Vectors Equal to Zero | "Covariance" is used in many distinct senses. It can be
a property of a bivariate population,
a property of a bivariate distribution,
a property of a paired dataset, or
an estimator of (1) or (2) based on a sample.
Because any finite collection of ordered pairs $((x_1,y_1), \ldots, (x_n,y_n))$ can be considered an i... | Covariance of Non-Random Vectors Equal to Zero | "Covariance" is used in many distinct senses. It can be
a property of a bivariate population,
a property of a bivariate distribution,
a property of a paired dataset, or
an estimator of (1) or (2) ba | Covariance of Non-Random Vectors Equal to Zero
"Covariance" is used in many distinct senses. It can be
a property of a bivariate population,
a property of a bivariate distribution,
a property of a paired dataset, or
an estimator of (1) or (2) based on a sample.
Because any finite collection of ordered pairs $((x_1,y... | Covariance of Non-Random Vectors Equal to Zero
"Covariance" is used in many distinct senses. It can be
a property of a bivariate population,
a property of a bivariate distribution,
a property of a paired dataset, or
an estimator of (1) or (2) ba |
35,415 | Covariance of Non-Random Vectors Equal to Zero | You have a misconception. Using the cov function on a pair of vectors computes the sample covariance of the two vectors. That is, it is assuming X and Y are vectors of observations of two one-dimensional random variables. That is why it doesn't give zero as an answer. What is zero (a matrix filled with zeroes, actually... | Covariance of Non-Random Vectors Equal to Zero | You have a misconception. Using the cov function on a pair of vectors computes the sample covariance of the two vectors. That is, it is assuming X and Y are vectors of observations of two one-dimensio | Covariance of Non-Random Vectors Equal to Zero
You have a misconception. Using the cov function on a pair of vectors computes the sample covariance of the two vectors. That is, it is assuming X and Y are vectors of observations of two one-dimensional random variables. That is why it doesn't give zero as an answer. What... | Covariance of Non-Random Vectors Equal to Zero
You have a misconception. Using the cov function on a pair of vectors computes the sample covariance of the two vectors. That is, it is assuming X and Y are vectors of observations of two one-dimensio |
35,416 | Covariance of Non-Random Vectors Equal to Zero | Simply put a non-random vector has component elements that are constant -- they do not change by definition. Since they do not change, there is no variability in their values. Hence their variances are always zero. | Covariance of Non-Random Vectors Equal to Zero | Simply put a non-random vector has component elements that are constant -- they do not change by definition. Since they do not change, there is no variability in their values. Hence their variances | Covariance of Non-Random Vectors Equal to Zero
Simply put a non-random vector has component elements that are constant -- they do not change by definition. Since they do not change, there is no variability in their values. Hence their variances are always zero. | Covariance of Non-Random Vectors Equal to Zero
Simply put a non-random vector has component elements that are constant -- they do not change by definition. Since they do not change, there is no variability in their values. Hence their variances |
35,417 | How to best evaluate a time series prediction algorithm? | What you are proposing is known as a "rolling origin" evaluation in the forecasting literature. And yes, this method of evaluating forecasting algorithms is very widely used.
If you find that performance is a bottleneck, you could do subsampling. Don't use every possible origin. Instead, use, e.g., every fifth possible... | How to best evaluate a time series prediction algorithm? | What you are proposing is known as a "rolling origin" evaluation in the forecasting literature. And yes, this method of evaluating forecasting algorithms is very widely used.
If you find that performa | How to best evaluate a time series prediction algorithm?
What you are proposing is known as a "rolling origin" evaluation in the forecasting literature. And yes, this method of evaluating forecasting algorithms is very widely used.
If you find that performance is a bottleneck, you could do subsampling. Don't use every ... | How to best evaluate a time series prediction algorithm?
What you are proposing is known as a "rolling origin" evaluation in the forecasting literature. And yes, this method of evaluating forecasting algorithms is very widely used.
If you find that performa |
35,418 | Estimators independence in simple linear regression | This is tantamount to showing that $\widehat{\boldsymbol{\beta}}$, the vector of estimates, is independent of the residual vector $\mathbf{e}$. I trust that you are familiar with the matrix notation of the model, it makes the proof quite short.
Recall that the OLS estimator is given by $\left( \mathbf{X}^{T}\mathbf{X} ... | Estimators independence in simple linear regression | This is tantamount to showing that $\widehat{\boldsymbol{\beta}}$, the vector of estimates, is independent of the residual vector $\mathbf{e}$. I trust that you are familiar with the matrix notation o | Estimators independence in simple linear regression
This is tantamount to showing that $\widehat{\boldsymbol{\beta}}$, the vector of estimates, is independent of the residual vector $\mathbf{e}$. I trust that you are familiar with the matrix notation of the model, it makes the proof quite short.
Recall that the OLS est... | Estimators independence in simple linear regression
This is tantamount to showing that $\widehat{\boldsymbol{\beta}}$, the vector of estimates, is independent of the residual vector $\mathbf{e}$. I trust that you are familiar with the matrix notation o |
35,419 | T-test using only summary data in a box plot | Since you have the sample means and your hypothesis relates to population means, I've assumed you'll definitely want to use the sample means in what follows.
With some distributional assumptions, you can certainly get somewhere.
If the sample sizes are quite large you could assume a distribution in order to scale the ... | T-test using only summary data in a box plot | Since you have the sample means and your hypothesis relates to population means, I've assumed you'll definitely want to use the sample means in what follows.
With some distributional assumptions, you | T-test using only summary data in a box plot
Since you have the sample means and your hypothesis relates to population means, I've assumed you'll definitely want to use the sample means in what follows.
With some distributional assumptions, you can certainly get somewhere.
If the sample sizes are quite large you could... | T-test using only summary data in a box plot
Since you have the sample means and your hypothesis relates to population means, I've assumed you'll definitely want to use the sample means in what follows.
With some distributional assumptions, you |
35,420 | Log vs square root link for Poisson data in R | You're confusing the effect of a data-transformation with the use of a link function in a GLM.
If you do a log-transform of the response, it will "straighten the relationship" if $E(Y|x)$ is of the form $\exp(a+bx)$. Similarly, if you take the square root of the response, it will make the variance nearly constant, if t... | Log vs square root link for Poisson data in R | You're confusing the effect of a data-transformation with the use of a link function in a GLM.
If you do a log-transform of the response, it will "straighten the relationship" if $E(Y|x)$ is of the fo | Log vs square root link for Poisson data in R
You're confusing the effect of a data-transformation with the use of a link function in a GLM.
If you do a log-transform of the response, it will "straighten the relationship" if $E(Y|x)$ is of the form $\exp(a+bx)$. Similarly, if you take the square root of the response, i... | Log vs square root link for Poisson data in R
You're confusing the effect of a data-transformation with the use of a link function in a GLM.
If you do a log-transform of the response, it will "straighten the relationship" if $E(Y|x)$ is of the fo |
35,421 | Log vs square root link for Poisson data in R | If you are fitting a GLiM with a Poisson distribution specified for the response, you do not have to try to stabilize the conditional variance of the response. That is automatically taken care of for you. The Poisson GLiM does not assume constant variance in the sense that a regular linear (Gaussian) regression model... | Log vs square root link for Poisson data in R | If you are fitting a GLiM with a Poisson distribution specified for the response, you do not have to try to stabilize the conditional variance of the response. That is automatically taken care of for | Log vs square root link for Poisson data in R
If you are fitting a GLiM with a Poisson distribution specified for the response, you do not have to try to stabilize the conditional variance of the response. That is automatically taken care of for you. The Poisson GLiM does not assume constant variance in the sense tha... | Log vs square root link for Poisson data in R
If you are fitting a GLiM with a Poisson distribution specified for the response, you do not have to try to stabilize the conditional variance of the response. That is automatically taken care of for |
35,422 | Moment-generating function (MGF) of non-central chi-squared distribution | Let $Z$ have a standard normal distribution, with mean $0$ and variance $1$, then $(Z+\mu)^2$ has a noncentral chi-squared distribution with one degree of freedom. The moment-generating function of $(Z+\mu)^2$ then is
\begin{equation}
E[e^{t(Z+\mu)^2}] = \int_{-\infty}^{+\infty} e^{t(z+\mu)^2} f_Z(z) \text{d}z
\end{eq... | Moment-generating function (MGF) of non-central chi-squared distribution | Let $Z$ have a standard normal distribution, with mean $0$ and variance $1$, then $(Z+\mu)^2$ has a noncentral chi-squared distribution with one degree of freedom. The moment-generating function of $( | Moment-generating function (MGF) of non-central chi-squared distribution
Let $Z$ have a standard normal distribution, with mean $0$ and variance $1$, then $(Z+\mu)^2$ has a noncentral chi-squared distribution with one degree of freedom. The moment-generating function of $(Z+\mu)^2$ then is
\begin{equation}
E[e^{t(Z+\m... | Moment-generating function (MGF) of non-central chi-squared distribution
Let $Z$ have a standard normal distribution, with mean $0$ and variance $1$, then $(Z+\mu)^2$ has a noncentral chi-squared distribution with one degree of freedom. The moment-generating function of $( |
35,423 | How exactly are standardized residuals calculated | The statistical tools in Excel have always been black boxes. There's nothing for it but to do some forensic reverse-engineering. By performing a simple regression in Excel 2013, involving the data $x=(1,2,3,4,5,6,7,8,9)$ and $y=(2,1,4,3,6,5,9,8,7)$, and requesting "standardized residuals" in the dialog, I obtained ou... | How exactly are standardized residuals calculated | The statistical tools in Excel have always been black boxes. There's nothing for it but to do some forensic reverse-engineering. By performing a simple regression in Excel 2013, involving the data $ | How exactly are standardized residuals calculated
The statistical tools in Excel have always been black boxes. There's nothing for it but to do some forensic reverse-engineering. By performing a simple regression in Excel 2013, involving the data $x=(1,2,3,4,5,6,7,8,9)$ and $y=(2,1,4,3,6,5,9,8,7)$, and requesting "st... | How exactly are standardized residuals calculated
The statistical tools in Excel have always been black boxes. There's nothing for it but to do some forensic reverse-engineering. By performing a simple regression in Excel 2013, involving the data $ |
35,424 | How exactly are standardized residuals calculated | In R :
modeGlob <- lm(rnorm(100)~ abs(rnorm(100))) #Your model.
hii <- hatvalues(modeGlob) # hat matrix.
rst <- modeGlob$residuals / (summary(modeGlob)$sigma * sqrt(1-hii)) # manually calculate standardized residuals.
identical(rstandard(modeGlob) , rst) # check, this must be TRUE.
plot(rstanda... | How exactly are standardized residuals calculated | In R :
modeGlob <- lm(rnorm(100)~ abs(rnorm(100))) #Your model.
hii <- hatvalues(modeGlob) # hat matrix.
rst <- modeGlob$residuals / (summary(modeGlob)$sigma * sqrt(1-hii)) # manually c | How exactly are standardized residuals calculated
In R :
modeGlob <- lm(rnorm(100)~ abs(rnorm(100))) #Your model.
hii <- hatvalues(modeGlob) # hat matrix.
rst <- modeGlob$residuals / (summary(modeGlob)$sigma * sqrt(1-hii)) # manually calculate standardized residuals.
identical(rstandard(modeGlob) , ... | How exactly are standardized residuals calculated
In R :
modeGlob <- lm(rnorm(100)~ abs(rnorm(100))) #Your model.
hii <- hatvalues(modeGlob) # hat matrix.
rst <- modeGlob$residuals / (summary(modeGlob)$sigma * sqrt(1-hii)) # manually c |
35,425 | Introductory graduate-level survey sampling textbook? | Sampling: Design and Analysis by Sharon Lohr (quoted in your link) is probably the easiest book. Thomas Lumley's "Survey analysis in R" is even easier, but it doesn't show you the theories.
To judge whether you're ok to read the book by Lohr, do you know?
Sample mean vs Population mean?
Central limit theorem?
Normal d... | Introductory graduate-level survey sampling textbook? | Sampling: Design and Analysis by Sharon Lohr (quoted in your link) is probably the easiest book. Thomas Lumley's "Survey analysis in R" is even easier, but it doesn't show you the theories.
To judge w | Introductory graduate-level survey sampling textbook?
Sampling: Design and Analysis by Sharon Lohr (quoted in your link) is probably the easiest book. Thomas Lumley's "Survey analysis in R" is even easier, but it doesn't show you the theories.
To judge whether you're ok to read the book by Lohr, do you know?
Sample me... | Introductory graduate-level survey sampling textbook?
Sampling: Design and Analysis by Sharon Lohr (quoted in your link) is probably the easiest book. Thomas Lumley's "Survey analysis in R" is even easier, but it doesn't show you the theories.
To judge w |
35,426 | Introductory graduate-level survey sampling textbook? | I was going to recommend Sampling: Design and Analysis by Sharon Lohr, but it was already mentioned. Not much heavy on math, it's an easy intro book that covers most of the basic topics and uses plots and pictures to build on intuition.
A more mathy book is Cochran Sampling Techniques. It's more comprehensive and it ha... | Introductory graduate-level survey sampling textbook? | I was going to recommend Sampling: Design and Analysis by Sharon Lohr, but it was already mentioned. Not much heavy on math, it's an easy intro book that covers most of the basic topics and uses plots | Introductory graduate-level survey sampling textbook?
I was going to recommend Sampling: Design and Analysis by Sharon Lohr, but it was already mentioned. Not much heavy on math, it's an easy intro book that covers most of the basic topics and uses plots and pictures to build on intuition.
A more mathy book is Cochran ... | Introductory graduate-level survey sampling textbook?
I was going to recommend Sampling: Design and Analysis by Sharon Lohr, but it was already mentioned. Not much heavy on math, it's an easy intro book that covers most of the basic topics and uses plots |
35,427 | Why is post treatment bias a bias and not just multicollinearity? | First, let’s clear up a difference between the terms, and then discuss the respective problems that each causes.
Multi-collinearity refers to a problematic relationship between multiple right-hand-side variables (usually control variables) caused by their being highly correlated, regardless of causal ordering. Post-tre... | Why is post treatment bias a bias and not just multicollinearity? | First, let’s clear up a difference between the terms, and then discuss the respective problems that each causes.
Multi-collinearity refers to a problematic relationship between multiple right-hand-sid | Why is post treatment bias a bias and not just multicollinearity?
First, let’s clear up a difference between the terms, and then discuss the respective problems that each causes.
Multi-collinearity refers to a problematic relationship between multiple right-hand-side variables (usually control variables) caused by thei... | Why is post treatment bias a bias and not just multicollinearity?
First, let’s clear up a difference between the terms, and then discuss the respective problems that each causes.
Multi-collinearity refers to a problematic relationship between multiple right-hand-sid |
35,428 | Estimate number of breakpoints in regression | Some remarks:
You need to estimate two parameters in each segment (intercept and slope). Hence breakpoints() requires that there are at least three observations in each segment...otherwise you cannot estimate the parameters (without getting a perfect fit).
But three is the minimal value that is technically possible. W... | Estimate number of breakpoints in regression | Some remarks:
You need to estimate two parameters in each segment (intercept and slope). Hence breakpoints() requires that there are at least three observations in each segment...otherwise you cannot | Estimate number of breakpoints in regression
Some remarks:
You need to estimate two parameters in each segment (intercept and slope). Hence breakpoints() requires that there are at least three observations in each segment...otherwise you cannot estimate the parameters (without getting a perfect fit).
But three is the ... | Estimate number of breakpoints in regression
Some remarks:
You need to estimate two parameters in each segment (intercept and slope). Hence breakpoints() requires that there are at least three observations in each segment...otherwise you cannot |
35,429 | A model for non-negative data with many zeros: pros and cons of Tweedie GLM | You're right to think that a Box-Cox transformation won't deal with the zeros issue (nor indeed would any other transformation).
The Tweedie might be suitable, and is sometimes used for data like these*, but the probability of a zero is related to the $p$ (the power in the variance function).
*\ another issue to consid... | A model for non-negative data with many zeros: pros and cons of Tweedie GLM | You're right to think that a Box-Cox transformation won't deal with the zeros issue (nor indeed would any other transformation).
The Tweedie might be suitable, and is sometimes used for data like thes | A model for non-negative data with many zeros: pros and cons of Tweedie GLM
You're right to think that a Box-Cox transformation won't deal with the zeros issue (nor indeed would any other transformation).
The Tweedie might be suitable, and is sometimes used for data like these*, but the probability of a zero is related... | A model for non-negative data with many zeros: pros and cons of Tweedie GLM
You're right to think that a Box-Cox transformation won't deal with the zeros issue (nor indeed would any other transformation).
The Tweedie might be suitable, and is sometimes used for data like thes |
35,430 | Rank and z-transform instead of Wilcoxon? | (Pulls Conover [1] off the bookshelf...)
This idea is quite old; it dates back at least to van der Waerden (1952/1953) [2][3], who suggested a test that corresponds to the Kruskal Wallis but with ranks replaced by normal scores. (The idea of using ordered random normal values rather than an approximation of their expec... | Rank and z-transform instead of Wilcoxon? | (Pulls Conover [1] off the bookshelf...)
This idea is quite old; it dates back at least to van der Waerden (1952/1953) [2][3], who suggested a test that corresponds to the Kruskal Wallis but with rank | Rank and z-transform instead of Wilcoxon?
(Pulls Conover [1] off the bookshelf...)
This idea is quite old; it dates back at least to van der Waerden (1952/1953) [2][3], who suggested a test that corresponds to the Kruskal Wallis but with ranks replaced by normal scores. (The idea of using ordered random normal values r... | Rank and z-transform instead of Wilcoxon?
(Pulls Conover [1] off the bookshelf...)
This idea is quite old; it dates back at least to van der Waerden (1952/1953) [2][3], who suggested a test that corresponds to the Kruskal Wallis but with rank |
35,431 | Exact definition of Maxout | None of the above; maxout networks don't follow the architecture you assumed.
From the beginning of the "description of maxout" section in the paper you linked, which defined maxout:
Given an input $x \in \mathbb{R}^d$ ($x$ may be $v$, or may be a hidden layer’s state), a maxout hidden layer implements the function
$$... | Exact definition of Maxout | None of the above; maxout networks don't follow the architecture you assumed.
From the beginning of the "description of maxout" section in the paper you linked, which defined maxout:
Given an input $ | Exact definition of Maxout
None of the above; maxout networks don't follow the architecture you assumed.
From the beginning of the "description of maxout" section in the paper you linked, which defined maxout:
Given an input $x \in \mathbb{R}^d$ ($x$ may be $v$, or may be a hidden layer’s state), a maxout hidden layer... | Exact definition of Maxout
None of the above; maxout networks don't follow the architecture you assumed.
From the beginning of the "description of maxout" section in the paper you linked, which defined maxout:
Given an input $ |
35,432 | My Test accuracy is pretty bad compared to cross-validation accuracy | Hastie et al discuss this precise issue in their book, The Elements of Statistical Learning. They conclude that cross-validation is NOT an estimate of test-error conditional on the training set. Rather, they believe it is an estimate of the unconditional test error. In other words, this is the expected test error if... | My Test accuracy is pretty bad compared to cross-validation accuracy | Hastie et al discuss this precise issue in their book, The Elements of Statistical Learning. They conclude that cross-validation is NOT an estimate of test-error conditional on the training set. Rat | My Test accuracy is pretty bad compared to cross-validation accuracy
Hastie et al discuss this precise issue in their book, The Elements of Statistical Learning. They conclude that cross-validation is NOT an estimate of test-error conditional on the training set. Rather, they believe it is an estimate of the uncondit... | My Test accuracy is pretty bad compared to cross-validation accuracy
Hastie et al discuss this precise issue in their book, The Elements of Statistical Learning. They conclude that cross-validation is NOT an estimate of test-error conditional on the training set. Rat |
35,433 | My Test accuracy is pretty bad compared to cross-validation accuracy | I'd suspect something is wrong with how you created the hold out set. Ie either it wasn't randomized or needed to be done with stratified sampling.
This sort of thing can also happen if you did feature selection or engineering outside of the CV loop as you'll produce features that look good across the cv folds but don'... | My Test accuracy is pretty bad compared to cross-validation accuracy | I'd suspect something is wrong with how you created the hold out set. Ie either it wasn't randomized or needed to be done with stratified sampling.
This sort of thing can also happen if you did featur | My Test accuracy is pretty bad compared to cross-validation accuracy
I'd suspect something is wrong with how you created the hold out set. Ie either it wasn't randomized or needed to be done with stratified sampling.
This sort of thing can also happen if you did feature selection or engineering outside of the CV loop a... | My Test accuracy is pretty bad compared to cross-validation accuracy
I'd suspect something is wrong with how you created the hold out set. Ie either it wasn't randomized or needed to be done with stratified sampling.
This sort of thing can also happen if you did featur |
35,434 | PDF of a sum of dependent variables | Find the pdf of: $\quad A+D+\sqrt{(A-D)^2+4BC}, \quad $ where $A,B,C,D$ are iid $Uniform(0,1)$
Let $U = 4 BC$, where $U$ has pdf: $\quad g(u) = \frac{1}{4} \log \left(\frac{4}{u}\right) \quad \text{for } 0<u<4$.
This reduces the problem from 4 to 3 independent random variables. Then, by independence, the joint pdf ... | PDF of a sum of dependent variables | Find the pdf of: $\quad A+D+\sqrt{(A-D)^2+4BC}, \quad $ where $A,B,C,D$ are iid $Uniform(0,1)$
Let $U = 4 BC$, where $U$ has pdf: $\quad g(u) = \frac{1}{4} \log \left(\frac{4}{u}\right) \quad \tex | PDF of a sum of dependent variables
Find the pdf of: $\quad A+D+\sqrt{(A-D)^2+4BC}, \quad $ where $A,B,C,D$ are iid $Uniform(0,1)$
Let $U = 4 BC$, where $U$ has pdf: $\quad g(u) = \frac{1}{4} \log \left(\frac{4}{u}\right) \quad \text{for } 0<u<4$.
This reduces the problem from 4 to 3 independent random variables. T... | PDF of a sum of dependent variables
Find the pdf of: $\quad A+D+\sqrt{(A-D)^2+4BC}, \quad $ where $A,B,C,D$ are iid $Uniform(0,1)$
Let $U = 4 BC$, where $U$ has pdf: $\quad g(u) = \frac{1}{4} \log \left(\frac{4}{u}\right) \quad \tex |
35,435 | PDF of a sum of dependent variables | Just after reading wolfies answer I understood I could calculate the final distribution from the very beginning without all the mid-point steps:
M[x_] := M[x] =
Evaluate@FullSimplify@
Integrate[
Boole[a + d + Sqrt[(a - d)^2 + 4 b c] <= x], {a, 0, 1}, {b, 0,
1}, {c, 0, 1}, {d, 0, 1}] gives the CDF and... | PDF of a sum of dependent variables | Just after reading wolfies answer I understood I could calculate the final distribution from the very beginning without all the mid-point steps:
M[x_] := M[x] =
Evaluate@FullSimplify@
Integrate | PDF of a sum of dependent variables
Just after reading wolfies answer I understood I could calculate the final distribution from the very beginning without all the mid-point steps:
M[x_] := M[x] =
Evaluate@FullSimplify@
Integrate[
Boole[a + d + Sqrt[(a - d)^2 + 4 b c] <= x], {a, 0, 1}, {b, 0,
1}, {c,... | PDF of a sum of dependent variables
Just after reading wolfies answer I understood I could calculate the final distribution from the very beginning without all the mid-point steps:
M[x_] := M[x] =
Evaluate@FullSimplify@
Integrate |
35,436 | Likelihood Ratio for the Bivariate Normal distribution | As has been made clear in the comments, the OP is interested in the Likelihood ratio when the common variance is also estimated, and not known.
The joint density of one pair of $\{X_i, Y_i$}, given also the maintained assumptions on the parameter values is
$$ f(x_i,y_i) = \frac{1}{2 \pi \sigma^2\sqrt{3/4}} \ \exp\lef... | Likelihood Ratio for the Bivariate Normal distribution | As has been made clear in the comments, the OP is interested in the Likelihood ratio when the common variance is also estimated, and not known.
The joint density of one pair of $\{X_i, Y_i$}, given al | Likelihood Ratio for the Bivariate Normal distribution
As has been made clear in the comments, the OP is interested in the Likelihood ratio when the common variance is also estimated, and not known.
The joint density of one pair of $\{X_i, Y_i$}, given also the maintained assumptions on the parameter values is
$$ f(x_i... | Likelihood Ratio for the Bivariate Normal distribution
As has been made clear in the comments, the OP is interested in the Likelihood ratio when the common variance is also estimated, and not known.
The joint density of one pair of $\{X_i, Y_i$}, given al |
35,437 | Likelihood Ratio for the Bivariate Normal distribution | I would like to suggest this way to simplify the likelihood ratio $\Lambda$.
I am not a native English speaker so feel free to correct my grammar errors.
Let me introduce these statistics $U, V$ which are given by linear combination of X and Y as
$\begin{pmatrix} U \\ V \end{pmatrix} =\begin{pmatrix} 1 & -{1 \over 2} ... | Likelihood Ratio for the Bivariate Normal distribution | I would like to suggest this way to simplify the likelihood ratio $\Lambda$.
I am not a native English speaker so feel free to correct my grammar errors.
Let me introduce these statistics $U, V$ which | Likelihood Ratio for the Bivariate Normal distribution
I would like to suggest this way to simplify the likelihood ratio $\Lambda$.
I am not a native English speaker so feel free to correct my grammar errors.
Let me introduce these statistics $U, V$ which are given by linear combination of X and Y as
$\begin{pmatrix} ... | Likelihood Ratio for the Bivariate Normal distribution
I would like to suggest this way to simplify the likelihood ratio $\Lambda$.
I am not a native English speaker so feel free to correct my grammar errors.
Let me introduce these statistics $U, V$ which |
35,438 | Likelihood Ratio for the Bivariate Normal distribution | It is my understanding that there are likelihood ratios and log likelihood ratios, the latter being the log of the quotient as opposed to the quotient of logs. I think this is where you have gone wrong. Best of luck! | Likelihood Ratio for the Bivariate Normal distribution | It is my understanding that there are likelihood ratios and log likelihood ratios, the latter being the log of the quotient as opposed to the quotient of logs. I think this is where you have gone wro | Likelihood Ratio for the Bivariate Normal distribution
It is my understanding that there are likelihood ratios and log likelihood ratios, the latter being the log of the quotient as opposed to the quotient of logs. I think this is where you have gone wrong. Best of luck! | Likelihood Ratio for the Bivariate Normal distribution
It is my understanding that there are likelihood ratios and log likelihood ratios, the latter being the log of the quotient as opposed to the quotient of logs. I think this is where you have gone wro |
35,439 | Likelihood Ratio for the Bivariate Normal distribution | I am fairly confident that it reduces to a statistic with an F distribution. The numerator of the likelihood ratio you have provided is a chi-squared distribution multiplied by a constant (having 2*(n-1)) under HO. Also, under HO, X == Y, therefore the denominator can also be written as a chi-squared variable (having... | Likelihood Ratio for the Bivariate Normal distribution | I am fairly confident that it reduces to a statistic with an F distribution. The numerator of the likelihood ratio you have provided is a chi-squared distribution multiplied by a constant (having 2*( | Likelihood Ratio for the Bivariate Normal distribution
I am fairly confident that it reduces to a statistic with an F distribution. The numerator of the likelihood ratio you have provided is a chi-squared distribution multiplied by a constant (having 2*(n-1)) under HO. Also, under HO, X == Y, therefore the denominato... | Likelihood Ratio for the Bivariate Normal distribution
I am fairly confident that it reduces to a statistic with an F distribution. The numerator of the likelihood ratio you have provided is a chi-squared distribution multiplied by a constant (having 2*( |
35,440 | Likelihood Ratio for the Bivariate Normal distribution | I am fairly confident that it reduces to a statistic with an F distribution too. The numerator of the likelihood ratio you have provided is a chi-squared distribution multiplied by a constant, and the same holds for the denominator. The cross product XY is the sum of two independent chi-squared variables since var (x)... | Likelihood Ratio for the Bivariate Normal distribution | I am fairly confident that it reduces to a statistic with an F distribution too. The numerator of the likelihood ratio you have provided is a chi-squared distribution multiplied by a constant, and the | Likelihood Ratio for the Bivariate Normal distribution
I am fairly confident that it reduces to a statistic with an F distribution too. The numerator of the likelihood ratio you have provided is a chi-squared distribution multiplied by a constant, and the same holds for the denominator. The cross product XY is the sum... | Likelihood Ratio for the Bivariate Normal distribution
I am fairly confident that it reduces to a statistic with an F distribution too. The numerator of the likelihood ratio you have provided is a chi-squared distribution multiplied by a constant, and the |
35,441 | Choice between different robust regressions in R | In the notation I will use, $p$ will be the number of design variables (including the constant term), $n$ the number of observations with $n\geq2p+1$ (if this last condition was not met, the package would not have returned a fit but an error, so I assume it is met). I will denote by $\hat{\boldsymbol\beta}_{FLTS}$ the ... | Choice between different robust regressions in R | In the notation I will use, $p$ will be the number of design variables (including the constant term), $n$ the number of observations with $n\geq2p+1$ (if this last condition was not met, the package w | Choice between different robust regressions in R
In the notation I will use, $p$ will be the number of design variables (including the constant term), $n$ the number of observations with $n\geq2p+1$ (if this last condition was not met, the package would not have returned a fit but an error, so I assume it is met). I wi... | Choice between different robust regressions in R
In the notation I will use, $p$ will be the number of design variables (including the constant term), $n$ the number of observations with $n\geq2p+1$ (if this last condition was not met, the package w |
35,442 | Convert hazards ratio to odds ratio | If there was an extremely low proportion of subjects with an event in all experiments (let's say <10%) and the hazard and odds ratios are vey close to 1, then hazard, odds and relative risk ratios will be relatively close to each other.
If that is not the case the fundamental differences between these measures will be ... | Convert hazards ratio to odds ratio | If there was an extremely low proportion of subjects with an event in all experiments (let's say <10%) and the hazard and odds ratios are vey close to 1, then hazard, odds and relative risk ratios wil | Convert hazards ratio to odds ratio
If there was an extremely low proportion of subjects with an event in all experiments (let's say <10%) and the hazard and odds ratios are vey close to 1, then hazard, odds and relative risk ratios will be relatively close to each other.
If that is not the case the fundamental differe... | Convert hazards ratio to odds ratio
If there was an extremely low proportion of subjects with an event in all experiments (let's say <10%) and the hazard and odds ratios are vey close to 1, then hazard, odds and relative risk ratios wil |
35,443 | Convert hazards ratio to odds ratio | $$\text{RR} = (1 - e^{\text{HR}\ln(1-r)})/r$$ where HR is the hazard ratio and r is the rate for the reference group. If r is not reported, it is probably reported elsewhere (e.g. baseline death rate).
See Shor et al. (2017) doi: 10.1016/j.socscimed.2017.05.049
Zhang and Yu (1998), doi: 10.1001/jama.280.19.1690 prov... | Convert hazards ratio to odds ratio | $$\text{RR} = (1 - e^{\text{HR}\ln(1-r)})/r$$ where HR is the hazard ratio and r is the rate for the reference group. If r is not reported, it is probably reported elsewhere (e.g. baseline death rate | Convert hazards ratio to odds ratio
$$\text{RR} = (1 - e^{\text{HR}\ln(1-r)})/r$$ where HR is the hazard ratio and r is the rate for the reference group. If r is not reported, it is probably reported elsewhere (e.g. baseline death rate).
See Shor et al. (2017) doi: 10.1016/j.socscimed.2017.05.049
Zhang and Yu (1998)... | Convert hazards ratio to odds ratio
$$\text{RR} = (1 - e^{\text{HR}\ln(1-r)})/r$$ where HR is the hazard ratio and r is the rate for the reference group. If r is not reported, it is probably reported elsewhere (e.g. baseline death rate |
35,444 | Convert hazards ratio to odds ratio | Exploiting the assumption that hazard ratios are asymptotically similar to relative risks, you can use exploit the formula recommendeed by Grant et al, BMJ 2014:
RR = OR / (1 - p + (p * OR)
where RR is the relative risk, OR is the odds ratio, and p is the control event rate, which leads to the following:
OR = ((1 - p)... | Convert hazards ratio to odds ratio | Exploiting the assumption that hazard ratios are asymptotically similar to relative risks, you can use exploit the formula recommendeed by Grant et al, BMJ 2014:
RR = OR / (1 - p + (p * OR)
where RR | Convert hazards ratio to odds ratio
Exploiting the assumption that hazard ratios are asymptotically similar to relative risks, you can use exploit the formula recommendeed by Grant et al, BMJ 2014:
RR = OR / (1 - p + (p * OR)
where RR is the relative risk, OR is the odds ratio, and p is the control event rate, which l... | Convert hazards ratio to odds ratio
Exploiting the assumption that hazard ratios are asymptotically similar to relative risks, you can use exploit the formula recommendeed by Grant et al, BMJ 2014:
RR = OR / (1 - p + (p * OR)
where RR |
35,445 | Convert hazards ratio to odds ratio | See also this paper on the relation between OR, RR, and HR
Stare, J. & Maucort-Boulch, D. Odds ratio, hazard ratio and relative risk. Advances in Methodology and Statistics 13, 59–67 (2016).
Available in https://mz.mf.uni-lj.si/article/view/159/262 | Convert hazards ratio to odds ratio | See also this paper on the relation between OR, RR, and HR
Stare, J. & Maucort-Boulch, D. Odds ratio, hazard ratio and relative risk. Advances in Methodology and Statistics 13, 59–67 (2016).
Available | Convert hazards ratio to odds ratio
See also this paper on the relation between OR, RR, and HR
Stare, J. & Maucort-Boulch, D. Odds ratio, hazard ratio and relative risk. Advances in Methodology and Statistics 13, 59–67 (2016).
Available in https://mz.mf.uni-lj.si/article/view/159/262 | Convert hazards ratio to odds ratio
See also this paper on the relation between OR, RR, and HR
Stare, J. & Maucort-Boulch, D. Odds ratio, hazard ratio and relative risk. Advances in Methodology and Statistics 13, 59–67 (2016).
Available |
35,446 | Are time series methods only good for forecasting? | Usually you want to forecast the behaviour of a system to improve your reaction to and interaction with that system. But at the end of the day, forecasting is only a last resort, if it is not feasible to control the system. Moreover, forecasting with nothing but time series is something you usually only do if your syst... | Are time series methods only good for forecasting? | Usually you want to forecast the behaviour of a system to improve your reaction to and interaction with that system. But at the end of the day, forecasting is only a last resort, if it is not feasible | Are time series methods only good for forecasting?
Usually you want to forecast the behaviour of a system to improve your reaction to and interaction with that system. But at the end of the day, forecasting is only a last resort, if it is not feasible to control the system. Moreover, forecasting with nothing but time s... | Are time series methods only good for forecasting?
Usually you want to forecast the behaviour of a system to improve your reaction to and interaction with that system. But at the end of the day, forecasting is only a last resort, if it is not feasible |
35,447 | Are time series methods only good for forecasting? | I would say no. Time series methods can reveal something about the structure of the problem in hand, not just about some forecasts done only with series own history.
For example state-space model form can be used to model time varying regression with several varieties. And also structural time series can be casted int... | Are time series methods only good for forecasting? | I would say no. Time series methods can reveal something about the structure of the problem in hand, not just about some forecasts done only with series own history.
For example state-space model for | Are time series methods only good for forecasting?
I would say no. Time series methods can reveal something about the structure of the problem in hand, not just about some forecasts done only with series own history.
For example state-space model form can be used to model time varying regression with several varieties... | Are time series methods only good for forecasting?
I would say no. Time series methods can reveal something about the structure of the problem in hand, not just about some forecasts done only with series own history.
For example state-space model for |
35,448 | Are time series methods only good for forecasting? | No. I'll give you one use of time series, which is not related to forecasting: spectral analysis.
FFT is the work horse in spectral analysis, but it works best when your series are essentially infinite, or very long. Analyzing sound waves is a good application for FFT. However, in social sciences the series are usuall... | Are time series methods only good for forecasting? | No. I'll give you one use of time series, which is not related to forecasting: spectral analysis.
FFT is the work horse in spectral analysis, but it works best when your series are essentially infini | Are time series methods only good for forecasting?
No. I'll give you one use of time series, which is not related to forecasting: spectral analysis.
FFT is the work horse in spectral analysis, but it works best when your series are essentially infinite, or very long. Analyzing sound waves is a good application for FFT... | Are time series methods only good for forecasting?
No. I'll give you one use of time series, which is not related to forecasting: spectral analysis.
FFT is the work horse in spectral analysis, but it works best when your series are essentially infini |
35,449 | Applied statistics vs Mathematical statistics | There are not only mathematical statistics and applied statistics, but also statistics (in general). You could say that statistics is about why and applied statistics is about how. Mathematical statistics is a branch of mathematics and generally a scientific discipline (the same as statistics). Applied statistics, on t... | Applied statistics vs Mathematical statistics | There are not only mathematical statistics and applied statistics, but also statistics (in general). You could say that statistics is about why and applied statistics is about how. Mathematical statis | Applied statistics vs Mathematical statistics
There are not only mathematical statistics and applied statistics, but also statistics (in general). You could say that statistics is about why and applied statistics is about how. Mathematical statistics is a branch of mathematics and generally a scientific discipline (the... | Applied statistics vs Mathematical statistics
There are not only mathematical statistics and applied statistics, but also statistics (in general). You could say that statistics is about why and applied statistics is about how. Mathematical statis |
35,450 | Applied statistics vs Mathematical statistics | If you're simply taking a book on techniques and learning how to plug things into R/SAS/STATA, you're really not doing applied statistics, imo. The best applied statistics courses/programs involve a healthy dose of theory. The difference between the two really is one of emphasis. In an applied course, you're learning t... | Applied statistics vs Mathematical statistics | If you're simply taking a book on techniques and learning how to plug things into R/SAS/STATA, you're really not doing applied statistics, imo. The best applied statistics courses/programs involve a h | Applied statistics vs Mathematical statistics
If you're simply taking a book on techniques and learning how to plug things into R/SAS/STATA, you're really not doing applied statistics, imo. The best applied statistics courses/programs involve a healthy dose of theory. The difference between the two really is one of emp... | Applied statistics vs Mathematical statistics
If you're simply taking a book on techniques and learning how to plug things into R/SAS/STATA, you're really not doing applied statistics, imo. The best applied statistics courses/programs involve a h |
35,451 | Adding a value to each element of a column in R [closed] | Here you have every possibility:
x <- matrix(1:9, 3, 3)
add 5 to column 1:
x[, 1] + 5
add 5 to row 1:
x[1, ] + 5
add 1 to the first row, 2 to second, 3 to third:
x + 1:3
the same with columns:
t(t(x) + 1:3)
add 5 to all the cells:
x + 5 | Adding a value to each element of a column in R [closed] | Here you have every possibility:
x <- matrix(1:9, 3, 3)
add 5 to column 1:
x[, 1] + 5
add 5 to row 1:
x[1, ] + 5
add 1 to the first row, 2 to second, 3 to third:
x + 1:3
the same with columns:
t( | Adding a value to each element of a column in R [closed]
Here you have every possibility:
x <- matrix(1:9, 3, 3)
add 5 to column 1:
x[, 1] + 5
add 5 to row 1:
x[1, ] + 5
add 1 to the first row, 2 to second, 3 to third:
x + 1:3
the same with columns:
t(t(x) + 1:3)
add 5 to all the cells:
x + 5 | Adding a value to each element of a column in R [closed]
Here you have every possibility:
x <- matrix(1:9, 3, 3)
add 5 to column 1:
x[, 1] + 5
add 5 to row 1:
x[1, ] + 5
add 1 to the first row, 2 to second, 3 to third:
x + 1:3
the same with columns:
t( |
35,452 | Adding a value to each element of a column in R [closed] | R vectorizes operations (here: addition) automatically.
> c(1,2,3,4,5)+5
[1] 6 7 8 9 10
(Such questions are better at StackOverflow in the R tag.) | Adding a value to each element of a column in R [closed] | R vectorizes operations (here: addition) automatically.
> c(1,2,3,4,5)+5
[1] 6 7 8 9 10
(Such questions are better at StackOverflow in the R tag.) | Adding a value to each element of a column in R [closed]
R vectorizes operations (here: addition) automatically.
> c(1,2,3,4,5)+5
[1] 6 7 8 9 10
(Such questions are better at StackOverflow in the R tag.) | Adding a value to each element of a column in R [closed]
R vectorizes operations (here: addition) automatically.
> c(1,2,3,4,5)+5
[1] 6 7 8 9 10
(Such questions are better at StackOverflow in the R tag.) |
35,453 | Under which conditions do PCA and FA yield similar results? | This is an excellent question, but unfortunately (or maybe fortunately?) I have only recently written a very long answer in a related thread, addressing your question almost exactly. I would kindly ask you to look there and see if that answers your question.
Very briefly, if we just focus on PCA and FA loadings $\mathb... | Under which conditions do PCA and FA yield similar results? | This is an excellent question, but unfortunately (or maybe fortunately?) I have only recently written a very long answer in a related thread, addressing your question almost exactly. I would kindly as | Under which conditions do PCA and FA yield similar results?
This is an excellent question, but unfortunately (or maybe fortunately?) I have only recently written a very long answer in a related thread, addressing your question almost exactly. I would kindly ask you to look there and see if that answers your question.
V... | Under which conditions do PCA and FA yield similar results?
This is an excellent question, but unfortunately (or maybe fortunately?) I have only recently written a very long answer in a related thread, addressing your question almost exactly. I would kindly as |
35,454 | Testing whether data follows T-Distribution | Here's how to run KS-test on $t$-distribution.
Suppose you have a sample which you suspect is from $t$-distribution, and has size = $n$
Estimate the t-distribution parameters from the sample.
Generate $M$ samples of size $n$ from the estimated distribution.
For each sample obtain KS statistics using the estimated dis... | Testing whether data follows T-Distribution | Here's how to run KS-test on $t$-distribution.
Suppose you have a sample which you suspect is from $t$-distribution, and has size = $n$
Estimate the t-distribution parameters from the sample.
Genera | Testing whether data follows T-Distribution
Here's how to run KS-test on $t$-distribution.
Suppose you have a sample which you suspect is from $t$-distribution, and has size = $n$
Estimate the t-distribution parameters from the sample.
Generate $M$ samples of size $n$ from the estimated distribution.
For each sample ... | Testing whether data follows T-Distribution
Here's how to run KS-test on $t$-distribution.
Suppose you have a sample which you suspect is from $t$-distribution, and has size = $n$
Estimate the t-distribution parameters from the sample.
Genera |
35,455 | Testing whether data follows T-Distribution | Unless you have prespecified the mean and variance before you see the data, a straight Kolmogorov-Smirnov test is not suitable - indeed once you estimate parameters it's no longer distribution free.
Your p-values will be quite wrong - your actual significance level will be much lower than your nominal rate and power w... | Testing whether data follows T-Distribution | Unless you have prespecified the mean and variance before you see the data, a straight Kolmogorov-Smirnov test is not suitable - indeed once you estimate parameters it's no longer distribution free.
| Testing whether data follows T-Distribution
Unless you have prespecified the mean and variance before you see the data, a straight Kolmogorov-Smirnov test is not suitable - indeed once you estimate parameters it's no longer distribution free.
Your p-values will be quite wrong - your actual significance level will be m... | Testing whether data follows T-Distribution
Unless you have prespecified the mean and variance before you see the data, a straight Kolmogorov-Smirnov test is not suitable - indeed once you estimate parameters it's no longer distribution free.
|
35,456 | Why does a goodness of fit test use the chi square distribution rather than the hypothesised distribution? [duplicate] | There are two different distributions in play - the distribution of your data (or strictly speaking, the hypothesised distribution of the population they are drawn from), and the distribution of your test statistic under the assumption that the null hypothesis is correct. This is a little subtlety that I find can catch... | Why does a goodness of fit test use the chi square distribution rather than the hypothesised distrib | There are two different distributions in play - the distribution of your data (or strictly speaking, the hypothesised distribution of the population they are drawn from), and the distribution of your | Why does a goodness of fit test use the chi square distribution rather than the hypothesised distribution? [duplicate]
There are two different distributions in play - the distribution of your data (or strictly speaking, the hypothesised distribution of the population they are drawn from), and the distribution of your t... | Why does a goodness of fit test use the chi square distribution rather than the hypothesised distrib
There are two different distributions in play - the distribution of your data (or strictly speaking, the hypothesised distribution of the population they are drawn from), and the distribution of your |
35,457 | Finding peaks in power spectrum of a signal in R | You can think of it as a problem of analytically locating the local maxima
that are graphically observed. The code below locates those maxima by means of a one-dimensional optimization algorithm that is applied across overlapping intervals that cover the entire x-axis. At each interval the objective function is define... | Finding peaks in power spectrum of a signal in R | You can think of it as a problem of analytically locating the local maxima
that are graphically observed. The code below locates those maxima by means of a one-dimensional optimization algorithm that | Finding peaks in power spectrum of a signal in R
You can think of it as a problem of analytically locating the local maxima
that are graphically observed. The code below locates those maxima by means of a one-dimensional optimization algorithm that is applied across overlapping intervals that cover the entire x-axis. ... | Finding peaks in power spectrum of a signal in R
You can think of it as a problem of analytically locating the local maxima
that are graphically observed. The code below locates those maxima by means of a one-dimensional optimization algorithm that |
35,458 | Confidence Interval on a random quantity? | Geometric view of the problem and distributions of $\vec{b}\cdot \vec{a}$ and $|\vec{b}|^2$
Below is geometrical view of the problem. The direction of $\vec{a}$ doesn't really matter and we can just use the lengths of these vectors $|\vec{a}|$ and $|\vec{b}|$ which give all neccesary information.
The distribution of t... | Confidence Interval on a random quantity? | Geometric view of the problem and distributions of $\vec{b}\cdot \vec{a}$ and $|\vec{b}|^2$
Below is geometrical view of the problem. The direction of $\vec{a}$ doesn't really matter and we can just u | Confidence Interval on a random quantity?
Geometric view of the problem and distributions of $\vec{b}\cdot \vec{a}$ and $|\vec{b}|^2$
Below is geometrical view of the problem. The direction of $\vec{a}$ doesn't really matter and we can just use the lengths of these vectors $|\vec{a}|$ and $|\vec{b}|$ which give all nec... | Confidence Interval on a random quantity?
Geometric view of the problem and distributions of $\vec{b}\cdot \vec{a}$ and $|\vec{b}|^2$
Below is geometrical view of the problem. The direction of $\vec{a}$ doesn't really matter and we can just u |
35,459 | Confidence Interval on a random quantity? | I will switch notation to something more familiar. I hope it is not confusing.
I don't see how one could estimate the $c$-function with a completely unbiased estimator. But I will provide an unbiased estimator for "part" of the $c$-function, and provide a formula for the remaining bias, so that it can be assessed by s... | Confidence Interval on a random quantity? | I will switch notation to something more familiar. I hope it is not confusing.
I don't see how one could estimate the $c$-function with a completely unbiased estimator. But I will provide an unbiased | Confidence Interval on a random quantity?
I will switch notation to something more familiar. I hope it is not confusing.
I don't see how one could estimate the $c$-function with a completely unbiased estimator. But I will provide an unbiased estimator for "part" of the $c$-function, and provide a formula for the remai... | Confidence Interval on a random quantity?
I will switch notation to something more familiar. I hope it is not confusing.
I don't see how one could estimate the $c$-function with a completely unbiased estimator. But I will provide an unbiased |
35,460 | Confidence Interval on a random quantity? | An approach that almost works is as follows: Note that $\left(\vec{b}^{\top}\vec{b} - \vec{b}^{\top}\vec{a}\right) / \sqrt{\vec{b}^{\top}\vec{b}}$ 'looks like' $\vec{z}^{\top} \vec{c}$, where $\vec{c}$ is a unit-length vector (it is actually $\vec{b}$ scaled to unit length), and $\vec{z} = \vec{b} - \vec{a} \sim \mathc... | Confidence Interval on a random quantity? | An approach that almost works is as follows: Note that $\left(\vec{b}^{\top}\vec{b} - \vec{b}^{\top}\vec{a}\right) / \sqrt{\vec{b}^{\top}\vec{b}}$ 'looks like' $\vec{z}^{\top} \vec{c}$, where $\vec{c} | Confidence Interval on a random quantity?
An approach that almost works is as follows: Note that $\left(\vec{b}^{\top}\vec{b} - \vec{b}^{\top}\vec{a}\right) / \sqrt{\vec{b}^{\top}\vec{b}}$ 'looks like' $\vec{z}^{\top} \vec{c}$, where $\vec{c}$ is a unit-length vector (it is actually $\vec{b}$ scaled to unit length), an... | Confidence Interval on a random quantity?
An approach that almost works is as follows: Note that $\left(\vec{b}^{\top}\vec{b} - \vec{b}^{\top}\vec{a}\right) / \sqrt{\vec{b}^{\top}\vec{b}}$ 'looks like' $\vec{z}^{\top} \vec{c}$, where $\vec{c} |
35,461 | Confidence Interval on a random quantity? | For the case $p=1$, we can find a two sided interval.
In this case we can assume that $0 < a$ is the population parameter,
and we observe $b=\mathcal{N}\left(a,1\right).$ We wish to
bound $ab$ in probability with some function of $|b|$
(We may only use absolute value of $b$ as it is the one
dimensional analogue of $\sq... | Confidence Interval on a random quantity? | For the case $p=1$, we can find a two sided interval.
In this case we can assume that $0 < a$ is the population parameter,
and we observe $b=\mathcal{N}\left(a,1\right).$ We wish to
bound $ab$ in prob | Confidence Interval on a random quantity?
For the case $p=1$, we can find a two sided interval.
In this case we can assume that $0 < a$ is the population parameter,
and we observe $b=\mathcal{N}\left(a,1\right).$ We wish to
bound $ab$ in probability with some function of $|b|$
(We may only use absolute value of $b$ as ... | Confidence Interval on a random quantity?
For the case $p=1$, we can find a two sided interval.
In this case we can assume that $0 < a$ is the population parameter,
and we observe $b=\mathcal{N}\left(a,1\right).$ We wish to
bound $ab$ in prob |
35,462 | Confidence Interval on a random quantity? | Again, the question is to find function $c()$ such that, if you fixed $\vec{a}$, then under $m$ independent draws of $\vec{b_i} = \vec{a} + \vec{z_i}$, the proportion of $i$ such that $\vec{b_i}^{\top}\vec{a} \le c\left(\vec{b_i},p,\alpha\right)$ should go to $\alpha$ as $m \to \infty$.
I will give a broken solution to... | Confidence Interval on a random quantity? | Again, the question is to find function $c()$ such that, if you fixed $\vec{a}$, then under $m$ independent draws of $\vec{b_i} = \vec{a} + \vec{z_i}$, the proportion of $i$ such that $\vec{b_i}^{\top | Confidence Interval on a random quantity?
Again, the question is to find function $c()$ such that, if you fixed $\vec{a}$, then under $m$ independent draws of $\vec{b_i} = \vec{a} + \vec{z_i}$, the proportion of $i$ such that $\vec{b_i}^{\top}\vec{a} \le c\left(\vec{b_i},p,\alpha\right)$ should go to $\alpha$ as $m \to... | Confidence Interval on a random quantity?
Again, the question is to find function $c()$ such that, if you fixed $\vec{a}$, then under $m$ independent draws of $\vec{b_i} = \vec{a} + \vec{z_i}$, the proportion of $i$ such that $\vec{b_i}^{\top |
35,463 | AB testing vs testing the null hypothesis | Is there a difference?
Yes. A null hypothesis test produces a test statistic and a p-value, the probability of a test statistic as extreme as the that of the data, under the assumption that the null hypothesis is true. In your example, prop.test tests the assumption that the $p_A$ and $p_B$ are equal. This is distinct... | AB testing vs testing the null hypothesis | Is there a difference?
Yes. A null hypothesis test produces a test statistic and a p-value, the probability of a test statistic as extreme as the that of the data, under the assumption that the null | AB testing vs testing the null hypothesis
Is there a difference?
Yes. A null hypothesis test produces a test statistic and a p-value, the probability of a test statistic as extreme as the that of the data, under the assumption that the null hypothesis is true. In your example, prop.test tests the assumption that the $... | AB testing vs testing the null hypothesis
Is there a difference?
Yes. A null hypothesis test produces a test statistic and a p-value, the probability of a test statistic as extreme as the that of the data, under the assumption that the null |
35,464 | Hyper-volume of the $\alpha$ contour of a multivariate Gaussian | Ok, this question seems to come up from time to time so I though I'll give a general answer.
In [1], the authors show that if $\pmb x_i\sim \mathcal{N}_p(\pmb \mu,\pmb \varSigma),i=1,\ldots,n$
with $\varSigma$ symmetric positive definite, and $S_{\alpha}$
$$S_{\alpha}=\{i: (\pmb x_i-\pmb\mu)'\varSigma^{-1}(\pmb x_i-\... | Hyper-volume of the $\alpha$ contour of a multivariate Gaussian | Ok, this question seems to come up from time to time so I though I'll give a general answer.
In [1], the authors show that if $\pmb x_i\sim \mathcal{N}_p(\pmb \mu,\pmb \varSigma),i=1,\ldots,n$
with | Hyper-volume of the $\alpha$ contour of a multivariate Gaussian
Ok, this question seems to come up from time to time so I though I'll give a general answer.
In [1], the authors show that if $\pmb x_i\sim \mathcal{N}_p(\pmb \mu,\pmb \varSigma),i=1,\ldots,n$
with $\varSigma$ symmetric positive definite, and $S_{\alpha}... | Hyper-volume of the $\alpha$ contour of a multivariate Gaussian
Ok, this question seems to come up from time to time so I though I'll give a general answer.
In [1], the authors show that if $\pmb x_i\sim \mathcal{N}_p(\pmb \mu,\pmb \varSigma),i=1,\ldots,n$
with |
35,465 | Hyper-volume of the $\alpha$ contour of a multivariate Gaussian | Say $X\sim N_n(0,\Sigma)$, where $\Sigma$ is positive definite with $n$ eigenvalues $\lambda_1,\lambda_2,\dots,\lambda_n$. Then the constant-density contours are ellipsoids with $i$th principal axis of $r_i = \sqrt{\chi^2_{\alpha,n}\lambda_i}$, and therefore the volume of the hyper-ellipsoid can be found as
$$
\big(
\... | Hyper-volume of the $\alpha$ contour of a multivariate Gaussian | Say $X\sim N_n(0,\Sigma)$, where $\Sigma$ is positive definite with $n$ eigenvalues $\lambda_1,\lambda_2,\dots,\lambda_n$. Then the constant-density contours are ellipsoids with $i$th principal axis o | Hyper-volume of the $\alpha$ contour of a multivariate Gaussian
Say $X\sim N_n(0,\Sigma)$, where $\Sigma$ is positive definite with $n$ eigenvalues $\lambda_1,\lambda_2,\dots,\lambda_n$. Then the constant-density contours are ellipsoids with $i$th principal axis of $r_i = \sqrt{\chi^2_{\alpha,n}\lambda_i}$, and therefo... | Hyper-volume of the $\alpha$ contour of a multivariate Gaussian
Say $X\sim N_n(0,\Sigma)$, where $\Sigma$ is positive definite with $n$ eigenvalues $\lambda_1,\lambda_2,\dots,\lambda_n$. Then the constant-density contours are ellipsoids with $i$th principal axis o |
35,466 | Calculating effect sizes and standard errors for the difference between two standardized mean differences | I can certainly give you an answer to the first part of your question.
Using your notation, let $d_{var_1}$ and $d_{var_2}$ denote the two d values (computed for the same two groups) based on two different dependent variables and let $v_{var_1}$ and $v_{var_2}$ denote the corresponding sampling variances, which are typ... | Calculating effect sizes and standard errors for the difference between two standardized mean differ | I can certainly give you an answer to the first part of your question.
Using your notation, let $d_{var_1}$ and $d_{var_2}$ denote the two d values (computed for the same two groups) based on two diff | Calculating effect sizes and standard errors for the difference between two standardized mean differences
I can certainly give you an answer to the first part of your question.
Using your notation, let $d_{var_1}$ and $d_{var_2}$ denote the two d values (computed for the same two groups) based on two different dependen... | Calculating effect sizes and standard errors for the difference between two standardized mean differ
I can certainly give you an answer to the first part of your question.
Using your notation, let $d_{var_1}$ and $d_{var_2}$ denote the two d values (computed for the same two groups) based on two diff |
35,467 | Calculating effect sizes and standard errors for the difference between two standardized mean differences | This question can be answered by using a structural equation modeling (SEM) approach. It can be used as long as the effect sizes are functions of the parameters, such as means, correlations, and standard deviations. The sampling covariance matrix is numerically derived by the use of Delta method automatically in SEM. C... | Calculating effect sizes and standard errors for the difference between two standardized mean differ | This question can be answered by using a structural equation modeling (SEM) approach. It can be used as long as the effect sizes are functions of the parameters, such as means, correlations, and stand | Calculating effect sizes and standard errors for the difference between two standardized mean differences
This question can be answered by using a structural equation modeling (SEM) approach. It can be used as long as the effect sizes are functions of the parameters, such as means, correlations, and standard deviations... | Calculating effect sizes and standard errors for the difference between two standardized mean differ
This question can be answered by using a structural equation modeling (SEM) approach. It can be used as long as the effect sizes are functions of the parameters, such as means, correlations, and stand |
35,468 | Calculating effect sizes and standard errors for the difference between two standardized mean differences | I am not completely certain how this solution was derived, but I thought I would post it anyway so that other people could evaluate it. I also thought that this information was worth posting as a full answer rather than leaving it buried in the comments of the answer provided by @Wolfgang.
According to a response that... | Calculating effect sizes and standard errors for the difference between two standardized mean differ | I am not completely certain how this solution was derived, but I thought I would post it anyway so that other people could evaluate it. I also thought that this information was worth posting as a ful | Calculating effect sizes and standard errors for the difference between two standardized mean differences
I am not completely certain how this solution was derived, but I thought I would post it anyway so that other people could evaluate it. I also thought that this information was worth posting as a full answer rathe... | Calculating effect sizes and standard errors for the difference between two standardized mean differ
I am not completely certain how this solution was derived, but I thought I would post it anyway so that other people could evaluate it. I also thought that this information was worth posting as a ful |
35,469 | Iterative process for removing extreme samples | The problem with your approach is that you start assuming that your data is normally distributed, when you already know it is not. Some outlier detection techniques are similar (it is sound) but make the same assumption.
Rather than using the mean and the standard deviation, you may prefer the MAD (median absolute devi... | Iterative process for removing extreme samples | The problem with your approach is that you start assuming that your data is normally distributed, when you already know it is not. Some outlier detection techniques are similar (it is sound) but make | Iterative process for removing extreme samples
The problem with your approach is that you start assuming that your data is normally distributed, when you already know it is not. Some outlier detection techniques are similar (it is sound) but make the same assumption.
Rather than using the mean and the standard deviatio... | Iterative process for removing extreme samples
The problem with your approach is that you start assuming that your data is normally distributed, when you already know it is not. Some outlier detection techniques are similar (it is sound) but make |
35,470 | Iterative process for removing extreme samples | Just a heed of warning! be very careful of the way you implement the algorithm you have mentioned. Personally, I am a little skeptical of it.
The reason is the curse of dimensionality. In a high dimensional problem, since all points lie on the boundary, they all look like outliers.
As a simple counterexample to your ... | Iterative process for removing extreme samples | Just a heed of warning! be very careful of the way you implement the algorithm you have mentioned. Personally, I am a little skeptical of it.
The reason is the curse of dimensionality. In a high dim | Iterative process for removing extreme samples
Just a heed of warning! be very careful of the way you implement the algorithm you have mentioned. Personally, I am a little skeptical of it.
The reason is the curse of dimensionality. In a high dimensional problem, since all points lie on the boundary, they all look lik... | Iterative process for removing extreme samples
Just a heed of warning! be very careful of the way you implement the algorithm you have mentioned. Personally, I am a little skeptical of it.
The reason is the curse of dimensionality. In a high dim |
35,471 | Computing inverse probability weights -- conditional (multivariate) density estimation? | The basic idea
As per Chen, Linton, and Robinson (2001), the "default" technique for conditional univariate kernel density estimation is to find, for bandwidths $a,b,c$,
$$\frac{\hat{f}_{ab}(y,z)}{\hat{f}_c(z)}=\hat{f}_{abc}(y|z)$$
Then, with numerator bandwidth $(a,b)$ and denominator bandwidth $c$ and $a=b=c$, the fo... | Computing inverse probability weights -- conditional (multivariate) density estimation? | The basic idea
As per Chen, Linton, and Robinson (2001), the "default" technique for conditional univariate kernel density estimation is to find, for bandwidths $a,b,c$,
$$\frac{\hat{f}_{ab}(y,z)}{\ha | Computing inverse probability weights -- conditional (multivariate) density estimation?
The basic idea
As per Chen, Linton, and Robinson (2001), the "default" technique for conditional univariate kernel density estimation is to find, for bandwidths $a,b,c$,
$$\frac{\hat{f}_{ab}(y,z)}{\hat{f}_c(z)}=\hat{f}_{abc}(y|z)$$
... | Computing inverse probability weights -- conditional (multivariate) density estimation?
The basic idea
As per Chen, Linton, and Robinson (2001), the "default" technique for conditional univariate kernel density estimation is to find, for bandwidths $a,b,c$,
$$\frac{\hat{f}_{ab}(y,z)}{\ha |
35,472 | Clustering algorithms for extremely sparse data | For text vectors, there are good known similarities - cosine, and the variations used e.g. in Lucene for text retrieval.
k-means, however, may be a bad fit. Because the means computed will not have a realistic sparsity, but will be much more dense.
Anyway, there exist some k-means variations for text, such as spherical... | Clustering algorithms for extremely sparse data | For text vectors, there are good known similarities - cosine, and the variations used e.g. in Lucene for text retrieval.
k-means, however, may be a bad fit. Because the means computed will not have a | Clustering algorithms for extremely sparse data
For text vectors, there are good known similarities - cosine, and the variations used e.g. in Lucene for text retrieval.
k-means, however, may be a bad fit. Because the means computed will not have a realistic sparsity, but will be much more dense.
Anyway, there exist som... | Clustering algorithms for extremely sparse data
For text vectors, there are good known similarities - cosine, and the variations used e.g. in Lucene for text retrieval.
k-means, however, may be a bad fit. Because the means computed will not have a |
35,473 | Fast missing data imputation in R for big data that is more sophisticated than simply imputing the means? | I used mice (multiple imputation by chained equation). It's fairly fast, and quite simple. I used it on 3000 obs. for c.a. 10 variables. Done in 10min on an old computer. Further, I believe it is one of the best multiple-imputation packages out there.
It can use regression to impute, among other methods.
You need to cr... | Fast missing data imputation in R for big data that is more sophisticated than simply imputing the m | I used mice (multiple imputation by chained equation). It's fairly fast, and quite simple. I used it on 3000 obs. for c.a. 10 variables. Done in 10min on an old computer. Further, I believe it is one | Fast missing data imputation in R for big data that is more sophisticated than simply imputing the means?
I used mice (multiple imputation by chained equation). It's fairly fast, and quite simple. I used it on 3000 obs. for c.a. 10 variables. Done in 10min on an old computer. Further, I believe it is one of the best mu... | Fast missing data imputation in R for big data that is more sophisticated than simply imputing the m
I used mice (multiple imputation by chained equation). It's fairly fast, and quite simple. I used it on 3000 obs. for c.a. 10 variables. Done in 10min on an old computer. Further, I believe it is one |
35,474 | Fast missing data imputation in R for big data that is more sophisticated than simply imputing the means? | The Hmisc package can probably do this with the imputation function (aregImpute). Agree that columns are plenty, but rows are few. Should probably be handled by Hisc... | Fast missing data imputation in R for big data that is more sophisticated than simply imputing the m | The Hmisc package can probably do this with the imputation function (aregImpute). Agree that columns are plenty, but rows are few. Should probably be handled by Hisc... | Fast missing data imputation in R for big data that is more sophisticated than simply imputing the means?
The Hmisc package can probably do this with the imputation function (aregImpute). Agree that columns are plenty, but rows are few. Should probably be handled by Hisc... | Fast missing data imputation in R for big data that is more sophisticated than simply imputing the m
The Hmisc package can probably do this with the imputation function (aregImpute). Agree that columns are plenty, but rows are few. Should probably be handled by Hisc... |
35,475 | OLS Coefficient estimator; Transformation from Matrix to sum of matrices form | $\textbf{X}$ is of dimension $\textbf{N}\times\textbf{K}$ and $\textbf{X}'$ of dimension $\textbf{K}\times\textbf{N}$, the product $(\textbf{X}'\textbf{X})$ is consequently of dimension $\textbf{K}\times\textbf{K}$.
Taking the invers of $\textbf{N}\times\textbf{N}$ does not change the dimension of the matrix. Conseque... | OLS Coefficient estimator; Transformation from Matrix to sum of matrices form | $\textbf{X}$ is of dimension $\textbf{N}\times\textbf{K}$ and $\textbf{X}'$ of dimension $\textbf{K}\times\textbf{N}$, the product $(\textbf{X}'\textbf{X})$ is consequently of dimension $\textbf{K}\t | OLS Coefficient estimator; Transformation from Matrix to sum of matrices form
$\textbf{X}$ is of dimension $\textbf{N}\times\textbf{K}$ and $\textbf{X}'$ of dimension $\textbf{K}\times\textbf{N}$, the product $(\textbf{X}'\textbf{X})$ is consequently of dimension $\textbf{K}\times\textbf{K}$.
Taking the invers of $\te... | OLS Coefficient estimator; Transformation from Matrix to sum of matrices form
$\textbf{X}$ is of dimension $\textbf{N}\times\textbf{K}$ and $\textbf{X}'$ of dimension $\textbf{K}\times\textbf{N}$, the product $(\textbf{X}'\textbf{X})$ is consequently of dimension $\textbf{K}\t |
35,476 | OLS Coefficient estimator; Transformation from Matrix to sum of matrices form | It appears that you're simply confused by the notation.
Here ${\bf x}_{i}$ is the column vector
${\bf x}_{i} = \left[\begin{array}{c}
x_{i,1} \\
x_{i,2} \\
\vdots \\
x_{i,n}
\end{array}
\right].$
It is somewhat confusing that the author has chosen to take the $i$th row of the matrix ${\bf X}$ and call its transpose... | OLS Coefficient estimator; Transformation from Matrix to sum of matrices form | It appears that you're simply confused by the notation.
Here ${\bf x}_{i}$ is the column vector
${\bf x}_{i} = \left[\begin{array}{c}
x_{i,1} \\
x_{i,2} \\
\vdots \\
x_{i,n}
\end{array}
\right].$
| OLS Coefficient estimator; Transformation from Matrix to sum of matrices form
It appears that you're simply confused by the notation.
Here ${\bf x}_{i}$ is the column vector
${\bf x}_{i} = \left[\begin{array}{c}
x_{i,1} \\
x_{i,2} \\
\vdots \\
x_{i,n}
\end{array}
\right].$
It is somewhat confusing that the author h... | OLS Coefficient estimator; Transformation from Matrix to sum of matrices form
It appears that you're simply confused by the notation.
Here ${\bf x}_{i}$ is the column vector
${\bf x}_{i} = \left[\begin{array}{c}
x_{i,1} \\
x_{i,2} \\
\vdots \\
x_{i,n}
\end{array}
\right].$
|
35,477 | OLS Coefficient estimator; Transformation from Matrix to sum of matrices form | You are referring to Cameron & Trivedi, page 16, aren't you?
There they say that "vectors are defined as column vectors". This is why in $y_i=\mathbf{x}_i'\boldsymbol{\beta}+u_i$ (same page) $\mathbf{x}_i$ is the column vector that contains... the $i$th row of the $N\times K$ $\mathbf{X}$ matrix.
So $\mathbf{x}_i'\bold... | OLS Coefficient estimator; Transformation from Matrix to sum of matrices form | You are referring to Cameron & Trivedi, page 16, aren't you?
There they say that "vectors are defined as column vectors". This is why in $y_i=\mathbf{x}_i'\boldsymbol{\beta}+u_i$ (same page) $\mathbf{ | OLS Coefficient estimator; Transformation from Matrix to sum of matrices form
You are referring to Cameron & Trivedi, page 16, aren't you?
There they say that "vectors are defined as column vectors". This is why in $y_i=\mathbf{x}_i'\boldsymbol{\beta}+u_i$ (same page) $\mathbf{x}_i$ is the column vector that contains..... | OLS Coefficient estimator; Transformation from Matrix to sum of matrices form
You are referring to Cameron & Trivedi, page 16, aren't you?
There they say that "vectors are defined as column vectors". This is why in $y_i=\mathbf{x}_i'\boldsymbol{\beta}+u_i$ (same page) $\mathbf{ |
35,478 | What does this residuals versus fitted plot mean about my model? | The first plot (Normal Q-Q plot) checks if residuals follow a normal distribution, which is an assumption of linear regression. If dots are over the line y=x it means the residuals are normally distributed. Your plot seems OK in this aspect.
The Residuals _versus_ Fitted plot is useful to illustrate if a linear model p... | What does this residuals versus fitted plot mean about my model? | The first plot (Normal Q-Q plot) checks if residuals follow a normal distribution, which is an assumption of linear regression. If dots are over the line y=x it means the residuals are normally distri | What does this residuals versus fitted plot mean about my model?
The first plot (Normal Q-Q plot) checks if residuals follow a normal distribution, which is an assumption of linear regression. If dots are over the line y=x it means the residuals are normally distributed. Your plot seems OK in this aspect.
The Residuals... | What does this residuals versus fitted plot mean about my model?
The first plot (Normal Q-Q plot) checks if residuals follow a normal distribution, which is an assumption of linear regression. If dots are over the line y=x it means the residuals are normally distri |
35,479 | What are "second-order dependencies" and "higher order dependencies" in the data? | PCA is based on variances and covariances, $\mathrm E[x_i x_j]$ (assuming mean-free variables). These are measures of second-order dependencies because the data enter in the form of terms of order 2. After PCA, the principal components have 0 covariance between them, so second-order dependencies have been removed. Howe... | What are "second-order dependencies" and "higher order dependencies" in the data? | PCA is based on variances and covariances, $\mathrm E[x_i x_j]$ (assuming mean-free variables). These are measures of second-order dependencies because the data enter in the form of terms of order 2. | What are "second-order dependencies" and "higher order dependencies" in the data?
PCA is based on variances and covariances, $\mathrm E[x_i x_j]$ (assuming mean-free variables). These are measures of second-order dependencies because the data enter in the form of terms of order 2. After PCA, the principal components ha... | What are "second-order dependencies" and "higher order dependencies" in the data?
PCA is based on variances and covariances, $\mathrm E[x_i x_j]$ (assuming mean-free variables). These are measures of second-order dependencies because the data enter in the form of terms of order 2. |
35,480 | What are "second-order dependencies" and "higher order dependencies" in the data? | In the context of this paper, it appears as if they are using to ‘second order dependencies’ to refer to cases where $X$ and $Y$ are orthogonal to each other, and higher order dependencies when $X$ and $Y$ are not. Finding orthogonal axes is the basis for the principal component analysis, because you are trying to find... | What are "second-order dependencies" and "higher order dependencies" in the data? | In the context of this paper, it appears as if they are using to ‘second order dependencies’ to refer to cases where $X$ and $Y$ are orthogonal to each other, and higher order dependencies when $X$ an | What are "second-order dependencies" and "higher order dependencies" in the data?
In the context of this paper, it appears as if they are using to ‘second order dependencies’ to refer to cases where $X$ and $Y$ are orthogonal to each other, and higher order dependencies when $X$ and $Y$ are not. Finding orthogonal axes... | What are "second-order dependencies" and "higher order dependencies" in the data?
In the context of this paper, it appears as if they are using to ‘second order dependencies’ to refer to cases where $X$ and $Y$ are orthogonal to each other, and higher order dependencies when $X$ an |
35,481 | $\phi$-divergence? | Ok found it myself. It was part of the following paper:
Jiménez-Gamero, María-Dolores, et al. "Minimum $\phi$-divergence estimation in misspecified multinomial models." Computational Statistics & Data Analysis 55.12 (2011): 3365-3378.
$\phi: [0,\infty) \to \mathbb{R}$ is a strictly convex function, twice continuously d... | $\phi$-divergence? | Ok found it myself. It was part of the following paper:
Jiménez-Gamero, María-Dolores, et al. "Minimum $\phi$-divergence estimation in misspecified multinomial models." Computational Statistics & Data | $\phi$-divergence?
Ok found it myself. It was part of the following paper:
Jiménez-Gamero, María-Dolores, et al. "Minimum $\phi$-divergence estimation in misspecified multinomial models." Computational Statistics & Data Analysis 55.12 (2011): 3365-3378.
$\phi: [0,\infty) \to \mathbb{R}$ is a strictly convex function, t... | $\phi$-divergence?
Ok found it myself. It was part of the following paper:
Jiménez-Gamero, María-Dolores, et al. "Minimum $\phi$-divergence estimation in misspecified multinomial models." Computational Statistics & Data |
35,482 | $\phi$-divergence? | This paper by Love and Bayraksan gives this introduction: '$\phi$-divergences are used in statistics to measure the "distance" between two distributions,' and this formal definition:
$I_{\phi}(p,q) = \sum_{\omega = 1}^{n}{q_\omega\phi(\frac{p_\omega}{q_\omega})}$
where $p, q$ are probability vectors and $\phi$ is a fun... | $\phi$-divergence? | This paper by Love and Bayraksan gives this introduction: '$\phi$-divergences are used in statistics to measure the "distance" between two distributions,' and this formal definition:
$I_{\phi}(p,q) = | $\phi$-divergence?
This paper by Love and Bayraksan gives this introduction: '$\phi$-divergences are used in statistics to measure the "distance" between two distributions,' and this formal definition:
$I_{\phi}(p,q) = \sum_{\omega = 1}^{n}{q_\omega\phi(\frac{p_\omega}{q_\omega})}$
where $p, q$ are probability vectors ... | $\phi$-divergence?
This paper by Love and Bayraksan gives this introduction: '$\phi$-divergences are used in statistics to measure the "distance" between two distributions,' and this formal definition:
$I_{\phi}(p,q) = |
35,483 | $\phi$-divergence? | According to Jager and Wellner this term was invented by I. Csiszar (1963), but his paper is in german. Jager and Wellner use it to construct goodness-of-fit tests and they give the following definition:
$K(u,v) = v \phi(\frac{u}{v}) + (1-v)\phi(\frac{1-u}{1-v})$ | $\phi$-divergence? | According to Jager and Wellner this term was invented by I. Csiszar (1963), but his paper is in german. Jager and Wellner use it to construct goodness-of-fit tests and they give the following definiti | $\phi$-divergence?
According to Jager and Wellner this term was invented by I. Csiszar (1963), but his paper is in german. Jager and Wellner use it to construct goodness-of-fit tests and they give the following definition:
$K(u,v) = v \phi(\frac{u}{v}) + (1-v)\phi(\frac{1-u}{1-v})$ | $\phi$-divergence?
According to Jager and Wellner this term was invented by I. Csiszar (1963), but his paper is in german. Jager and Wellner use it to construct goodness-of-fit tests and they give the following definiti |
35,484 | Hierarchical clustering of correlation matrix | To apply most hierarchical clustering/heatmap tools you'll need to convert your correlation matrix into a distance matrix (ie 0 is close together, higher is further apart). This blog post covers some simple methods with R code.
However, a more computationally efficient method is to convert the correlation matrix to a g... | Hierarchical clustering of correlation matrix | To apply most hierarchical clustering/heatmap tools you'll need to convert your correlation matrix into a distance matrix (ie 0 is close together, higher is further apart). This blog post covers some | Hierarchical clustering of correlation matrix
To apply most hierarchical clustering/heatmap tools you'll need to convert your correlation matrix into a distance matrix (ie 0 is close together, higher is further apart). This blog post covers some simple methods with R code.
However, a more computationally efficient meth... | Hierarchical clustering of correlation matrix
To apply most hierarchical clustering/heatmap tools you'll need to convert your correlation matrix into a distance matrix (ie 0 is close together, higher is further apart). This blog post covers some |
35,485 | R: multiple linear regression model and prediction model | newdata should contain a column for each of your predictive variables, alt and sdist. (Any variables except the one you're predicting.) For example:
newdata = data.frame(alt = newAltVector, sdist = newSdistVector)
predictions = predict.lm(model, newdata)
predictions will then contain a fitted y value for each new x. I... | R: multiple linear regression model and prediction model | newdata should contain a column for each of your predictive variables, alt and sdist. (Any variables except the one you're predicting.) For example:
newdata = data.frame(alt = newAltVector, sdist = ne | R: multiple linear regression model and prediction model
newdata should contain a column for each of your predictive variables, alt and sdist. (Any variables except the one you're predicting.) For example:
newdata = data.frame(alt = newAltVector, sdist = newSdistVector)
predictions = predict.lm(model, newdata)
predict... | R: multiple linear regression model and prediction model
newdata should contain a column for each of your predictive variables, alt and sdist. (Any variables except the one you're predicting.) For example:
newdata = data.frame(alt = newAltVector, sdist = ne |
35,486 | Connecting the dots in a graph | There are a variety of reasons to connect the points in a graph. If you're only showing one category of values (i.e. if there is a line there would only be one) then the rule of continuous versus discrete is generally good to abide by. However, even discrete or categorical values can be connected when multiple lines mi... | Connecting the dots in a graph | There are a variety of reasons to connect the points in a graph. If you're only showing one category of values (i.e. if there is a line there would only be one) then the rule of continuous versus disc | Connecting the dots in a graph
There are a variety of reasons to connect the points in a graph. If you're only showing one category of values (i.e. if there is a line there would only be one) then the rule of continuous versus discrete is generally good to abide by. However, even discrete or categorical values can be c... | Connecting the dots in a graph
There are a variety of reasons to connect the points in a graph. If you're only showing one category of values (i.e. if there is a line there would only be one) then the rule of continuous versus disc |
35,487 | Connecting the dots in a graph | IMHO, whoever first omitted the precise timing of changes in number of cars is the first one responsible for any misleading results. If you had this information (even if measured with error), time would be a proper continuous variable, not a grouped continuous variable (see Anderson, 1984) necessarily. You'd be free to... | Connecting the dots in a graph | IMHO, whoever first omitted the precise timing of changes in number of cars is the first one responsible for any misleading results. If you had this information (even if measured with error), time wou | Connecting the dots in a graph
IMHO, whoever first omitted the precise timing of changes in number of cars is the first one responsible for any misleading results. If you had this information (even if measured with error), time would be a proper continuous variable, not a grouped continuous variable (see Anderson, 1984... | Connecting the dots in a graph
IMHO, whoever first omitted the precise timing of changes in number of cars is the first one responsible for any misleading results. If you had this information (even if measured with error), time wou |
35,488 | Connecting the dots in a graph | A continuous line indicates a continuum. If averages should be plotted, I would consider either using a bar diagram or a stair-step diagram. Plotting individual points is also possible, and when averages are concerned, you can probably add standard deviation information as necessary. | Connecting the dots in a graph | A continuous line indicates a continuum. If averages should be plotted, I would consider either using a bar diagram or a stair-step diagram. Plotting individual points is also possible, and when avera | Connecting the dots in a graph
A continuous line indicates a continuum. If averages should be plotted, I would consider either using a bar diagram or a stair-step diagram. Plotting individual points is also possible, and when averages are concerned, you can probably add standard deviation information as necessary. | Connecting the dots in a graph
A continuous line indicates a continuum. If averages should be plotted, I would consider either using a bar diagram or a stair-step diagram. Plotting individual points is also possible, and when avera |
35,489 | Connecting the dots in a graph | I would not connect those points because those are discrete values. Depending on the amount of data points you could either use a column/bar chart or just points. | Connecting the dots in a graph | I would not connect those points because those are discrete values. Depending on the amount of data points you could either use a column/bar chart or just points. | Connecting the dots in a graph
I would not connect those points because those are discrete values. Depending on the amount of data points you could either use a column/bar chart or just points. | Connecting the dots in a graph
I would not connect those points because those are discrete values. Depending on the amount of data points you could either use a column/bar chart or just points. |
35,490 | How to model football (soccer) scores | The state of the art for football prediction - that can be found in the academic literature - is Dixon and Robinson (1998) "A Birth Process Model for Association Football Matches", available without a pay wall here: http://www2.imperial.ac.uk/~ejm/M3S4/Problems/football.pdf
Their model of interacting non-homogeneous Po... | How to model football (soccer) scores | The state of the art for football prediction - that can be found in the academic literature - is Dixon and Robinson (1998) "A Birth Process Model for Association Football Matches", available without a | How to model football (soccer) scores
The state of the art for football prediction - that can be found in the academic literature - is Dixon and Robinson (1998) "A Birth Process Model for Association Football Matches", available without a pay wall here: http://www2.imperial.ac.uk/~ejm/M3S4/Problems/football.pdf
Their m... | How to model football (soccer) scores
The state of the art for football prediction - that can be found in the academic literature - is Dixon and Robinson (1998) "A Birth Process Model for Association Football Matches", available without a |
35,491 | Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian posterior? | Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian posterior?
Generally speaking, you do need to - it's just that sometimes it's so easy that you might not notice you did it.
With 'textbook' problems you can often take $\pi(x|\theta) \propto L_x(\theta)\pi(\theta)$, th... | Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian | Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian posterior?
Generally speaking, you do need to - it's just that sometimes it's so easy that you mig | Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian posterior?
Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian posterior?
Generally speaking, you do need to - it's just that sometimes it's so easy that you might not n... | Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian
Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian posterior?
Generally speaking, you do need to - it's just that sometimes it's so easy that you mig |
35,492 | Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian posterior? | Your problem is equivalent to the following: Suppose you have a function $f(x)$ such that $\int f(x) dx < \infty$, and you are looking for a constant $c$ such that $\int cf(x) dx = 1$. Clearly, $c = 1/ \int f(x) dx$ would work, but perhaps it isn't easy to compute $\int f(x) dx$. In your quest to find $c$, perhaps you ... | Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian | Your problem is equivalent to the following: Suppose you have a function $f(x)$ such that $\int f(x) dx < \infty$, and you are looking for a constant $c$ such that $\int cf(x) dx = 1$. Clearly, $c = 1 | Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian posterior?
Your problem is equivalent to the following: Suppose you have a function $f(x)$ such that $\int f(x) dx < \infty$, and you are looking for a constant $c$ such that $\int cf(x) dx = 1$. Clearly, $c = 1/ \int f... | Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian
Your problem is equivalent to the following: Suppose you have a function $f(x)$ such that $\int f(x) dx < \infty$, and you are looking for a constant $c$ such that $\int cf(x) dx = 1$. Clearly, $c = 1 |
35,493 | Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian posterior? | The "formal proof" you are looking for is called Bayes' Theorem (see also Posterior probability) which states that:
$$\pi(\theta\vert{\bf x}) = \dfrac{f({\bf x}\vert\theta)\pi(\theta)}{\pi({\bf x})}.$$
The left-hand side represents the posterior distribution and IT IS a distribution as long as the prior is proper. From... | Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian | The "formal proof" you are looking for is called Bayes' Theorem (see also Posterior probability) which states that:
$$\pi(\theta\vert{\bf x}) = \dfrac{f({\bf x}\vert\theta)\pi(\theta)}{\pi({\bf x})}.$ | Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian posterior?
The "formal proof" you are looking for is called Bayes' Theorem (see also Posterior probability) which states that:
$$\pi(\theta\vert{\bf x}) = \dfrac{f({\bf x}\vert\theta)\pi(\theta)}{\pi({\bf x})}.$$
The le... | Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian
The "formal proof" you are looking for is called Bayes' Theorem (see also Posterior probability) which states that:
$$\pi(\theta\vert{\bf x}) = \dfrac{f({\bf x}\vert\theta)\pi(\theta)}{\pi({\bf x})}.$ |
35,494 | Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian posterior? | $$π(θ|x)=[f(x|θ)π(θ)]/π(x)$$
In simple terms, the denominator, or the marginal distribution of the RHS of your Bayes theorem is just a constant that is used to make the RHS numerator a pdf. If you know what kind of distribution your RHS numerator, i.e, the Likelihood function * prior distribution follows, then you can ... | Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian | $$π(θ|x)=[f(x|θ)π(θ)]/π(x)$$
In simple terms, the denominator, or the marginal distribution of the RHS of your Bayes theorem is just a constant that is used to make the RHS numerator a pdf. If you kno | Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian posterior?
$$π(θ|x)=[f(x|θ)π(θ)]/π(x)$$
In simple terms, the denominator, or the marginal distribution of the RHS of your Bayes theorem is just a constant that is used to make the RHS numerator a pdf. If you know what k... | Theoretically, why do we not need to compute a marginal distribution constant for finding a Bayesian
$$π(θ|x)=[f(x|θ)π(θ)]/π(x)$$
In simple terms, the denominator, or the marginal distribution of the RHS of your Bayes theorem is just a constant that is used to make the RHS numerator a pdf. If you kno |
35,495 | Robust monotonic regression in R | I note that after you delete the last point, you only have seven values of which two (28.6%!) are outliers. Many robust methods don't have a breakdown point quite that high (e.g., Theil regression breaks down right at that point for n=7, though at large $n$ it goes to 29.3%), but if you must have such a high breakdown ... | Robust monotonic regression in R | I note that after you delete the last point, you only have seven values of which two (28.6%!) are outliers. Many robust methods don't have a breakdown point quite that high (e.g., Theil regression bre | Robust monotonic regression in R
I note that after you delete the last point, you only have seven values of which two (28.6%!) are outliers. Many robust methods don't have a breakdown point quite that high (e.g., Theil regression breaks down right at that point for n=7, though at large $n$ it goes to 29.3%), but if you... | Robust monotonic regression in R
I note that after you delete the last point, you only have seven values of which two (28.6%!) are outliers. Many robust methods don't have a breakdown point quite that high (e.g., Theil regression bre |
35,496 | What's the activation function used in the nodes of hidden layer from nnet library in R? | This is the implemented function (extracted from the C-sources; filennet.c, lines 156-165):
static double
sigmoid(double sum)
{
if (sum < -15.0)
return (0.0);
else if (sum > 15.0)
return (1.0);
else
return (1.0 / (1.0 + exp(-sum)));
} | What's the activation function used in the nodes of hidden layer from nnet library in R? | This is the implemented function (extracted from the C-sources; filennet.c, lines 156-165):
static double
sigmoid(double sum)
{
if (sum < -15.0)
return (0.0);
else if (sum > 15.0)
retu | What's the activation function used in the nodes of hidden layer from nnet library in R?
This is the implemented function (extracted from the C-sources; filennet.c, lines 156-165):
static double
sigmoid(double sum)
{
if (sum < -15.0)
return (0.0);
else if (sum > 15.0)
return (1.0);
else
return (... | What's the activation function used in the nodes of hidden layer from nnet library in R?
This is the implemented function (extracted from the C-sources; filennet.c, lines 156-165):
static double
sigmoid(double sum)
{
if (sum < -15.0)
return (0.0);
else if (sum > 15.0)
retu |
35,497 | High concordance in cox PH model even though PH assumption is violated | In reverse order:
3) The concordance is simply the proportion of pairs of cases in which the case with the higher-risk predictor had an event before the case with the lower-risk predictor. With a single numeric predictor, the concordance will be the same for any monotone transformation of the predictor even though the ... | High concordance in cox PH model even though PH assumption is violated | In reverse order:
3) The concordance is simply the proportion of pairs of cases in which the case with the higher-risk predictor had an event before the case with the lower-risk predictor. With a sing | High concordance in cox PH model even though PH assumption is violated
In reverse order:
3) The concordance is simply the proportion of pairs of cases in which the case with the higher-risk predictor had an event before the case with the lower-risk predictor. With a single numeric predictor, the concordance will be the... | High concordance in cox PH model even though PH assumption is violated
In reverse order:
3) The concordance is simply the proportion of pairs of cases in which the case with the higher-risk predictor had an event before the case with the lower-risk predictor. With a sing |
35,498 | Is the residual, e, an estimator of the error, $\epsilon$? | Certainly the residuals are some sort of estimators of $\epsilon$ (to be clear, the definition of the residual is the estimator, the observed residual is an estimate). If the model is correct, then they may sometimes be a fairly good estimate.
Indeed
$e = y - \hat y = X\beta + \epsilon - X(X'X)^{-1} X'(X\beta + \epsil... | Is the residual, e, an estimator of the error, $\epsilon$? | Certainly the residuals are some sort of estimators of $\epsilon$ (to be clear, the definition of the residual is the estimator, the observed residual is an estimate). If the model is correct, then t | Is the residual, e, an estimator of the error, $\epsilon$?
Certainly the residuals are some sort of estimators of $\epsilon$ (to be clear, the definition of the residual is the estimator, the observed residual is an estimate). If the model is correct, then they may sometimes be a fairly good estimate.
Indeed
$e = y - ... | Is the residual, e, an estimator of the error, $\epsilon$?
Certainly the residuals are some sort of estimators of $\epsilon$ (to be clear, the definition of the residual is the estimator, the observed residual is an estimate). If the model is correct, then t |
35,499 | Is a large control sample better than a balanced sample size when the treatment group is small? | Your colleagues are incorrect.
It's possible that they're basing their suggestion on the fact that the robustness of typical parametric tests, like a t-test, to violations of assumptions is severely compromised with imbalanced N's. But if you don't violate them then a higher N is better, even if unbalanced. And you ca... | Is a large control sample better than a balanced sample size when the treatment group is small? | Your colleagues are incorrect.
It's possible that they're basing their suggestion on the fact that the robustness of typical parametric tests, like a t-test, to violations of assumptions is severely | Is a large control sample better than a balanced sample size when the treatment group is small?
Your colleagues are incorrect.
It's possible that they're basing their suggestion on the fact that the robustness of typical parametric tests, like a t-test, to violations of assumptions is severely compromised with imbalan... | Is a large control sample better than a balanced sample size when the treatment group is small?
Your colleagues are incorrect.
It's possible that they're basing their suggestion on the fact that the robustness of typical parametric tests, like a t-test, to violations of assumptions is severely |
35,500 | Non-random small sample - What conclusions can I get? | whuber is right that, technically, statistical inference will not be accurate if randomization was not used. However, in practice, random sampling is often impossible, so it is common (and inevitable and unfortunate) practice that people use inference on non-random samples and generalize the results to the entire popul... | Non-random small sample - What conclusions can I get? | whuber is right that, technically, statistical inference will not be accurate if randomization was not used. However, in practice, random sampling is often impossible, so it is common (and inevitable | Non-random small sample - What conclusions can I get?
whuber is right that, technically, statistical inference will not be accurate if randomization was not used. However, in practice, random sampling is often impossible, so it is common (and inevitable and unfortunate) practice that people use inference on non-random ... | Non-random small sample - What conclusions can I get?
whuber is right that, technically, statistical inference will not be accurate if randomization was not used. However, in practice, random sampling is often impossible, so it is common (and inevitable |
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