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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52,701 | Comparing coefficients in logistic regression | For those still looking at this old post, I found an article by King that might be useful: (King, J.E. (2007). Standardized coefficients in logistic regression. Paper presented at the annual meeting of the Southwest Educational Research Association, San Antonio, TX. February, 1-12.) | Comparing coefficients in logistic regression | For those still looking at this old post, I found an article by King that might be useful: (King, J.E. (2007). Standardized coefficients in logistic regression. Paper presented at the annual meeting o | Comparing coefficients in logistic regression
For those still looking at this old post, I found an article by King that might be useful: (King, J.E. (2007). Standardized coefficients in logistic regression. Paper presented at the annual meeting of the Southwest Educational Research Association, San Antonio, TX. Februar... | Comparing coefficients in logistic regression
For those still looking at this old post, I found an article by King that might be useful: (King, J.E. (2007). Standardized coefficients in logistic regression. Paper presented at the annual meeting o |
52,702 | Showing $\mathbb{E}[T_n] = \theta \mathbb{E}_1[T_n]$ is scale equivariant? | Your random variables belong to what is called a scale family. The first step should be to show that if $X\sim F_1$ then $\theta\cdot X\sim F_\theta$.
A statistic $T_n(X_1,\ldots,X_n)$ is usually said to be scale invariant if $$T_n(\theta X_1,\ldots,\theta X_n)=T_n(X_1,\ldots,X_n),$$
i.e. if rescaling the data leaves t... | Showing $\mathbb{E}[T_n] = \theta \mathbb{E}_1[T_n]$ is scale equivariant? | Your random variables belong to what is called a scale family. The first step should be to show that if $X\sim F_1$ then $\theta\cdot X\sim F_\theta$.
A statistic $T_n(X_1,\ldots,X_n)$ is usually said | Showing $\mathbb{E}[T_n] = \theta \mathbb{E}_1[T_n]$ is scale equivariant?
Your random variables belong to what is called a scale family. The first step should be to show that if $X\sim F_1$ then $\theta\cdot X\sim F_\theta$.
A statistic $T_n(X_1,\ldots,X_n)$ is usually said to be scale invariant if $$T_n(\theta X_1,\l... | Showing $\mathbb{E}[T_n] = \theta \mathbb{E}_1[T_n]$ is scale equivariant?
Your random variables belong to what is called a scale family. The first step should be to show that if $X\sim F_1$ then $\theta\cdot X\sim F_\theta$.
A statistic $T_n(X_1,\ldots,X_n)$ is usually said |
52,703 | Showing $\mathbb{E}[T_n] = \theta \mathbb{E}_1[T_n]$ is scale equivariant? | For completeness here is the solution (adding in the missing steps that @manst wanted me to think about).
\begin{align*}
\mathbb{E}_\theta[T_n] &= \int \ldots \int t_n (x_1, \ldots , x_n) f_\theta(x_1), \ldots , f_\theta(x_n) \text{d}x_1, \ldots , \text{d}x_n \\
\end{align*}
Since $F_\theta(x) = F(\frac{x}{\theta})$ ... | Showing $\mathbb{E}[T_n] = \theta \mathbb{E}_1[T_n]$ is scale equivariant? | For completeness here is the solution (adding in the missing steps that @manst wanted me to think about).
\begin{align*}
\mathbb{E}_\theta[T_n] &= \int \ldots \int t_n (x_1, \ldots , x_n) f_\theta(x | Showing $\mathbb{E}[T_n] = \theta \mathbb{E}_1[T_n]$ is scale equivariant?
For completeness here is the solution (adding in the missing steps that @manst wanted me to think about).
\begin{align*}
\mathbb{E}_\theta[T_n] &= \int \ldots \int t_n (x_1, \ldots , x_n) f_\theta(x_1), \ldots , f_\theta(x_n) \text{d}x_1, \ldo... | Showing $\mathbb{E}[T_n] = \theta \mathbb{E}_1[T_n]$ is scale equivariant?
For completeness here is the solution (adding in the missing steps that @manst wanted me to think about).
\begin{align*}
\mathbb{E}_\theta[T_n] &= \int \ldots \int t_n (x_1, \ldots , x_n) f_\theta(x |
52,704 | Simple introduction to MCMC with Dirichlet process prior? | Its not a paper, but I found some Matlab code that implements a DP prior for an infinite Gaussian mixture model. The code uses Gibbs sampling to infer a GMM (and the number of components in the mixture) over some input data. The code is pretty readable and it has helped me quite a bit to see the DP in action in a concr... | Simple introduction to MCMC with Dirichlet process prior? | Its not a paper, but I found some Matlab code that implements a DP prior for an infinite Gaussian mixture model. The code uses Gibbs sampling to infer a GMM (and the number of components in the mixtur | Simple introduction to MCMC with Dirichlet process prior?
Its not a paper, but I found some Matlab code that implements a DP prior for an infinite Gaussian mixture model. The code uses Gibbs sampling to infer a GMM (and the number of components in the mixture) over some input data. The code is pretty readable and it ha... | Simple introduction to MCMC with Dirichlet process prior?
Its not a paper, but I found some Matlab code that implements a DP prior for an infinite Gaussian mixture model. The code uses Gibbs sampling to infer a GMM (and the number of components in the mixtur |
52,705 | Simple introduction to MCMC with Dirichlet process prior? | MCMC sampling for DPMM is quite challenging and that's for many reasons,
the main one being that the model is infinite and the distribution is not
that easy to work with. Employing algorithms such as metropolis is non-trivial
since there are actually quite a few degrees of freedom in how you specify
your proposal distr... | Simple introduction to MCMC with Dirichlet process prior? | MCMC sampling for DPMM is quite challenging and that's for many reasons,
the main one being that the model is infinite and the distribution is not
that easy to work with. Employing algorithms such as | Simple introduction to MCMC with Dirichlet process prior?
MCMC sampling for DPMM is quite challenging and that's for many reasons,
the main one being that the model is infinite and the distribution is not
that easy to work with. Employing algorithms such as metropolis is non-trivial
since there are actually quite a few... | Simple introduction to MCMC with Dirichlet process prior?
MCMC sampling for DPMM is quite challenging and that's for many reasons,
the main one being that the model is infinite and the distribution is not
that easy to work with. Employing algorithms such as |
52,706 | Simple introduction to MCMC with Dirichlet process prior? | I have the same feeling. This is as closest as I've come:
http://www.cs.cmu.edu/~kbe/dp_tutorial.pdf
The algorithm explained starting at page 37 is understandable, however I still wish to see a very simple example written out step by step so I'm more confident of which each term means.
I attempted to implement the alg... | Simple introduction to MCMC with Dirichlet process prior? | I have the same feeling. This is as closest as I've come:
http://www.cs.cmu.edu/~kbe/dp_tutorial.pdf
The algorithm explained starting at page 37 is understandable, however I still wish to see a very | Simple introduction to MCMC with Dirichlet process prior?
I have the same feeling. This is as closest as I've come:
http://www.cs.cmu.edu/~kbe/dp_tutorial.pdf
The algorithm explained starting at page 37 is understandable, however I still wish to see a very simple example written out step by step so I'm more confident ... | Simple introduction to MCMC with Dirichlet process prior?
I have the same feeling. This is as closest as I've come:
http://www.cs.cmu.edu/~kbe/dp_tutorial.pdf
The algorithm explained starting at page 37 is understandable, however I still wish to see a very |
52,707 | Simple introduction to MCMC with Dirichlet process prior? | My belief is that there can hardly be such a paper, because the concepts and implementation details are not straighforward. Hence, even the best papers will be somewhat involved and you need to go through that. | Simple introduction to MCMC with Dirichlet process prior? | My belief is that there can hardly be such a paper, because the concepts and implementation details are not straighforward. Hence, even the best papers will be somewhat involved and you need to go thr | Simple introduction to MCMC with Dirichlet process prior?
My belief is that there can hardly be such a paper, because the concepts and implementation details are not straighforward. Hence, even the best papers will be somewhat involved and you need to go through that. | Simple introduction to MCMC with Dirichlet process prior?
My belief is that there can hardly be such a paper, because the concepts and implementation details are not straighforward. Hence, even the best papers will be somewhat involved and you need to go thr |
52,708 | Simple introduction to MCMC with Dirichlet process prior? | (Edited) Since, no one had added this. Let me contribute here.
Sethuraman's stick breaking representation for Dirichlet Process is incredibly useful for understanding DP model and also for simulating DP. Basically, Sethuraman tells us that one can think of the weights which appear in Dirichlet Process as a product of s... | Simple introduction to MCMC with Dirichlet process prior? | (Edited) Since, no one had added this. Let me contribute here.
Sethuraman's stick breaking representation for Dirichlet Process is incredibly useful for understanding DP model and also for simulating | Simple introduction to MCMC with Dirichlet process prior?
(Edited) Since, no one had added this. Let me contribute here.
Sethuraman's stick breaking representation for Dirichlet Process is incredibly useful for understanding DP model and also for simulating DP. Basically, Sethuraman tells us that one can think of the w... | Simple introduction to MCMC with Dirichlet process prior?
(Edited) Since, no one had added this. Let me contribute here.
Sethuraman's stick breaking representation for Dirichlet Process is incredibly useful for understanding DP model and also for simulating |
52,709 | Mean and standard deviation of Gaussian Distribution | You can estimate them. The best estimate of the mean of the Gaussian distribution is the mean of your sample- that is, the sum of your sample divided by the number of elements in it.
$$\bar{x} = \frac{1}{n}\sum_{i=1}^nx_i$$
The most common estimate of the standard deviation of a Gaussian distribution is
$$\bar{s} = \sq... | Mean and standard deviation of Gaussian Distribution | You can estimate them. The best estimate of the mean of the Gaussian distribution is the mean of your sample- that is, the sum of your sample divided by the number of elements in it.
$$\bar{x} = \frac | Mean and standard deviation of Gaussian Distribution
You can estimate them. The best estimate of the mean of the Gaussian distribution is the mean of your sample- that is, the sum of your sample divided by the number of elements in it.
$$\bar{x} = \frac{1}{n}\sum_{i=1}^nx_i$$
The most common estimate of the standard de... | Mean and standard deviation of Gaussian Distribution
You can estimate them. The best estimate of the mean of the Gaussian distribution is the mean of your sample- that is, the sum of your sample divided by the number of elements in it.
$$\bar{x} = \frac |
52,710 | When are order statistics not sufficient? | The order statistics are just the sorted data values, so for any case where the data is univariate iid, the order statistics have the exact same information as the original data (just in a different order). If the order in the data matters (not iid, e.g. time series) then the order statistics don't have that informati... | When are order statistics not sufficient? | The order statistics are just the sorted data values, so for any case where the data is univariate iid, the order statistics have the exact same information as the original data (just in a different o | When are order statistics not sufficient?
The order statistics are just the sorted data values, so for any case where the data is univariate iid, the order statistics have the exact same information as the original data (just in a different order). If the order in the data matters (not iid, e.g. time series) then the ... | When are order statistics not sufficient?
The order statistics are just the sorted data values, so for any case where the data is univariate iid, the order statistics have the exact same information as the original data (just in a different o |
52,711 | How is it possible that these variances are equal? | They look about equal to me.
A good visual test to estimate or compare standard deviations (after checking for obvious outliers) is to look at the range of a dataset. For a given sample size, the range will typically be near a fixed multiple of the SD. With around 250 independent samples of a normal distribution, for... | How is it possible that these variances are equal? | They look about equal to me.
A good visual test to estimate or compare standard deviations (after checking for obvious outliers) is to look at the range of a dataset. For a given sample size, the ran | How is it possible that these variances are equal?
They look about equal to me.
A good visual test to estimate or compare standard deviations (after checking for obvious outliers) is to look at the range of a dataset. For a given sample size, the range will typically be near a fixed multiple of the SD. With around 25... | How is it possible that these variances are equal?
They look about equal to me.
A good visual test to estimate or compare standard deviations (after checking for obvious outliers) is to look at the range of a dataset. For a given sample size, the ran |
52,712 | Should a predictor, significant on its own but not with other predictors, be included in an overall multinomial logistic regression? | It depends whether you are doing...
a) predictive research, where you don't care about what is causally responsible, only what serves as an efficient set of indicators, or
b) explanatory research, where you want to disentangle causal relationships as much as you can.
In the latter, when multiple correlated predictors v... | Should a predictor, significant on its own but not with other predictors, be included in an overall | It depends whether you are doing...
a) predictive research, where you don't care about what is causally responsible, only what serves as an efficient set of indicators, or
b) explanatory research, whe | Should a predictor, significant on its own but not with other predictors, be included in an overall multinomial logistic regression?
It depends whether you are doing...
a) predictive research, where you don't care about what is causally responsible, only what serves as an efficient set of indicators, or
b) explanatory ... | Should a predictor, significant on its own but not with other predictors, be included in an overall
It depends whether you are doing...
a) predictive research, where you don't care about what is causally responsible, only what serves as an efficient set of indicators, or
b) explanatory research, whe |
52,713 | Should a predictor, significant on its own but not with other predictors, be included in an overall multinomial logistic regression? | As @rolando2 mentioned, this depends very much on what your trying to accomplish or what question(s) you are trying to answer.
If you are trying to find a good model for prediction then rather than just deciding on whethere to include a term or not, it is better to use some type of shrinkage method such as penalized re... | Should a predictor, significant on its own but not with other predictors, be included in an overall | As @rolando2 mentioned, this depends very much on what your trying to accomplish or what question(s) you are trying to answer.
If you are trying to find a good model for prediction then rather than ju | Should a predictor, significant on its own but not with other predictors, be included in an overall multinomial logistic regression?
As @rolando2 mentioned, this depends very much on what your trying to accomplish or what question(s) you are trying to answer.
If you are trying to find a good model for prediction then r... | Should a predictor, significant on its own but not with other predictors, be included in an overall
As @rolando2 mentioned, this depends very much on what your trying to accomplish or what question(s) you are trying to answer.
If you are trying to find a good model for prediction then rather than ju |
52,714 | Should a predictor, significant on its own but not with other predictors, be included in an overall multinomial logistic regression? | If predictive accuracy is the main objective, then it is generally better to use regularisation to address problems such as correlated predictor variables and not perform any feature selection. This is because feature selection is difficult. Most often feature selection is peformed by optimising some feature selectio... | Should a predictor, significant on its own but not with other predictors, be included in an overall | If predictive accuracy is the main objective, then it is generally better to use regularisation to address problems such as correlated predictor variables and not perform any feature selection. This | Should a predictor, significant on its own but not with other predictors, be included in an overall multinomial logistic regression?
If predictive accuracy is the main objective, then it is generally better to use regularisation to address problems such as correlated predictor variables and not perform any feature sele... | Should a predictor, significant on its own but not with other predictors, be included in an overall
If predictive accuracy is the main objective, then it is generally better to use regularisation to address problems such as correlated predictor variables and not perform any feature selection. This |
52,715 | Recursive partitioning using rpart() method in R | Perhaps you misunderstood the message? It is saying that, having built the tree using the control parameters specified, only the variables mpa_a and tc_b have been involved in splits. All the variables were considered, but just these two were needed.
That tree seems quite small; do you have only a small sample of obser... | Recursive partitioning using rpart() method in R | Perhaps you misunderstood the message? It is saying that, having built the tree using the control parameters specified, only the variables mpa_a and tc_b have been involved in splits. All the variable | Recursive partitioning using rpart() method in R
Perhaps you misunderstood the message? It is saying that, having built the tree using the control parameters specified, only the variables mpa_a and tc_b have been involved in splits. All the variables were considered, but just these two were needed.
That tree seems quit... | Recursive partitioning using rpart() method in R
Perhaps you misunderstood the message? It is saying that, having built the tree using the control parameters specified, only the variables mpa_a and tc_b have been involved in splits. All the variable |
52,716 | Recursive partitioning using rpart() method in R | If the number of observations is less than around 20,000 the trees built by rpart do not have a reliable structure. That is, if you were to use the bootstrap to repeat the process, you will see many different trees that are called 'optimal'. | Recursive partitioning using rpart() method in R | If the number of observations is less than around 20,000 the trees built by rpart do not have a reliable structure. That is, if you were to use the bootstrap to repeat the process, you will see many | Recursive partitioning using rpart() method in R
If the number of observations is less than around 20,000 the trees built by rpart do not have a reliable structure. That is, if you were to use the bootstrap to repeat the process, you will see many different trees that are called 'optimal'. | Recursive partitioning using rpart() method in R
If the number of observations is less than around 20,000 the trees built by rpart do not have a reliable structure. That is, if you were to use the bootstrap to repeat the process, you will see many |
52,717 | ARMA modeling in R | Simplest way to arrive at values for $p$ and $q$ is using auto.arima function from package forecast. There is no simplest way in any statistical package to arrive at good values. The main reason for that is that there is no universal definition of good.
Since you mention overfitting, one possible way is to fit arima m... | ARMA modeling in R | Simplest way to arrive at values for $p$ and $q$ is using auto.arima function from package forecast. There is no simplest way in any statistical package to arrive at good values. The main reason for t | ARMA modeling in R
Simplest way to arrive at values for $p$ and $q$ is using auto.arima function from package forecast. There is no simplest way in any statistical package to arrive at good values. The main reason for that is that there is no universal definition of good.
Since you mention overfitting, one possible wa... | ARMA modeling in R
Simplest way to arrive at values for $p$ and $q$ is using auto.arima function from package forecast. There is no simplest way in any statistical package to arrive at good values. The main reason for t |
52,718 | ARMA modeling in R | One option is to fit a series of ARMA models with combinations of $p$ and $q$ and work with the model that has the best "fit". Here I evaluate "fit" using BIC to attempt to penalise overly complex fits. An example is shown below for the in-built Mauna Loa $\mathrm{CO}_2$ concentration data set
## load the data
data(co2... | ARMA modeling in R | One option is to fit a series of ARMA models with combinations of $p$ and $q$ and work with the model that has the best "fit". Here I evaluate "fit" using BIC to attempt to penalise overly complex fit | ARMA modeling in R
One option is to fit a series of ARMA models with combinations of $p$ and $q$ and work with the model that has the best "fit". Here I evaluate "fit" using BIC to attempt to penalise overly complex fits. An example is shown below for the in-built Mauna Loa $\mathrm{CO}_2$ concentration data set
## loa... | ARMA modeling in R
One option is to fit a series of ARMA models with combinations of $p$ and $q$ and work with the model that has the best "fit". Here I evaluate "fit" using BIC to attempt to penalise overly complex fit |
52,719 | Model performance metrics for ordinal response | A good measure is Somers' Dxy rank correlation, a generalization of ROC area for ordinal or continuous Y. It is computed for ordinal proportional odds regression in the lrm function in the rms package. | Model performance metrics for ordinal response | A good measure is Somers' Dxy rank correlation, a generalization of ROC area for ordinal or continuous Y. It is computed for ordinal proportional odds regression in the lrm function in the rms packag | Model performance metrics for ordinal response
A good measure is Somers' Dxy rank correlation, a generalization of ROC area for ordinal or continuous Y. It is computed for ordinal proportional odds regression in the lrm function in the rms package. | Model performance metrics for ordinal response
A good measure is Somers' Dxy rank correlation, a generalization of ROC area for ordinal or continuous Y. It is computed for ordinal proportional odds regression in the lrm function in the rms packag |
52,720 | How to produce Theil's U with package forecast 2.16 in R? | It does. Use the accuracy() command.
Update: here is an example.
library(forecast)
x <- EuStockMarkets[1:200,1]
f <- EuStockMarkets[201:300,1]
fit1 <- ses(x,h=100)
accuracy(fit1,f)
ME RMSE MAE MPE MAPE MASE ACF1 Theil's U
0.8065983 78.1801986 63.2728352 -0.1725009 3.787... | How to produce Theil's U with package forecast 2.16 in R? | It does. Use the accuracy() command.
Update: here is an example.
library(forecast)
x <- EuStockMarkets[1:200,1]
f <- EuStockMarkets[201:300,1]
fit1 <- ses(x,h=100)
accuracy(fit1,f)
ME RM | How to produce Theil's U with package forecast 2.16 in R?
It does. Use the accuracy() command.
Update: here is an example.
library(forecast)
x <- EuStockMarkets[1:200,1]
f <- EuStockMarkets[201:300,1]
fit1 <- ses(x,h=100)
accuracy(fit1,f)
ME RMSE MAE MPE MAPE MASE ACF1 Th... | How to produce Theil's U with package forecast 2.16 in R?
It does. Use the accuracy() command.
Update: here is an example.
library(forecast)
x <- EuStockMarkets[1:200,1]
f <- EuStockMarkets[201:300,1]
fit1 <- ses(x,h=100)
accuracy(fit1,f)
ME RM |
52,721 | Tutorial for using R to do multivariate regression? | This is my favorite one: Quick-R | Tutorial for using R to do multivariate regression? | This is my favorite one: Quick-R | Tutorial for using R to do multivariate regression?
This is my favorite one: Quick-R | Tutorial for using R to do multivariate regression?
This is my favorite one: Quick-R |
52,722 | Tutorial for using R to do multivariate regression? | +1 for Quick-R.
Another great resource that I (re)turn to regularly is the website of the UCLA Statistical Consulting Group. In particular, it sounds like you might find their data analysis examples useful. Many of the cases walk through the logic of inquiry and model design steps in addition to providing sample code a... | Tutorial for using R to do multivariate regression? | +1 for Quick-R.
Another great resource that I (re)turn to regularly is the website of the UCLA Statistical Consulting Group. In particular, it sounds like you might find their data analysis examples u | Tutorial for using R to do multivariate regression?
+1 for Quick-R.
Another great resource that I (re)turn to regularly is the website of the UCLA Statistical Consulting Group. In particular, it sounds like you might find their data analysis examples useful. Many of the cases walk through the logic of inquiry and model... | Tutorial for using R to do multivariate regression?
+1 for Quick-R.
Another great resource that I (re)turn to regularly is the website of the UCLA Statistical Consulting Group. In particular, it sounds like you might find their data analysis examples u |
52,723 | Concept of a random linear model | One problem with the approach you outline is that the regressors $x_i$ will (on average) be uncorrelated, and one situation in which variable selection methods have difficulty is highly correlated regressors.
I'm not sure the concept of a 'random' linear model is very useful here, as you have to decide on a probability... | Concept of a random linear model | One problem with the approach you outline is that the regressors $x_i$ will (on average) be uncorrelated, and one situation in which variable selection methods have difficulty is highly correlated reg | Concept of a random linear model
One problem with the approach you outline is that the regressors $x_i$ will (on average) be uncorrelated, and one situation in which variable selection methods have difficulty is highly correlated regressors.
I'm not sure the concept of a 'random' linear model is very useful here, as yo... | Concept of a random linear model
One problem with the approach you outline is that the regressors $x_i$ will (on average) be uncorrelated, and one situation in which variable selection methods have difficulty is highly correlated reg |
52,724 | Concept of a random linear model | To address @onestop's objection to non-correlated regressors, you could do the following:
Choose $n, k, l$, where $l$ is the number of latent factors.
Choose $\sigma_i$, the amount of 'idiosyncratic' volatility in the regressors.
Draw a $k \times l$ matrix, $F$, of exposures, uniformly on $(0,1)$. (you may want to no... | Concept of a random linear model | To address @onestop's objection to non-correlated regressors, you could do the following:
Choose $n, k, l$, where $l$ is the number of latent factors.
Choose $\sigma_i$, the amount of 'idiosyncratic | Concept of a random linear model
To address @onestop's objection to non-correlated regressors, you could do the following:
Choose $n, k, l$, where $l$ is the number of latent factors.
Choose $\sigma_i$, the amount of 'idiosyncratic' volatility in the regressors.
Draw a $k \times l$ matrix, $F$, of exposures, uniforml... | Concept of a random linear model
To address @onestop's objection to non-correlated regressors, you could do the following:
Choose $n, k, l$, where $l$ is the number of latent factors.
Choose $\sigma_i$, the amount of 'idiosyncratic |
52,725 | A "systematic" part of a random time series component? | The Burns reference that you are quoting seems to dividing the stochastic part into autocorrelation error, which is a byproduct of any time series analysis (and is systematic), vs. truly random error which is uncontrollable.
-Ralph Winters | A "systematic" part of a random time series component? | The Burns reference that you are quoting seems to dividing the stochastic part into autocorrelation error, which is a byproduct of any time series analysis (and is systematic), vs. truly random error | A "systematic" part of a random time series component?
The Burns reference that you are quoting seems to dividing the stochastic part into autocorrelation error, which is a byproduct of any time series analysis (and is systematic), vs. truly random error which is uncontrollable.
-Ralph Winters | A "systematic" part of a random time series component?
The Burns reference that you are quoting seems to dividing the stochastic part into autocorrelation error, which is a byproduct of any time series analysis (and is systematic), vs. truly random error |
52,726 | A "systematic" part of a random time series component? | "random" is often used as if it was a real property of the data under study, where it should be replaced with "uncertain". To give an example, if I ask you what how much money you earned over the past month, and you don't tell me, it is not "random", but just uncertain. However, treating the uncertainty as if it was ... | A "systematic" part of a random time series component? | "random" is often used as if it was a real property of the data under study, where it should be replaced with "uncertain". To give an example, if I ask you what how much money you earned over the pas | A "systematic" part of a random time series component?
"random" is often used as if it was a real property of the data under study, where it should be replaced with "uncertain". To give an example, if I ask you what how much money you earned over the past month, and you don't tell me, it is not "random", but just unce... | A "systematic" part of a random time series component?
"random" is often used as if it was a real property of the data under study, where it should be replaced with "uncertain". To give an example, if I ask you what how much money you earned over the pas |
52,727 | A "systematic" part of a random time series component? | Systematic and unsystematic are rather ambiguous terms. One of the possible explanations is given by @probabilityislogic. Another may be given here. Since the context you gave is time series, I think this might be related to Wold's theorem. Unfortunately wikipedia text captures the essence, but does not go into the d... | A "systematic" part of a random time series component? | Systematic and unsystematic are rather ambiguous terms. One of the possible explanations is given by @probabilityislogic. Another may be given here. Since the context you gave is time series, I think | A "systematic" part of a random time series component?
Systematic and unsystematic are rather ambiguous terms. One of the possible explanations is given by @probabilityislogic. Another may be given here. Since the context you gave is time series, I think this might be related to Wold's theorem. Unfortunately wikipedi... | A "systematic" part of a random time series component?
Systematic and unsystematic are rather ambiguous terms. One of the possible explanations is given by @probabilityislogic. Another may be given here. Since the context you gave is time series, I think |
52,728 | Testing if a coin is fair | It's neither because the alternative to being fair is that the coin favors heads or tails.
You are free to invent any test you like. For example, I could (idiosyncratically) decide the coin is unfair if and only if the number of heads is either 6 or 15 (the "critical region"), because this event occurs with only 5% ch... | Testing if a coin is fair | It's neither because the alternative to being fair is that the coin favors heads or tails.
You are free to invent any test you like. For example, I could (idiosyncratically) decide the coin is unfair | Testing if a coin is fair
It's neither because the alternative to being fair is that the coin favors heads or tails.
You are free to invent any test you like. For example, I could (idiosyncratically) decide the coin is unfair if and only if the number of heads is either 6 or 15 (the "critical region"), because this ev... | Testing if a coin is fair
It's neither because the alternative to being fair is that the coin favors heads or tails.
You are free to invent any test you like. For example, I could (idiosyncratically) decide the coin is unfair |
52,729 | References for use of symplectic geometry in statistics? | I know nothing whatsoever about symplectic geometry, but a bit of googling brought up a 1997 article in the Journal of Statistical Planning & Inference by Barndorff-Nielsen & Jupp, which contains this quote:
Some other links between statistics and symplectic geometry have been discussed
by Friedrich and Nakamura. Fr... | References for use of symplectic geometry in statistics? | I know nothing whatsoever about symplectic geometry, but a bit of googling brought up a 1997 article in the Journal of Statistical Planning & Inference by Barndorff-Nielsen & Jupp, which contains this | References for use of symplectic geometry in statistics?
I know nothing whatsoever about symplectic geometry, but a bit of googling brought up a 1997 article in the Journal of Statistical Planning & Inference by Barndorff-Nielsen & Jupp, which contains this quote:
Some other links between statistics and symplectic geo... | References for use of symplectic geometry in statistics?
I know nothing whatsoever about symplectic geometry, but a bit of googling brought up a 1997 article in the Journal of Statistical Planning & Inference by Barndorff-Nielsen & Jupp, which contains this |
52,730 | References for use of symplectic geometry in statistics? | A direct connection would be unexpected: the two fields appear to have little in common. For example, a modern introduction to symplectic geometry published by the American Mathematical Society appears to make no mention of mathematical statistics at all.
At best it seems any connection would come through mathematical... | References for use of symplectic geometry in statistics? | A direct connection would be unexpected: the two fields appear to have little in common. For example, a modern introduction to symplectic geometry published by the American Mathematical Society appea | References for use of symplectic geometry in statistics?
A direct connection would be unexpected: the two fields appear to have little in common. For example, a modern introduction to symplectic geometry published by the American Mathematical Society appears to make no mention of mathematical statistics at all.
At bes... | References for use of symplectic geometry in statistics?
A direct connection would be unexpected: the two fields appear to have little in common. For example, a modern introduction to symplectic geometry published by the American Mathematical Society appea |
52,731 | References for use of symplectic geometry in statistics? | Symplectic model of Statistical Physics and Information Geometry is given by Souriau model of "Lie groups Thermodynamics":
Lie Group Cohomology and (Multi)Symplectic Integrators: New Geometric Tools for Lie Group Machine Learning Based on Souriau Geometric Statistical Mechanics,
Lie Group Statistics and Lie Group Machi... | References for use of symplectic geometry in statistics? | Symplectic model of Statistical Physics and Information Geometry is given by Souriau model of "Lie groups Thermodynamics":
Lie Group Cohomology and (Multi)Symplectic Integrators: New Geometric Tools f | References for use of symplectic geometry in statistics?
Symplectic model of Statistical Physics and Information Geometry is given by Souriau model of "Lie groups Thermodynamics":
Lie Group Cohomology and (Multi)Symplectic Integrators: New Geometric Tools for Lie Group Machine Learning Based on Souriau Geometric Statis... | References for use of symplectic geometry in statistics?
Symplectic model of Statistical Physics and Information Geometry is given by Souriau model of "Lie groups Thermodynamics":
Lie Group Cohomology and (Multi)Symplectic Integrators: New Geometric Tools f |
52,732 | How to use Kernel Density Estimation for Prediction? | You can use conditional kernel density estimation to obtain the density of sales at time $t+h$ conditional on the values of sales at times $t, t-1, t-2, \dots$ This gives you a density forecast rather than a point forecast. The problem is that the conditioning is difficult in a density setting when the number of condit... | How to use Kernel Density Estimation for Prediction? | You can use conditional kernel density estimation to obtain the density of sales at time $t+h$ conditional on the values of sales at times $t, t-1, t-2, \dots$ This gives you a density forecast rather | How to use Kernel Density Estimation for Prediction?
You can use conditional kernel density estimation to obtain the density of sales at time $t+h$ conditional on the values of sales at times $t, t-1, t-2, \dots$ This gives you a density forecast rather than a point forecast. The problem is that the conditioning is dif... | How to use Kernel Density Estimation for Prediction?
You can use conditional kernel density estimation to obtain the density of sales at time $t+h$ conditional on the values of sales at times $t, t-1, t-2, \dots$ This gives you a density forecast rather |
52,733 | How to use Kernel Density Estimation for Prediction? | I would have thought that KDE bear little if any relationship to predicting future sales based on past sales. Sounds more like time series analysis to me, though that's really not my area. | How to use Kernel Density Estimation for Prediction? | I would have thought that KDE bear little if any relationship to predicting future sales based on past sales. Sounds more like time series analysis to me, though that's really not my area. | How to use Kernel Density Estimation for Prediction?
I would have thought that KDE bear little if any relationship to predicting future sales based on past sales. Sounds more like time series analysis to me, though that's really not my area. | How to use Kernel Density Estimation for Prediction?
I would have thought that KDE bear little if any relationship to predicting future sales based on past sales. Sounds more like time series analysis to me, though that's really not my area. |
52,734 | Libraries for forest and funnel plots | Well, i use graphviz, which has Java bindings (Grappa).
Although the dot language (graphviz's syntax) is simple, i prefer to use graphviz as a library through the excellent and production-stable python bindings, pygraphviz, and networkx.
Here's the code for a simple 'funnel diagram' using those tools; it's not the most... | Libraries for forest and funnel plots | Well, i use graphviz, which has Java bindings (Grappa).
Although the dot language (graphviz's syntax) is simple, i prefer to use graphviz as a library through the excellent and production-stable pytho | Libraries for forest and funnel plots
Well, i use graphviz, which has Java bindings (Grappa).
Although the dot language (graphviz's syntax) is simple, i prefer to use graphviz as a library through the excellent and production-stable python bindings, pygraphviz, and networkx.
Here's the code for a simple 'funnel diagram... | Libraries for forest and funnel plots
Well, i use graphviz, which has Java bindings (Grappa).
Although the dot language (graphviz's syntax) is simple, i prefer to use graphviz as a library through the excellent and production-stable pytho |
52,735 | Libraries for forest and funnel plots | The rmeta package in R can produce forest and funnel plots.
http://cran.r-project.org/web/packages/rmeta/index.html | Libraries for forest and funnel plots | The rmeta package in R can produce forest and funnel plots.
http://cran.r-project.org/web/packages/rmeta/index.html | Libraries for forest and funnel plots
The rmeta package in R can produce forest and funnel plots.
http://cran.r-project.org/web/packages/rmeta/index.html | Libraries for forest and funnel plots
The rmeta package in R can produce forest and funnel plots.
http://cran.r-project.org/web/packages/rmeta/index.html |
52,736 | Libraries for forest and funnel plots | In addition to the rmeta package there is also the meta package in R, which produce publication quality plots. | Libraries for forest and funnel plots | In addition to the rmeta package there is also the meta package in R, which produce publication quality plots. | Libraries for forest and funnel plots
In addition to the rmeta package there is also the meta package in R, which produce publication quality plots. | Libraries for forest and funnel plots
In addition to the rmeta package there is also the meta package in R, which produce publication quality plots. |
52,737 | Where is a good place to find survey results? | The best place to find survey data related to the social sciences is the ICPSR data clearinghouse: http://www.icpsr.umich.edu/icpsrweb/ICPSR/access/index.jsp
Also, the 'survey' tag on Infochimps has many interesting and free data sets: http://infochimps.org/tags/survey | Where is a good place to find survey results? | The best place to find survey data related to the social sciences is the ICPSR data clearinghouse: http://www.icpsr.umich.edu/icpsrweb/ICPSR/access/index.jsp
Also, the 'survey' tag on Infochimps has m | Where is a good place to find survey results?
The best place to find survey data related to the social sciences is the ICPSR data clearinghouse: http://www.icpsr.umich.edu/icpsrweb/ICPSR/access/index.jsp
Also, the 'survey' tag on Infochimps has many interesting and free data sets: http://infochimps.org/tags/survey | Where is a good place to find survey results?
The best place to find survey data related to the social sciences is the ICPSR data clearinghouse: http://www.icpsr.umich.edu/icpsrweb/ICPSR/access/index.jsp
Also, the 'survey' tag on Infochimps has m |
52,738 | Where is a good place to find survey results? | government websites usually .... I use the RITA a lot | Where is a good place to find survey results? | government websites usually .... I use the RITA a lot | Where is a good place to find survey results?
government websites usually .... I use the RITA a lot | Where is a good place to find survey results?
government websites usually .... I use the RITA a lot |
52,739 | When dealing with data imbalance, shouldn't we never compare models based on validation loss, or at least weight it? | You should use a loss that accurately reflects the "real world loss" you are trying to minimize by using your model (in the context of subsequent decisions). Then the "problem" disappears, or more precisely, never is a problem.
Suppose you have a rare disease, with an incidence of one in a hundred, but which is fatal. ... | When dealing with data imbalance, shouldn't we never compare models based on validation loss, or at | You should use a loss that accurately reflects the "real world loss" you are trying to minimize by using your model (in the context of subsequent decisions). Then the "problem" disappears, or more pre | When dealing with data imbalance, shouldn't we never compare models based on validation loss, or at least weight it?
You should use a loss that accurately reflects the "real world loss" you are trying to minimize by using your model (in the context of subsequent decisions). Then the "problem" disappears, or more precis... | When dealing with data imbalance, shouldn't we never compare models based on validation loss, or at
You should use a loss that accurately reflects the "real world loss" you are trying to minimize by using your model (in the context of subsequent decisions). Then the "problem" disappears, or more pre |
52,740 | When dealing with data imbalance, shouldn't we never compare models based on validation loss, or at least weight it? | Answering you with a question: if not validation loss then what? Certainly, the training metrics won't be any better here. The desirable scenario is that your validation set resembles the real-world data that you will see in prediction time. In such a case, if the real-world data is equally imbalanced, the performance ... | When dealing with data imbalance, shouldn't we never compare models based on validation loss, or at | Answering you with a question: if not validation loss then what? Certainly, the training metrics won't be any better here. The desirable scenario is that your validation set resembles the real-world d | When dealing with data imbalance, shouldn't we never compare models based on validation loss, or at least weight it?
Answering you with a question: if not validation loss then what? Certainly, the training metrics won't be any better here. The desirable scenario is that your validation set resembles the real-world data... | When dealing with data imbalance, shouldn't we never compare models based on validation loss, or at
Answering you with a question: if not validation loss then what? Certainly, the training metrics won't be any better here. The desirable scenario is that your validation set resembles the real-world d |
52,741 | Error in Gaussian Process Implementation | The problem is the ill conditioning of your kernel matrix. These are the singular values of your kernel matrix k:
As you can see, many of them are numerically zero. This leads to nonsense when you compute np.linalg.inv.
You have two options. The most common is to simply add a scaled identity matrix to your kernel matr... | Error in Gaussian Process Implementation | The problem is the ill conditioning of your kernel matrix. These are the singular values of your kernel matrix k:
As you can see, many of them are numerically zero. This leads to nonsense when you co | Error in Gaussian Process Implementation
The problem is the ill conditioning of your kernel matrix. These are the singular values of your kernel matrix k:
As you can see, many of them are numerically zero. This leads to nonsense when you compute np.linalg.inv.
You have two options. The most common is to simply add a s... | Error in Gaussian Process Implementation
The problem is the ill conditioning of your kernel matrix. These are the singular values of your kernel matrix k:
As you can see, many of them are numerically zero. This leads to nonsense when you co |
52,742 | Error in Gaussian Process Implementation | @John Madden gave a good answer pointing to the root cause of the problem, but adding to it, you should not invert that matrix directly in the first place. Matrix inversion is generally inefficient and not recommended for all kinds of applications. This also applies to Gaussian processes. An efficient algorithm is give... | Error in Gaussian Process Implementation | @John Madden gave a good answer pointing to the root cause of the problem, but adding to it, you should not invert that matrix directly in the first place. Matrix inversion is generally inefficient an | Error in Gaussian Process Implementation
@John Madden gave a good answer pointing to the root cause of the problem, but adding to it, you should not invert that matrix directly in the first place. Matrix inversion is generally inefficient and not recommended for all kinds of applications. This also applies to Gaussian ... | Error in Gaussian Process Implementation
@John Madden gave a good answer pointing to the root cause of the problem, but adding to it, you should not invert that matrix directly in the first place. Matrix inversion is generally inefficient an |
52,743 | Poisson regression intercept downward bias when true intercepts are small | The score function is exactly unbiased
$$E_{\beta_0}[\sum_i x_i(y_i-\mu_i)]=0$$
In your case that simplifies to
$$E_{\beta_0}[\sum y_i-\exp\beta_0]=0$$
The parameter estimate is a non-linear function of the score, so that tells us it won't be exactly unbiased.
Can we work out the direction of the bias? Well, the mean o... | Poisson regression intercept downward bias when true intercepts are small | The score function is exactly unbiased
$$E_{\beta_0}[\sum_i x_i(y_i-\mu_i)]=0$$
In your case that simplifies to
$$E_{\beta_0}[\sum y_i-\exp\beta_0]=0$$
The parameter estimate is a non-linear function | Poisson regression intercept downward bias when true intercepts are small
The score function is exactly unbiased
$$E_{\beta_0}[\sum_i x_i(y_i-\mu_i)]=0$$
In your case that simplifies to
$$E_{\beta_0}[\sum y_i-\exp\beta_0]=0$$
The parameter estimate is a non-linear function of the score, so that tells us it won't be exa... | Poisson regression intercept downward bias when true intercepts are small
The score function is exactly unbiased
$$E_{\beta_0}[\sum_i x_i(y_i-\mu_i)]=0$$
In your case that simplifies to
$$E_{\beta_0}[\sum y_i-\exp\beta_0]=0$$
The parameter estimate is a non-linear function |
52,744 | What exactly needs to be independent in GLMs? | What is actually required is conditional independence of the response variable. Conditional on the regressors, that is. A Poisson regression model - for independent data - is no different from an ordinary least squares model in this assumption except that the OLS conveniently expresses the random error as a separate pa... | What exactly needs to be independent in GLMs? | What is actually required is conditional independence of the response variable. Conditional on the regressors, that is. A Poisson regression model - for independent data - is no different from an ordi | What exactly needs to be independent in GLMs?
What is actually required is conditional independence of the response variable. Conditional on the regressors, that is. A Poisson regression model - for independent data - is no different from an ordinary least squares model in this assumption except that the OLS convenient... | What exactly needs to be independent in GLMs?
What is actually required is conditional independence of the response variable. Conditional on the regressors, that is. A Poisson regression model - for independent data - is no different from an ordi |
52,745 | What exactly needs to be independent in GLMs? | A general form of expressing a model is
$$Y_i = f(\textbf{X}_i,\boldsymbol\beta,\epsilon_i)$$
The function $f$ expresses the random variable $Y_i$ in terms of a random latent variable $\epsilon_i$, a fixed/known regressor variable $\textbf{X}_i$, and some distribution parameters $\boldsymbol\beta$.
Note:
Here the subs... | What exactly needs to be independent in GLMs? | A general form of expressing a model is
$$Y_i = f(\textbf{X}_i,\boldsymbol\beta,\epsilon_i)$$
The function $f$ expresses the random variable $Y_i$ in terms of a random latent variable $\epsilon_i$, a | What exactly needs to be independent in GLMs?
A general form of expressing a model is
$$Y_i = f(\textbf{X}_i,\boldsymbol\beta,\epsilon_i)$$
The function $f$ expresses the random variable $Y_i$ in terms of a random latent variable $\epsilon_i$, a fixed/known regressor variable $\textbf{X}_i$, and some distribution param... | What exactly needs to be independent in GLMs?
A general form of expressing a model is
$$Y_i = f(\textbf{X}_i,\boldsymbol\beta,\epsilon_i)$$
The function $f$ expresses the random variable $Y_i$ in terms of a random latent variable $\epsilon_i$, a |
52,746 | Boxplot | 5-Number-Summary | To clarify your doubt, consider the following example using the standard definition of the boxplot.
Suppose we have the following observations $x = (-40,0, 2, 3, 4,10, 40)$. The median is 3, the first quartile is $Q_1 = 1$, and the third quartile is $Q_3 = 7$, thus $\text{IQR} = 8$. Let $u = Q_3+1.5\times \text{IQR} =1... | Boxplot | 5-Number-Summary | To clarify your doubt, consider the following example using the standard definition of the boxplot.
Suppose we have the following observations $x = (-40,0, 2, 3, 4,10, 40)$. The median is 3, the first | Boxplot | 5-Number-Summary
To clarify your doubt, consider the following example using the standard definition of the boxplot.
Suppose we have the following observations $x = (-40,0, 2, 3, 4,10, 40)$. The median is 3, the first quartile is $Q_1 = 1$, and the third quartile is $Q_3 = 7$, thus $\text{IQR} = 8$. Let $u = ... | Boxplot | 5-Number-Summary
To clarify your doubt, consider the following example using the standard definition of the boxplot.
Suppose we have the following observations $x = (-40,0, 2, 3, 4,10, 40)$. The median is 3, the first |
52,747 | Reject null hypothesis and alternative hypothesis simultaneously? | To your first question, a chi-square goodness of fit test only tests if the frequency distribution is different from your expectation. In this case, it is only testing one categorical factor. A chi-square test of independence tries to test if there is a relationship between multiple categorical factors. So in your case... | Reject null hypothesis and alternative hypothesis simultaneously? | To your first question, a chi-square goodness of fit test only tests if the frequency distribution is different from your expectation. In this case, it is only testing one categorical factor. A chi-sq | Reject null hypothesis and alternative hypothesis simultaneously?
To your first question, a chi-square goodness of fit test only tests if the frequency distribution is different from your expectation. In this case, it is only testing one categorical factor. A chi-square test of independence tries to test if there is a ... | Reject null hypothesis and alternative hypothesis simultaneously?
To your first question, a chi-square goodness of fit test only tests if the frequency distribution is different from your expectation. In this case, it is only testing one categorical factor. A chi-sq |
52,748 | Reject null hypothesis and alternative hypothesis simultaneously? | It appears that you have not formulated your null and alternative hypotheses in a way that is consistent with what you want to test. Your null hypothesis should be that the frequency of the word in corpus B is greater than or equal to the frequency of the word in corpus A.
Given that, once we see that the observed fre... | Reject null hypothesis and alternative hypothesis simultaneously? | It appears that you have not formulated your null and alternative hypotheses in a way that is consistent with what you want to test. Your null hypothesis should be that the frequency of the word in c | Reject null hypothesis and alternative hypothesis simultaneously?
It appears that you have not formulated your null and alternative hypotheses in a way that is consistent with what you want to test. Your null hypothesis should be that the frequency of the word in corpus B is greater than or equal to the frequency of t... | Reject null hypothesis and alternative hypothesis simultaneously?
It appears that you have not formulated your null and alternative hypotheses in a way that is consistent with what you want to test. Your null hypothesis should be that the frequency of the word in c |
52,749 | Can we always write a random variable as conditional expectation plus independent error? | Suppose
$$
Y=X^2+u
$$
where $u|X\sim(0,X^2)$ has conditional heteroskedasticity. Then,
$$
\epsilon=Y-E(Y|X)=X^2+u-E(Y|X)=u,
$$
which has conditional mean zero but is not independent of $X$, as its second moment depends on $X$. | Can we always write a random variable as conditional expectation plus independent error? | Suppose
$$
Y=X^2+u
$$
where $u|X\sim(0,X^2)$ has conditional heteroskedasticity. Then,
$$
\epsilon=Y-E(Y|X)=X^2+u-E(Y|X)=u,
$$
which has conditional mean zero but is not independent of $X$, as its sec | Can we always write a random variable as conditional expectation plus independent error?
Suppose
$$
Y=X^2+u
$$
where $u|X\sim(0,X^2)$ has conditional heteroskedasticity. Then,
$$
\epsilon=Y-E(Y|X)=X^2+u-E(Y|X)=u,
$$
which has conditional mean zero but is not independent of $X$, as its second moment depends on $X$. | Can we always write a random variable as conditional expectation plus independent error?
Suppose
$$
Y=X^2+u
$$
where $u|X\sim(0,X^2)$ has conditional heteroskedasticity. Then,
$$
\epsilon=Y-E(Y|X)=X^2+u-E(Y|X)=u,
$$
which has conditional mean zero but is not independent of $X$, as its sec |
52,750 | What is a good technique for testing whether data is Rayleigh distributed? | Literally nothing you do with a sample will show you that the population distribution is Rayleigh (there's an infinite number of distributions that are not-Rayleigh, but nevertheless closer to your data than the Rayleigh is), but that's okay because you can bet the population distribution probably isn't exactly Rayleig... | What is a good technique for testing whether data is Rayleigh distributed? | Literally nothing you do with a sample will show you that the population distribution is Rayleigh (there's an infinite number of distributions that are not-Rayleigh, but nevertheless closer to your da | What is a good technique for testing whether data is Rayleigh distributed?
Literally nothing you do with a sample will show you that the population distribution is Rayleigh (there's an infinite number of distributions that are not-Rayleigh, but nevertheless closer to your data than the Rayleigh is), but that's okay bec... | What is a good technique for testing whether data is Rayleigh distributed?
Literally nothing you do with a sample will show you that the population distribution is Rayleigh (there's an infinite number of distributions that are not-Rayleigh, but nevertheless closer to your da |
52,751 | Do I need to test for autocorrelation or normality assumption if I am running the regression with standard errors? | With so many observations, tests for normality or autocorrelation will most likely end up giving extremely low $p$-values, suggesting to reject the null.
Using robust standard errors is fine and perfectly acceptable. Perhaps you may consider doing a bit of model selection (say, lasso, stepwise, subset regression, etc.)... | Do I need to test for autocorrelation or normality assumption if I am running the regression with st | With so many observations, tests for normality or autocorrelation will most likely end up giving extremely low $p$-values, suggesting to reject the null.
Using robust standard errors is fine and perfe | Do I need to test for autocorrelation or normality assumption if I am running the regression with standard errors?
With so many observations, tests for normality or autocorrelation will most likely end up giving extremely low $p$-values, suggesting to reject the null.
Using robust standard errors is fine and perfectly ... | Do I need to test for autocorrelation or normality assumption if I am running the regression with st
With so many observations, tests for normality or autocorrelation will most likely end up giving extremely low $p$-values, suggesting to reject the null.
Using robust standard errors is fine and perfe |
52,752 | Do I need to test for autocorrelation or normality assumption if I am running the regression with standard errors? | As @utobi correctly notes in another answer, with such a large data set almost any test of a violation of model assumptions will tend to produce "statistically significant" results that might be practically unimportant. You need to apply your understanding of the subject matter carefully.
A big question is how much you... | Do I need to test for autocorrelation or normality assumption if I am running the regression with st | As @utobi correctly notes in another answer, with such a large data set almost any test of a violation of model assumptions will tend to produce "statistically significant" results that might be pract | Do I need to test for autocorrelation or normality assumption if I am running the regression with standard errors?
As @utobi correctly notes in another answer, with such a large data set almost any test of a violation of model assumptions will tend to produce "statistically significant" results that might be practicall... | Do I need to test for autocorrelation or normality assumption if I am running the regression with st
As @utobi correctly notes in another answer, with such a large data set almost any test of a violation of model assumptions will tend to produce "statistically significant" results that might be pract |
52,753 | Degrees of freedom of a coin toss | Degrees of freedom apply to a parametrisation of a model, not to the observed outcome. We model a single coin toss by a Bernoulli($p$) distribution, which only has a single parameter, namely the $p$. "Heads" is an outcome, not a parameter, so it neither has degrees of freedom nor is to be counted in order to know the d... | Degrees of freedom of a coin toss | Degrees of freedom apply to a parametrisation of a model, not to the observed outcome. We model a single coin toss by a Bernoulli($p$) distribution, which only has a single parameter, namely the $p$. | Degrees of freedom of a coin toss
Degrees of freedom apply to a parametrisation of a model, not to the observed outcome. We model a single coin toss by a Bernoulli($p$) distribution, which only has a single parameter, namely the $p$. "Heads" is an outcome, not a parameter, so it neither has degrees of freedom nor is to... | Degrees of freedom of a coin toss
Degrees of freedom apply to a parametrisation of a model, not to the observed outcome. We model a single coin toss by a Bernoulli($p$) distribution, which only has a single parameter, namely the $p$. |
52,754 | What is "power cut"? | This is an interesting observation: the paragraph talks about experiments and how to analyze them if stopped early. So it's not a stretch to connect "power cut" with "statistical power", a concept relevant to planning scientific experiments. However, In All Likelihood takes an informal approach*, so the odds are (pun i... | What is "power cut"? | This is an interesting observation: the paragraph talks about experiments and how to analyze them if stopped early. So it's not a stretch to connect "power cut" with "statistical power", a concept rel | What is "power cut"?
This is an interesting observation: the paragraph talks about experiments and how to analyze them if stopped early. So it's not a stretch to connect "power cut" with "statistical power", a concept relevant to planning scientific experiments. However, In All Likelihood takes an informal approach*, s... | What is "power cut"?
This is an interesting observation: the paragraph talks about experiments and how to analyze them if stopped early. So it's not a stretch to connect "power cut" with "statistical power", a concept rel |
52,755 | What is a random variable in ADAM optimizer? | Converting my comment into an answer.
The sentence right below your screenshot in the paper is the answer.
The stochasticity might come from the evaluation at random subsamples (minibatches) of datapoints, or arise from inherent function noise. | What is a random variable in ADAM optimizer? | Converting my comment into an answer.
The sentence right below your screenshot in the paper is the answer.
The stochasticity might come from the evaluation at random subsamples (minibatches) of datap | What is a random variable in ADAM optimizer?
Converting my comment into an answer.
The sentence right below your screenshot in the paper is the answer.
The stochasticity might come from the evaluation at random subsamples (minibatches) of datapoints, or arise from inherent function noise. | What is a random variable in ADAM optimizer?
Converting my comment into an answer.
The sentence right below your screenshot in the paper is the answer.
The stochasticity might come from the evaluation at random subsamples (minibatches) of datap |
52,756 | Linear regression's (OLS) coefficient interpretation with heteroscedasticity | Heteroscedasticity makes it so that the OLS estimator is not the best linear unbiased estimator of the regression slopes and makes it so that the usual standard errors (and the quantities based on them, such as p-values and confidence intervals) are incorrect. It doesn't affect the interpretation of the regression coef... | Linear regression's (OLS) coefficient interpretation with heteroscedasticity | Heteroscedasticity makes it so that the OLS estimator is not the best linear unbiased estimator of the regression slopes and makes it so that the usual standard errors (and the quantities based on the | Linear regression's (OLS) coefficient interpretation with heteroscedasticity
Heteroscedasticity makes it so that the OLS estimator is not the best linear unbiased estimator of the regression slopes and makes it so that the usual standard errors (and the quantities based on them, such as p-values and confidence interval... | Linear regression's (OLS) coefficient interpretation with heteroscedasticity
Heteroscedasticity makes it so that the OLS estimator is not the best linear unbiased estimator of the regression slopes and makes it so that the usual standard errors (and the quantities based on the |
52,757 | Is it normal to have thousands of df in a logistic regression model? | The discrepancy between DF for different estimates likely means that these are the results of a mixed model. There were probably a bit more than 25.69 participants in the study (leading to 25.69 DF for fluency), but these people probably had over 100 measurements each, or over 2125 total (leading to 2125 DF on other co... | Is it normal to have thousands of df in a logistic regression model? | The discrepancy between DF for different estimates likely means that these are the results of a mixed model. There were probably a bit more than 25.69 participants in the study (leading to 25.69 DF fo | Is it normal to have thousands of df in a logistic regression model?
The discrepancy between DF for different estimates likely means that these are the results of a mixed model. There were probably a bit more than 25.69 participants in the study (leading to 25.69 DF for fluency), but these people probably had over 100 ... | Is it normal to have thousands of df in a logistic regression model?
The discrepancy between DF for different estimates likely means that these are the results of a mixed model. There were probably a bit more than 25.69 participants in the study (leading to 25.69 DF fo |
52,758 | Show that, for any real numbers a and b such that m ≤ a ≤ b or m ≥ a ≥ b, E|Y − a| ≤ E|Y − b| ,where Y be a random variable with finite expectation | Intuition
As explained at Expectation of a function of a random variable from CDF, an integration by parts shows that when a random variable $X$ has a (cumulative) distribution function $F,$ the expectation of $|X-a|$ is the sum of the shaded areas shown:
The left hand region is the area under $F$ to the left of $a$ w... | Show that, for any real numbers a and b such that m ≤ a ≤ b or m ≥ a ≥ b, E|Y − a| ≤ E|Y − b| ,where | Intuition
As explained at Expectation of a function of a random variable from CDF, an integration by parts shows that when a random variable $X$ has a (cumulative) distribution function $F,$ the expec | Show that, for any real numbers a and b such that m ≤ a ≤ b or m ≥ a ≥ b, E|Y − a| ≤ E|Y − b| ,where Y be a random variable with finite expectation
Intuition
As explained at Expectation of a function of a random variable from CDF, an integration by parts shows that when a random variable $X$ has a (cumulative) distribu... | Show that, for any real numbers a and b such that m ≤ a ≤ b or m ≥ a ≥ b, E|Y − a| ≤ E|Y − b| ,where
Intuition
As explained at Expectation of a function of a random variable from CDF, an integration by parts shows that when a random variable $X$ has a (cumulative) distribution function $F,$ the expec |
52,759 | Computing p-value vs. constructing confidence interval from sample for proportions | My confusion is, are these two methods really equivalent?
No the methods are indeed not equivalent.
Note that there are also many different ways to construct the confidence intervals (and different ways to express hypothesis tests). The use of the parameter estimate $\hat{p}$ in the expression $N(\hat{p}, \hat{p}(1-\h... | Computing p-value vs. constructing confidence interval from sample for proportions | My confusion is, are these two methods really equivalent?
No the methods are indeed not equivalent.
Note that there are also many different ways to construct the confidence intervals (and different w | Computing p-value vs. constructing confidence interval from sample for proportions
My confusion is, are these two methods really equivalent?
No the methods are indeed not equivalent.
Note that there are also many different ways to construct the confidence intervals (and different ways to express hypothesis tests). The... | Computing p-value vs. constructing confidence interval from sample for proportions
My confusion is, are these two methods really equivalent?
No the methods are indeed not equivalent.
Note that there are also many different ways to construct the confidence intervals (and different w |
52,760 | Computing p-value vs. constructing confidence interval from sample for proportions | A confidence interval based on normal approximation for the Bernoulli where $\hat p(1−\hat p)$ (by the way $\hat p=\bar X_n$) is plugged in for the variance estimator involves two approximations (one by the Central Limit Theorem, the other by variance estimation) and is therefore not equivalent to a test that does not ... | Computing p-value vs. constructing confidence interval from sample for proportions | A confidence interval based on normal approximation for the Bernoulli where $\hat p(1−\hat p)$ (by the way $\hat p=\bar X_n$) is plugged in for the variance estimator involves two approximations (one | Computing p-value vs. constructing confidence interval from sample for proportions
A confidence interval based on normal approximation for the Bernoulli where $\hat p(1−\hat p)$ (by the way $\hat p=\bar X_n$) is plugged in for the variance estimator involves two approximations (one by the Central Limit Theorem, the oth... | Computing p-value vs. constructing confidence interval from sample for proportions
A confidence interval based on normal approximation for the Bernoulli where $\hat p(1−\hat p)$ (by the way $\hat p=\bar X_n$) is plugged in for the variance estimator involves two approximations (one |
52,761 | Computing p-value vs. constructing confidence interval from sample for proportions | Suppose you have $n = 100$ independent observations $X_i$
from a Bernoulli distribution with Success probability $p.$
Then $$T_{100} = \sum_{i=1}^{100} X_i \sim\mathsf{Binom}(n=100,p).$$
Suppose you want to test $H_0: p = 0.5$ against $H_a: p \ne 0.5$
In particular, you might observe $T = 38$ Successes in $n = 100$ tri... | Computing p-value vs. constructing confidence interval from sample for proportions | Suppose you have $n = 100$ independent observations $X_i$
from a Bernoulli distribution with Success probability $p.$
Then $$T_{100} = \sum_{i=1}^{100} X_i \sim\mathsf{Binom}(n=100,p).$$
Suppose you w | Computing p-value vs. constructing confidence interval from sample for proportions
Suppose you have $n = 100$ independent observations $X_i$
from a Bernoulli distribution with Success probability $p.$
Then $$T_{100} = \sum_{i=1}^{100} X_i \sim\mathsf{Binom}(n=100,p).$$
Suppose you want to test $H_0: p = 0.5$ against $H... | Computing p-value vs. constructing confidence interval from sample for proportions
Suppose you have $n = 100$ independent observations $X_i$
from a Bernoulli distribution with Success probability $p.$
Then $$T_{100} = \sum_{i=1}^{100} X_i \sim\mathsf{Binom}(n=100,p).$$
Suppose you w |
52,762 | help with formula to calculate Bayesian ranking of M-star reviews | This is sloppy writing, and the author should be embarrassed :)
$N$ is the total number of ratings, and $S$ is the sum of "scores". Scores can be 1 or 0 (as in a binary voting system), or fractional (as in a star-rating system). I made a poor choice of variable names, and should have said:
An M-star rating system can ... | help with formula to calculate Bayesian ranking of M-star reviews | This is sloppy writing, and the author should be embarrassed :)
$N$ is the total number of ratings, and $S$ is the sum of "scores". Scores can be 1 or 0 (as in a binary voting system), or fractional ( | help with formula to calculate Bayesian ranking of M-star reviews
This is sloppy writing, and the author should be embarrassed :)
$N$ is the total number of ratings, and $S$ is the sum of "scores". Scores can be 1 or 0 (as in a binary voting system), or fractional (as in a star-rating system). I made a poor choice of v... | help with formula to calculate Bayesian ranking of M-star reviews
This is sloppy writing, and the author should be embarrassed :)
$N$ is the total number of ratings, and $S$ is the sum of "scores". Scores can be 1 or 0 (as in a binary voting system), or fractional ( |
52,763 | Ridge regression subtlety on intercept | I will give you an unrigorous but intuitive reason as to why the intercept is not penalized. When we estimate a penalized model, we usually scale and centre the predictors. This means that the intercept is estimated to be the mean of the outcome variable.
Note that the mean of the outcome variable is the simplest pre... | Ridge regression subtlety on intercept | I will give you an unrigorous but intuitive reason as to why the intercept is not penalized. When we estimate a penalized model, we usually scale and centre the predictors. This means that the inter | Ridge regression subtlety on intercept
I will give you an unrigorous but intuitive reason as to why the intercept is not penalized. When we estimate a penalized model, we usually scale and centre the predictors. This means that the intercept is estimated to be the mean of the outcome variable.
Note that the mean of t... | Ridge regression subtlety on intercept
I will give you an unrigorous but intuitive reason as to why the intercept is not penalized. When we estimate a penalized model, we usually scale and centre the predictors. This means that the inter |
52,764 | Log-linear and GLM (Poisson) regression | The term "log-linear" isn't uniquely defined. Even Wikipedia doesn't seem to come to internal agreement. Its entry on log-linear analysis has to do with modeling counts in contingency tables, while its log-linear model entry describes your approach to modeling. I try to avoid that terminology and just say what's being ... | Log-linear and GLM (Poisson) regression | The term "log-linear" isn't uniquely defined. Even Wikipedia doesn't seem to come to internal agreement. Its entry on log-linear analysis has to do with modeling counts in contingency tables, while it | Log-linear and GLM (Poisson) regression
The term "log-linear" isn't uniquely defined. Even Wikipedia doesn't seem to come to internal agreement. Its entry on log-linear analysis has to do with modeling counts in contingency tables, while its log-linear model entry describes your approach to modeling. I try to avoid tha... | Log-linear and GLM (Poisson) regression
The term "log-linear" isn't uniquely defined. Even Wikipedia doesn't seem to come to internal agreement. Its entry on log-linear analysis has to do with modeling counts in contingency tables, while it |
52,765 | Log-linear and GLM (Poisson) regression | Let $y$ be your outcome (accounting amount) and let $x_1, x_2, x_3$ be your three predictors (for one individual). Then your approach is modeling
$$\log y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_3 + \varepsilon$$
Taking the exponential of both sides gives
$$y = \exp \left( \beta_0 + \beta_1 x_1 + \beta_2 x_2 ... | Log-linear and GLM (Poisson) regression | Let $y$ be your outcome (accounting amount) and let $x_1, x_2, x_3$ be your three predictors (for one individual). Then your approach is modeling
$$\log y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta | Log-linear and GLM (Poisson) regression
Let $y$ be your outcome (accounting amount) and let $x_1, x_2, x_3$ be your three predictors (for one individual). Then your approach is modeling
$$\log y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_3 + \varepsilon$$
Taking the exponential of both sides gives
$$y = \exp \le... | Log-linear and GLM (Poisson) regression
Let $y$ be your outcome (accounting amount) and let $x_1, x_2, x_3$ be your three predictors (for one individual). Then your approach is modeling
$$\log y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta |
52,766 | When do I need something "fancier" than multiple regression? | For my money, if your goal is to understand the relationship between your predictors and the outcome, multiple regression is absolutely fine here, BUT you need to worry a bit about multiple comparisons.
You have lots of predictors. Even if none of your predictors are really related to the outcome, just by chance you wo... | When do I need something "fancier" than multiple regression? | For my money, if your goal is to understand the relationship between your predictors and the outcome, multiple regression is absolutely fine here, BUT you need to worry a bit about multiple comparison | When do I need something "fancier" than multiple regression?
For my money, if your goal is to understand the relationship between your predictors and the outcome, multiple regression is absolutely fine here, BUT you need to worry a bit about multiple comparisons.
You have lots of predictors. Even if none of your predic... | When do I need something "fancier" than multiple regression?
For my money, if your goal is to understand the relationship between your predictors and the outcome, multiple regression is absolutely fine here, BUT you need to worry a bit about multiple comparison |
52,767 | When do I need something "fancier" than multiple regression? | To @Eoin's point, the apparent variable importance is a very unstable quantity when the sample size is not in the millions. What exposes the difficulty of the task and provides actionable information is to use the bootstrap to get confidence intervals on importance ranks of all the predictors simultaneously. The more... | When do I need something "fancier" than multiple regression? | To @Eoin's point, the apparent variable importance is a very unstable quantity when the sample size is not in the millions. What exposes the difficulty of the task and provides actionable information | When do I need something "fancier" than multiple regression?
To @Eoin's point, the apparent variable importance is a very unstable quantity when the sample size is not in the millions. What exposes the difficulty of the task and provides actionable information is to use the bootstrap to get confidence intervals on imp... | When do I need something "fancier" than multiple regression?
To @Eoin's point, the apparent variable importance is a very unstable quantity when the sample size is not in the millions. What exposes the difficulty of the task and provides actionable information |
52,768 | When do I need something "fancier" than multiple regression? | It's always a balance trying to balance predictive ability and interpretation. You can try to use LASSO or other shrinkage methods if you would like to emphasize prediction a bit more than multiple regression.
This may improve predictive ability while preserving some level of interpretability. If you transformed your ... | When do I need something "fancier" than multiple regression? | It's always a balance trying to balance predictive ability and interpretation. You can try to use LASSO or other shrinkage methods if you would like to emphasize prediction a bit more than multiple re | When do I need something "fancier" than multiple regression?
It's always a balance trying to balance predictive ability and interpretation. You can try to use LASSO or other shrinkage methods if you would like to emphasize prediction a bit more than multiple regression.
This may improve predictive ability while preserv... | When do I need something "fancier" than multiple regression?
It's always a balance trying to balance predictive ability and interpretation. You can try to use LASSO or other shrinkage methods if you would like to emphasize prediction a bit more than multiple re |
52,769 | When do I need something "fancier" than multiple regression? | Something fancier than a univariable or multiple regression model is needed when there is a very clear, very complicated non-linear relationship between the endpoint and covariates that cannot be addressed using a routine link function or transformed covariate. If your paneled scatter plots show clouds of data points ... | When do I need something "fancier" than multiple regression? | Something fancier than a univariable or multiple regression model is needed when there is a very clear, very complicated non-linear relationship between the endpoint and covariates that cannot be addr | When do I need something "fancier" than multiple regression?
Something fancier than a univariable or multiple regression model is needed when there is a very clear, very complicated non-linear relationship between the endpoint and covariates that cannot be addressed using a routine link function or transformed covariat... | When do I need something "fancier" than multiple regression?
Something fancier than a univariable or multiple regression model is needed when there is a very clear, very complicated non-linear relationship between the endpoint and covariates that cannot be addr |
52,770 | Schoenfeld residuals - Plain English explanation, please! | What's plotted starts with a variance-weighted transformation of the Schoenfeld residuals for a covariate, into what are called "scaled Schoenfeld residuals." Those are then added to the corresponding time-invariant coefficient estimate from the Cox model under the proportional hazards (PH) assumption and smoothed. The... | Schoenfeld residuals - Plain English explanation, please! | What's plotted starts with a variance-weighted transformation of the Schoenfeld residuals for a covariate, into what are called "scaled Schoenfeld residuals." Those are then added to the corresponding | Schoenfeld residuals - Plain English explanation, please!
What's plotted starts with a variance-weighted transformation of the Schoenfeld residuals for a covariate, into what are called "scaled Schoenfeld residuals." Those are then added to the corresponding time-invariant coefficient estimate from the Cox model under ... | Schoenfeld residuals - Plain English explanation, please!
What's plotted starts with a variance-weighted transformation of the Schoenfeld residuals for a covariate, into what are called "scaled Schoenfeld residuals." Those are then added to the corresponding |
52,771 | What are relatively simple simulations that succeed with an irrational probability? | I think the details may be somewhat different
for each 'desired irrational constant', but
here is a strategy that may work for many such
constants.
Here is a simple algorithm that estimates $\pi/4,$ the area in the unit square beneath
the quarter unit-circle with center at the origin.
set.seed(2021)
x = runif(10^6); y ... | What are relatively simple simulations that succeed with an irrational probability? | I think the details may be somewhat different
for each 'desired irrational constant', but
here is a strategy that may work for many such
constants.
Here is a simple algorithm that estimates $\pi/4,$ t | What are relatively simple simulations that succeed with an irrational probability?
I think the details may be somewhat different
for each 'desired irrational constant', but
here is a strategy that may work for many such
constants.
Here is a simple algorithm that estimates $\pi/4,$ the area in the unit square beneath
t... | What are relatively simple simulations that succeed with an irrational probability?
I think the details may be somewhat different
for each 'desired irrational constant', but
here is a strategy that may work for many such
constants.
Here is a simple algorithm that estimates $\pi/4,$ t |
52,772 | What are relatively simple simulations that succeed with an irrational probability? | There is a universal algorithm. It doesn't matter whether the probability is irrational or not.
It suffices to implement a procedure to output either $0$ or $1$ that will (a) almost surely terminate and (b) output $1$ with a probability $\phi,$ where $\phi$ is any number in the interval $[0,1]$ (rational or irrational)... | What are relatively simple simulations that succeed with an irrational probability? | There is a universal algorithm. It doesn't matter whether the probability is irrational or not.
It suffices to implement a procedure to output either $0$ or $1$ that will (a) almost surely terminate a | What are relatively simple simulations that succeed with an irrational probability?
There is a universal algorithm. It doesn't matter whether the probability is irrational or not.
It suffices to implement a procedure to output either $0$ or $1$ that will (a) almost surely terminate and (b) output $1$ with a probability... | What are relatively simple simulations that succeed with an irrational probability?
There is a universal algorithm. It doesn't matter whether the probability is irrational or not.
It suffices to implement a procedure to output either $0$ or $1$ that will (a) almost surely terminate a |
52,773 | What can cause exploding statistic values and p-values near zero with the Wilcoxon-Mann-Whitney test? | Nothing out of the ordinary is going on from the sound of it.
In almost all cases, I get huge values for the statistic
Have you looked at the range of possible values for the statistic?
For the usual form of the U-statistic, it can take values between $0$ and $mn$ where $m$ and $n$ are the two sample sizes.
If you d... | What can cause exploding statistic values and p-values near zero with the Wilcoxon-Mann-Whitney test | Nothing out of the ordinary is going on from the sound of it.
In almost all cases, I get huge values for the statistic
Have you looked at the range of possible values for the statistic?
For the usu | What can cause exploding statistic values and p-values near zero with the Wilcoxon-Mann-Whitney test?
Nothing out of the ordinary is going on from the sound of it.
In almost all cases, I get huge values for the statistic
Have you looked at the range of possible values for the statistic?
For the usual form of the U-s... | What can cause exploding statistic values and p-values near zero with the Wilcoxon-Mann-Whitney test
Nothing out of the ordinary is going on from the sound of it.
In almost all cases, I get huge values for the statistic
Have you looked at the range of possible values for the statistic?
For the usu |
52,774 | How to interpret negative values for -2LL, AIC, and BIC? | The bottom line is that (as Jeremy Miles says) the value of the negative log-likelihood doesn't really matter, only differences between the negative log-likelihoods. But you might still wonder why you are getting negative values.
Reproducing an answer of mine from here:
Technically, a probability cannot be >1, so a log... | How to interpret negative values for -2LL, AIC, and BIC? | The bottom line is that (as Jeremy Miles says) the value of the negative log-likelihood doesn't really matter, only differences between the negative log-likelihoods. But you might still wonder why you | How to interpret negative values for -2LL, AIC, and BIC?
The bottom line is that (as Jeremy Miles says) the value of the negative log-likelihood doesn't really matter, only differences between the negative log-likelihoods. But you might still wonder why you are getting negative values.
Reproducing an answer of mine fro... | How to interpret negative values for -2LL, AIC, and BIC?
The bottom line is that (as Jeremy Miles says) the value of the negative log-likelihood doesn't really matter, only differences between the negative log-likelihoods. But you might still wonder why you |
52,775 | How to interpret negative values for -2LL, AIC, and BIC? | Yes.
-2 LL means -2 multiplied by the log likelihood.
AIC, BIC etc are (as far as I know) only interpreted in relation to other values from different models. An AIC of -100 doesn't mean anything on its own. It means something when a different model, using the same data, has an AIC of -90, so the difference is 10. The d... | How to interpret negative values for -2LL, AIC, and BIC? | Yes.
-2 LL means -2 multiplied by the log likelihood.
AIC, BIC etc are (as far as I know) only interpreted in relation to other values from different models. An AIC of -100 doesn't mean anything on it | How to interpret negative values for -2LL, AIC, and BIC?
Yes.
-2 LL means -2 multiplied by the log likelihood.
AIC, BIC etc are (as far as I know) only interpreted in relation to other values from different models. An AIC of -100 doesn't mean anything on its own. It means something when a different model, using the sam... | How to interpret negative values for -2LL, AIC, and BIC?
Yes.
-2 LL means -2 multiplied by the log likelihood.
AIC, BIC etc are (as far as I know) only interpreted in relation to other values from different models. An AIC of -100 doesn't mean anything on it |
52,776 | What are some examples when the Average Treatment Effect on the Treated/Control (ATT,ATC) is more sought after than the ATE? | I'm writing a paper about this very topic, so I'll just summarize here and update with a link to the paper when it's ready. (Edit: Here is the arxiv version.) In short, the ATE, ATT, and ATC can be described as follows:
The ATE is the average effect of mandating a policy of treatment for everyone vs. mandating a polic... | What are some examples when the Average Treatment Effect on the Treated/Control (ATT,ATC) is more so | I'm writing a paper about this very topic, so I'll just summarize here and update with a link to the paper when it's ready. (Edit: Here is the arxiv version.) In short, the ATE, ATT, and ATC can be de | What are some examples when the Average Treatment Effect on the Treated/Control (ATT,ATC) is more sought after than the ATE?
I'm writing a paper about this very topic, so I'll just summarize here and update with a link to the paper when it's ready. (Edit: Here is the arxiv version.) In short, the ATE, ATT, and ATC can ... | What are some examples when the Average Treatment Effect on the Treated/Control (ATT,ATC) is more so
I'm writing a paper about this very topic, so I'll just summarize here and update with a link to the paper when it's ready. (Edit: Here is the arxiv version.) In short, the ATE, ATT, and ATC can be de |
52,777 | Why use RBF kernel if less is needed? | One way of looking at it is to say that the RBF kernel dynamically scales the feature space with the number of points. As we know from geometry, for $p$ points you can always draw an at most $(p-1)$-dimensional hyperplane through them. That's the inherent dimensionality of the space implied by the RBF kernel. But, as y... | Why use RBF kernel if less is needed? | One way of looking at it is to say that the RBF kernel dynamically scales the feature space with the number of points. As we know from geometry, for $p$ points you can always draw an at most $(p-1)$-d | Why use RBF kernel if less is needed?
One way of looking at it is to say that the RBF kernel dynamically scales the feature space with the number of points. As we know from geometry, for $p$ points you can always draw an at most $(p-1)$-dimensional hyperplane through them. That's the inherent dimensionality of the spac... | Why use RBF kernel if less is needed?
One way of looking at it is to say that the RBF kernel dynamically scales the feature space with the number of points. As we know from geometry, for $p$ points you can always draw an at most $(p-1)$-d |
52,778 | Why use RBF kernel if less is needed? | While the points are notionally mapped into an infinite-dimensional space, they will necessarily lie within an at-most $p$-dimensional sub-space (as there are only $p$ points). Note that the (notionally infinite-dimensional) primal weight vector is a linear combination of the images of the support vectors in the featu... | Why use RBF kernel if less is needed? | While the points are notionally mapped into an infinite-dimensional space, they will necessarily lie within an at-most $p$-dimensional sub-space (as there are only $p$ points). Note that the (notiona | Why use RBF kernel if less is needed?
While the points are notionally mapped into an infinite-dimensional space, they will necessarily lie within an at-most $p$-dimensional sub-space (as there are only $p$ points). Note that the (notionally infinite-dimensional) primal weight vector is a linear combination of the imag... | Why use RBF kernel if less is needed?
While the points are notionally mapped into an infinite-dimensional space, they will necessarily lie within an at-most $p$-dimensional sub-space (as there are only $p$ points). Note that the (notiona |
52,779 | understanding uniformly distributed success probability | This is a straightforward application of a standard introductory Bayesian example, namely that a beta prior is conjugate for a Bernoulli sampling distribution. Any introductory Bayesian statistics textbook will explain this in detail.
In brief, the idea is that if your prior distribution on a parameter is $\theta\sim B... | understanding uniformly distributed success probability | This is a straightforward application of a standard introductory Bayesian example, namely that a beta prior is conjugate for a Bernoulli sampling distribution. Any introductory Bayesian statistics tex | understanding uniformly distributed success probability
This is a straightforward application of a standard introductory Bayesian example, namely that a beta prior is conjugate for a Bernoulli sampling distribution. Any introductory Bayesian statistics textbook will explain this in detail.
In brief, the idea is that if... | understanding uniformly distributed success probability
This is a straightforward application of a standard introductory Bayesian example, namely that a beta prior is conjugate for a Bernoulli sampling distribution. Any introductory Bayesian statistics tex |
52,780 | Incorrect implementation of a t-test | You missed the pairing. Your observations aren’t independent, since they come from the same subjects, just at different times. Taking paired differences and testing those differences is the correct approach. There is greater power (ability to reject a false null) when you do the pairing. | Incorrect implementation of a t-test | You missed the pairing. Your observations aren’t independent, since they come from the same subjects, just at different times. Taking paired differences and testing those differences is the correct ap | Incorrect implementation of a t-test
You missed the pairing. Your observations aren’t independent, since they come from the same subjects, just at different times. Taking paired differences and testing those differences is the correct approach. There is greater power (ability to reject a false null) when you do the pai... | Incorrect implementation of a t-test
You missed the pairing. Your observations aren’t independent, since they come from the same subjects, just at different times. Taking paired differences and testing those differences is the correct ap |
52,781 | Is there any hypothesis test for two binomial distribution without normal approximation? | You can just use a Fisher Exact Test. Let us know if you have trouble following what it does.
Not super related, but if you're thinking of difference of binomials, it's nice to convince yourself that if $p_1 \neq p_2$, then the difference is not itself a binomial! I think that's kinda fun to think about. | Is there any hypothesis test for two binomial distribution without normal approximation? | You can just use a Fisher Exact Test. Let us know if you have trouble following what it does.
Not super related, but if you're thinking of difference of binomials, it's nice to convince yourself that | Is there any hypothesis test for two binomial distribution without normal approximation?
You can just use a Fisher Exact Test. Let us know if you have trouble following what it does.
Not super related, but if you're thinking of difference of binomials, it's nice to convince yourself that if $p_1 \neq p_2$, then the dif... | Is there any hypothesis test for two binomial distribution without normal approximation?
You can just use a Fisher Exact Test. Let us know if you have trouble following what it does.
Not super related, but if you're thinking of difference of binomials, it's nice to convince yourself that |
52,782 | Is there any hypothesis test for two binomial distribution without normal approximation? | So my question is, is there any statistical test available for given two binomial distributions $A \sim \mathrm{Bin}(n, p_a)$ and $B \sim \mathrm{Bin}(m, p_b)$ where $n$ and $m$ are the sample size of A and B to test if $p_a$ and $p_b$ are different without approximation to normal/Poisson distribution?
One way to do t... | Is there any hypothesis test for two binomial distribution without normal approximation? | So my question is, is there any statistical test available for given two binomial distributions $A \sim \mathrm{Bin}(n, p_a)$ and $B \sim \mathrm{Bin}(m, p_b)$ where $n$ and $m$ are the sample size of | Is there any hypothesis test for two binomial distribution without normal approximation?
So my question is, is there any statistical test available for given two binomial distributions $A \sim \mathrm{Bin}(n, p_a)$ and $B \sim \mathrm{Bin}(m, p_b)$ where $n$ and $m$ are the sample size of A and B to test if $p_a$ and $... | Is there any hypothesis test for two binomial distribution without normal approximation?
So my question is, is there any statistical test available for given two binomial distributions $A \sim \mathrm{Bin}(n, p_a)$ and $B \sim \mathrm{Bin}(m, p_b)$ where $n$ and $m$ are the sample size of |
52,783 | Proof that the mean of predicted values in OLS regression is equal to the mean of original values? [duplicate] | That is, for the set of predicted values $\{\hat{Y}_1, \hat{Y}_2, ...\}$ and the set of original values $\{Y_1, Y_2, ...\}$, the means of the sets are always equal.
The difference between the predicted values and the original values are the residuals
$$\hat{Y}_i = Y_i + r_i$$
So you can write
$$\begin{array}{}
\frac{... | Proof that the mean of predicted values in OLS regression is equal to the mean of original values? [ | That is, for the set of predicted values $\{\hat{Y}_1, \hat{Y}_2, ...\}$ and the set of original values $\{Y_1, Y_2, ...\}$, the means of the sets are always equal.
The difference between the predict | Proof that the mean of predicted values in OLS regression is equal to the mean of original values? [duplicate]
That is, for the set of predicted values $\{\hat{Y}_1, \hat{Y}_2, ...\}$ and the set of original values $\{Y_1, Y_2, ...\}$, the means of the sets are always equal.
The difference between the predicted values... | Proof that the mean of predicted values in OLS regression is equal to the mean of original values? [
That is, for the set of predicted values $\{\hat{Y}_1, \hat{Y}_2, ...\}$ and the set of original values $\{Y_1, Y_2, ...\}$, the means of the sets are always equal.
The difference between the predict |
52,784 | Proof that the mean of predicted values in OLS regression is equal to the mean of original values? [duplicate] | In matrix notation, the fitted values can be written as $\hat y=Py$, with the projection matrix $P=X(X'X)^{-1}X'$, wich can be verified by plugging in the definition of the OLS estimator into the formula for the fitted values, $\hat y =X\hat\beta$.
Their mean is, with $\iota$ a vector of ones,
$$
\iota'Py/n,
$$
as the ... | Proof that the mean of predicted values in OLS regression is equal to the mean of original values? [ | In matrix notation, the fitted values can be written as $\hat y=Py$, with the projection matrix $P=X(X'X)^{-1}X'$, wich can be verified by plugging in the definition of the OLS estimator into the form | Proof that the mean of predicted values in OLS regression is equal to the mean of original values? [duplicate]
In matrix notation, the fitted values can be written as $\hat y=Py$, with the projection matrix $P=X(X'X)^{-1}X'$, wich can be verified by plugging in the definition of the OLS estimator into the formula for t... | Proof that the mean of predicted values in OLS regression is equal to the mean of original values? [
In matrix notation, the fitted values can be written as $\hat y=Py$, with the projection matrix $P=X(X'X)^{-1}X'$, wich can be verified by plugging in the definition of the OLS estimator into the form |
52,785 | Proof that the mean of predicted values in OLS regression is equal to the mean of original values? [duplicate] | It's intuitively clear. If you have the correct model as the linear regression, the residuals should be distributed with mean zero. If you take the average on the residuals, you are left only with the predicted values.
For example, if your model is
$y = c + ax + \epsilon$,
where
$c$ is constant vector,
$a$ is coef... | Proof that the mean of predicted values in OLS regression is equal to the mean of original values? [ | It's intuitively clear. If you have the correct model as the linear regression, the residuals should be distributed with mean zero. If you take the average on the residuals, you are left only with the | Proof that the mean of predicted values in OLS regression is equal to the mean of original values? [duplicate]
It's intuitively clear. If you have the correct model as the linear regression, the residuals should be distributed with mean zero. If you take the average on the residuals, you are left only with the predicte... | Proof that the mean of predicted values in OLS regression is equal to the mean of original values? [
It's intuitively clear. If you have the correct model as the linear regression, the residuals should be distributed with mean zero. If you take the average on the residuals, you are left only with the |
52,786 | What are the differences between tests for overidentification in 2SLS | There are a lot of questions here, so I'll first give an overview, and then explain a bit more. You have 4 tests you're asking about: Hausman test, Sargan test, a Wald test of exogeneity, and a Hansen J Test. To fix some notation, let $Z$ be a vector of instruments, and consider $Y = \beta_1 X_1 + \beta_2 X_2 + e$, whe... | What are the differences between tests for overidentification in 2SLS | There are a lot of questions here, so I'll first give an overview, and then explain a bit more. You have 4 tests you're asking about: Hausman test, Sargan test, a Wald test of exogeneity, and a Hansen | What are the differences between tests for overidentification in 2SLS
There are a lot of questions here, so I'll first give an overview, and then explain a bit more. You have 4 tests you're asking about: Hausman test, Sargan test, a Wald test of exogeneity, and a Hansen J Test. To fix some notation, let $Z$ be a vector... | What are the differences between tests for overidentification in 2SLS
There are a lot of questions here, so I'll first give an overview, and then explain a bit more. You have 4 tests you're asking about: Hausman test, Sargan test, a Wald test of exogeneity, and a Hansen |
52,787 | How to do “broken stick linear regression” in R? | Here is how to do this for one cultivar:
plot(shoot ~ P, data = subset(DF, cultivar == "Dinninup"))
fit1 <- nls(shoot ~ ifelse(P < bp, m * P + c, m * bp + c),
data = subset(DF, cultivar == "Dinninup"),
start = list(c = 1, m = 0.05, bp = 25), na.action = na.omit)
summary(fit1)
#Formula: shoot ... | How to do “broken stick linear regression” in R? | Here is how to do this for one cultivar:
plot(shoot ~ P, data = subset(DF, cultivar == "Dinninup"))
fit1 <- nls(shoot ~ ifelse(P < bp, m * P + c, m * bp + c),
data = subset(DF, cultivar | How to do “broken stick linear regression” in R?
Here is how to do this for one cultivar:
plot(shoot ~ P, data = subset(DF, cultivar == "Dinninup"))
fit1 <- nls(shoot ~ ifelse(P < bp, m * P + c, m * bp + c),
data = subset(DF, cultivar == "Dinninup"),
start = list(c = 1, m = 0.05, bp = 25), na... | How to do “broken stick linear regression” in R?
Here is how to do this for one cultivar:
plot(shoot ~ P, data = subset(DF, cultivar == "Dinninup"))
fit1 <- nls(shoot ~ ifelse(P < bp, m * P + c, m * bp + c),
data = subset(DF, cultivar |
52,788 | How to do “broken stick linear regression” in R? | The package mcp was made just for scenarios like this. See below how I structured your data as df later.
Fit a change point model
First, let's define a slope followed by a joined plateau. We add varying (random) change point locations (the left-hand side of the equation):
model = list(
shoot ~ 1 + P, # intercept and... | How to do “broken stick linear regression” in R? | The package mcp was made just for scenarios like this. See below how I structured your data as df later.
Fit a change point model
First, let's define a slope followed by a joined plateau. We add varyi | How to do “broken stick linear regression” in R?
The package mcp was made just for scenarios like this. See below how I structured your data as df later.
Fit a change point model
First, let's define a slope followed by a joined plateau. We add varying (random) change point locations (the left-hand side of the equation)... | How to do “broken stick linear regression” in R?
The package mcp was made just for scenarios like this. See below how I structured your data as df later.
Fit a change point model
First, let's define a slope followed by a joined plateau. We add varyi |
52,789 | The best way of presenting the correlation / normality results of big data | This is a somewhat subjective question, but in general presenting a reader with cross correlations between 82 different factors is not particularly helpful, no matter how it is presented. The idea of exploratory analysis is to disseminate something useful to the reader without them having to necessarily go through all ... | The best way of presenting the correlation / normality results of big data | This is a somewhat subjective question, but in general presenting a reader with cross correlations between 82 different factors is not particularly helpful, no matter how it is presented. The idea of | The best way of presenting the correlation / normality results of big data
This is a somewhat subjective question, but in general presenting a reader with cross correlations between 82 different factors is not particularly helpful, no matter how it is presented. The idea of exploratory analysis is to disseminate someth... | The best way of presenting the correlation / normality results of big data
This is a somewhat subjective question, but in general presenting a reader with cross correlations between 82 different factors is not particularly helpful, no matter how it is presented. The idea of |
52,790 | The best way of presenting the correlation / normality results of big data | I will throw my 2 cents as I had to battle with exactly the same problem for presenting results for a 77x77 variables correlation matrix.
I tried just about anything you can think of in terms of conveniently visualizing a 77x77 matrix by using R, SPSS and Excel. From my experience, there is simply no magical pill/grap... | The best way of presenting the correlation / normality results of big data | I will throw my 2 cents as I had to battle with exactly the same problem for presenting results for a 77x77 variables correlation matrix.
I tried just about anything you can think of in terms of conv | The best way of presenting the correlation / normality results of big data
I will throw my 2 cents as I had to battle with exactly the same problem for presenting results for a 77x77 variables correlation matrix.
I tried just about anything you can think of in terms of conveniently visualizing a 77x77 matrix by using ... | The best way of presenting the correlation / normality results of big data
I will throw my 2 cents as I had to battle with exactly the same problem for presenting results for a 77x77 variables correlation matrix.
I tried just about anything you can think of in terms of conv |
52,791 | The best way of presenting the correlation / normality results of big data | Here is what I did once to report correlations results: prepare n-1 separate plots. On the x-axis of each plot, there were feature indexes from i+1 to n. On the y-axis of each plot, there were correlation results. I represented the plots in a grid. Sure, there were a lot of plots but they we much more readable. (you c... | The best way of presenting the correlation / normality results of big data | Here is what I did once to report correlations results: prepare n-1 separate plots. On the x-axis of each plot, there were feature indexes from i+1 to n. On the y-axis of each plot, there were correl | The best way of presenting the correlation / normality results of big data
Here is what I did once to report correlations results: prepare n-1 separate plots. On the x-axis of each plot, there were feature indexes from i+1 to n. On the y-axis of each plot, there were correlation results. I represented the plots in a g... | The best way of presenting the correlation / normality results of big data
Here is what I did once to report correlations results: prepare n-1 separate plots. On the x-axis of each plot, there were feature indexes from i+1 to n. On the y-axis of each plot, there were correl |
52,792 | The best way of presenting the correlation / normality results of big data | Not sure whether the following approach really will provide insight into the structure of the datasets looked at, but you could try to calculate a variance inflation factor for every column, based on the rest of the table as predictors in a linear regression model, and report the maximum VIF per data set (assuming rows... | The best way of presenting the correlation / normality results of big data | Not sure whether the following approach really will provide insight into the structure of the datasets looked at, but you could try to calculate a variance inflation factor for every column, based on | The best way of presenting the correlation / normality results of big data
Not sure whether the following approach really will provide insight into the structure of the datasets looked at, but you could try to calculate a variance inflation factor for every column, based on the rest of the table as predictors in a line... | The best way of presenting the correlation / normality results of big data
Not sure whether the following approach really will provide insight into the structure of the datasets looked at, but you could try to calculate a variance inflation factor for every column, based on |
52,793 | Why use both $\sin$ and $\cos$ functions in Transformer positional encoding? | The authors write
We chose this function because we hypothesized it would allow the
model to easily learn to attend by relative positions, since for any
fixed offset k, $PE_{pos+k}$ can be represented as a linear function of $PE_{pos}$.
Indeed, $\sin(x+k) = u\sin(x) + v \cos(x)$ for some constants $u, v$, and lik... | Why use both $\sin$ and $\cos$ functions in Transformer positional encoding? | The authors write
We chose this function because we hypothesized it would allow the
model to easily learn to attend by relative positions, since for any
fixed offset k, $PE_{pos+k}$ can be repres | Why use both $\sin$ and $\cos$ functions in Transformer positional encoding?
The authors write
We chose this function because we hypothesized it would allow the
model to easily learn to attend by relative positions, since for any
fixed offset k, $PE_{pos+k}$ can be represented as a linear function of $PE_{pos}$.
... | Why use both $\sin$ and $\cos$ functions in Transformer positional encoding?
The authors write
We chose this function because we hypothesized it would allow the
model to easily learn to attend by relative positions, since for any
fixed offset k, $PE_{pos+k}$ can be repres |
52,794 | LMER model with uneven time points | Short answer: this should be no problem. I'm pretty sure you'll have somewhat lower power than if you had a perfectly balanced design, but there is no fundamental difficulty.
Here's an example where I subsample the (complete/balanced) sleepstudy data set and show that it works fine (and the results don't change very mu... | LMER model with uneven time points | Short answer: this should be no problem. I'm pretty sure you'll have somewhat lower power than if you had a perfectly balanced design, but there is no fundamental difficulty.
Here's an example where I | LMER model with uneven time points
Short answer: this should be no problem. I'm pretty sure you'll have somewhat lower power than if you had a perfectly balanced design, but there is no fundamental difficulty.
Here's an example where I subsample the (complete/balanced) sleepstudy data set and show that it works fine (a... | LMER model with uneven time points
Short answer: this should be no problem. I'm pretty sure you'll have somewhat lower power than if you had a perfectly balanced design, but there is no fundamental difficulty.
Here's an example where I |
52,795 | LMER model with uneven time points | I was intrigued by the comment of @BenBolker that the power will be lower in an unbalanced design compared to a perfectly balanced one. The following simulation study seems to suggest that the power is the same:
simulate_mixed <- function (design = c("balanced", "unbalanced")) {
design <- match.arg(design)
n <-... | LMER model with uneven time points | I was intrigued by the comment of @BenBolker that the power will be lower in an unbalanced design compared to a perfectly balanced one. The following simulation study seems to suggest that the power i | LMER model with uneven time points
I was intrigued by the comment of @BenBolker that the power will be lower in an unbalanced design compared to a perfectly balanced one. The following simulation study seems to suggest that the power is the same:
simulate_mixed <- function (design = c("balanced", "unbalanced")) {
d... | LMER model with uneven time points
I was intrigued by the comment of @BenBolker that the power will be lower in an unbalanced design compared to a perfectly balanced one. The following simulation study seems to suggest that the power i |
52,796 | In a multilevel linear regression, how does the reference level affect other levels/factors and which reference level ought to be selected? | Terminology
The model you fitted with the lm() function in R is actually a linear regression model, not a multilevel linear regression model. In statistics, we reserve the multilevel terminology for situations where the data exhibit a natural form of nesting (e.g., students nested in schools).
Factors in R
The Smoke... | In a multilevel linear regression, how does the reference level affect other levels/factors and whic | Terminology
The model you fitted with the lm() function in R is actually a linear regression model, not a multilevel linear regression model. In statistics, we reserve the multilevel terminology for | In a multilevel linear regression, how does the reference level affect other levels/factors and which reference level ought to be selected?
Terminology
The model you fitted with the lm() function in R is actually a linear regression model, not a multilevel linear regression model. In statistics, we reserve the multile... | In a multilevel linear regression, how does the reference level affect other levels/factors and whic
Terminology
The model you fitted with the lm() function in R is actually a linear regression model, not a multilevel linear regression model. In statistics, we reserve the multilevel terminology for |
52,797 | Why isn't standard deviation $\frac{1}{n}\sqrt{\sum^n_{i=1}(x_i - \mu)^2}$? | You are missing the point that the definition of the standard deviation is the square root of the variance $V$ which is defined as
$$V = \frac 1n \sum_{i=1}^n (x_i-\mu)^2.$$
So why is $V$ defined the way it is? Well, a standard model is that the $x_i$ are a random sample from a distribution with known mean $\mu$ and un... | Why isn't standard deviation $\frac{1}{n}\sqrt{\sum^n_{i=1}(x_i - \mu)^2}$? | You are missing the point that the definition of the standard deviation is the square root of the variance $V$ which is defined as
$$V = \frac 1n \sum_{i=1}^n (x_i-\mu)^2.$$
So why is $V$ defined the | Why isn't standard deviation $\frac{1}{n}\sqrt{\sum^n_{i=1}(x_i - \mu)^2}$?
You are missing the point that the definition of the standard deviation is the square root of the variance $V$ which is defined as
$$V = \frac 1n \sum_{i=1}^n (x_i-\mu)^2.$$
So why is $V$ defined the way it is? Well, a standard model is that th... | Why isn't standard deviation $\frac{1}{n}\sqrt{\sum^n_{i=1}(x_i - \mu)^2}$?
You are missing the point that the definition of the standard deviation is the square root of the variance $V$ which is defined as
$$V = \frac 1n \sum_{i=1}^n (x_i-\mu)^2.$$
So why is $V$ defined the |
52,798 | Why isn't standard deviation $\frac{1}{n}\sqrt{\sum^n_{i=1}(x_i - \mu)^2}$? | An example might illustrate the point
Suppose we have a population where the relative frequency of being
value $20$ is $0.1$
value $25$ is $0.6$
value $30$ is $0.3$
I can tell you that the mean is $\mu = \sum_j x_j p_j =26$, the variance is $\sigma^2=\sum_j (x_j-\mu)^2 p_j =9$ and the standard deviation is $\sigma=3... | Why isn't standard deviation $\frac{1}{n}\sqrt{\sum^n_{i=1}(x_i - \mu)^2}$? | An example might illustrate the point
Suppose we have a population where the relative frequency of being
value $20$ is $0.1$
value $25$ is $0.6$
value $30$ is $0.3$
I can tell you that the mean is | Why isn't standard deviation $\frac{1}{n}\sqrt{\sum^n_{i=1}(x_i - \mu)^2}$?
An example might illustrate the point
Suppose we have a population where the relative frequency of being
value $20$ is $0.1$
value $25$ is $0.6$
value $30$ is $0.3$
I can tell you that the mean is $\mu = \sum_j x_j p_j =26$, the variance is ... | Why isn't standard deviation $\frac{1}{n}\sqrt{\sum^n_{i=1}(x_i - \mu)^2}$?
An example might illustrate the point
Suppose we have a population where the relative frequency of being
value $20$ is $0.1$
value $25$ is $0.6$
value $30$ is $0.3$
I can tell you that the mean is |
52,799 | Should I cross-validate metrics that were not optimised? | It is a good idea to bootstrap or cross-validate (e.g., 100 repeats of 10-fold cross-validation) indexes that were not optimized. For example, I recommend optimizing on a gold standard such as log-likelihood, penalized log-likelihood, or in a Bayesian model log-likelihood + log-prior. You can report measures such as ... | Should I cross-validate metrics that were not optimised? | It is a good idea to bootstrap or cross-validate (e.g., 100 repeats of 10-fold cross-validation) indexes that were not optimized. For example, I recommend optimizing on a gold standard such as log-li | Should I cross-validate metrics that were not optimised?
It is a good idea to bootstrap or cross-validate (e.g., 100 repeats of 10-fold cross-validation) indexes that were not optimized. For example, I recommend optimizing on a gold standard such as log-likelihood, penalized log-likelihood, or in a Bayesian model log-... | Should I cross-validate metrics that were not optimised?
It is a good idea to bootstrap or cross-validate (e.g., 100 repeats of 10-fold cross-validation) indexes that were not optimized. For example, I recommend optimizing on a gold standard such as log-li |
52,800 | Should I cross-validate metrics that were not optimised? | You will anyways need a validation (verification) of the performance of the optimized model. Regardless of the testing scheme you employ for this (resampling/[outer] cross validation/[outer] out-of-bootstrap, single train/test split, validation study), this is where you evaluate the performance for all parameters of in... | Should I cross-validate metrics that were not optimised? | You will anyways need a validation (verification) of the performance of the optimized model. Regardless of the testing scheme you employ for this (resampling/[outer] cross validation/[outer] out-of-bo | Should I cross-validate metrics that were not optimised?
You will anyways need a validation (verification) of the performance of the optimized model. Regardless of the testing scheme you employ for this (resampling/[outer] cross validation/[outer] out-of-bootstrap, single train/test split, validation study), this is wh... | Should I cross-validate metrics that were not optimised?
You will anyways need a validation (verification) of the performance of the optimized model. Regardless of the testing scheme you employ for this (resampling/[outer] cross validation/[outer] out-of-bo |
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