idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
|---|---|---|---|---|---|---|
35,701 | A statistical interaction is significant, but the author denies it. Why? | I don't have the required reputation to vote, so I'll add it as an answer instead.
I fully agree with what @whuber said. The typical approach in this kind of study is to a priori declare a level of significance. Quoted from the article, the authors indeed do this,
To accommodate the many comparisons made, two-tailed P... | A statistical interaction is significant, but the author denies it. Why? | I don't have the required reputation to vote, so I'll add it as an answer instead.
I fully agree with what @whuber said. The typical approach in this kind of study is to a priori declare a level of si | A statistical interaction is significant, but the author denies it. Why?
I don't have the required reputation to vote, so I'll add it as an answer instead.
I fully agree with what @whuber said. The typical approach in this kind of study is to a priori declare a level of significance. Quoted from the article, the author... | A statistical interaction is significant, but the author denies it. Why?
I don't have the required reputation to vote, so I'll add it as an answer instead.
I fully agree with what @whuber said. The typical approach in this kind of study is to a priori declare a level of si |
35,702 | The concept of efficiency | Efficiency is a "per se" concept in the sense that it is a measure of how variable (and biased) the estimator is from the "true" parameter. There is an actual numeric value for efficiency associated with a given estimator at a given sample-size for a given loss function. This actual number is related to the estimator... | The concept of efficiency | Efficiency is a "per se" concept in the sense that it is a measure of how variable (and biased) the estimator is from the "true" parameter. There is an actual numeric value for efficiency associated | The concept of efficiency
Efficiency is a "per se" concept in the sense that it is a measure of how variable (and biased) the estimator is from the "true" parameter. There is an actual numeric value for efficiency associated with a given estimator at a given sample-size for a given loss function. This actual number i... | The concept of efficiency
Efficiency is a "per se" concept in the sense that it is a measure of how variable (and biased) the estimator is from the "true" parameter. There is an actual numeric value for efficiency associated |
35,703 | The concept of efficiency | I wonder at the global relevance of a concept of efficiency outside [and even inside] the restricted case of unbiased estimators. The general (frequentist) version is that the variance of an estimator $δ$ of [any transform of] $θ$ with bias b(θ) is
$$
I(θ)⁻¹ (1+b'(θ))²
$$
while a Bayesian version is the van Trees inequ... | The concept of efficiency | I wonder at the global relevance of a concept of efficiency outside [and even inside] the restricted case of unbiased estimators. The general (frequentist) version is that the variance of an estimator | The concept of efficiency
I wonder at the global relevance of a concept of efficiency outside [and even inside] the restricted case of unbiased estimators. The general (frequentist) version is that the variance of an estimator $δ$ of [any transform of] $θ$ with bias b(θ) is
$$
I(θ)⁻¹ (1+b'(θ))²
$$
while a Bayesian vers... | The concept of efficiency
I wonder at the global relevance of a concept of efficiency outside [and even inside] the restricted case of unbiased estimators. The general (frequentist) version is that the variance of an estimator |
35,704 | The concept of efficiency | Yes an efficient estimator is one that attains the CRB, thus only unbiased estimators are considered. It's not a characterization it's a definition. | The concept of efficiency | Yes an efficient estimator is one that attains the CRB, thus only unbiased estimators are considered. It's not a characterization it's a definition. | The concept of efficiency
Yes an efficient estimator is one that attains the CRB, thus only unbiased estimators are considered. It's not a characterization it's a definition. | The concept of efficiency
Yes an efficient estimator is one that attains the CRB, thus only unbiased estimators are considered. It's not a characterization it's a definition. |
35,705 | Where is the explanatory effect of common variance among covariates accounted for in regression procedures? | Even though you say that the geometry of this is fairly clear to you, I think it is a good idea to review it. I made this back of an envelope sketch:
Left subplot is the same figure as in the book: consider two predictors $x_1$ and $x_2$; as vectors, $\mathbf x_1$ and $\mathbf x_2$ span a plane in the $n$-dimensional ... | Where is the explanatory effect of common variance among covariates accounted for in regression proc | Even though you say that the geometry of this is fairly clear to you, I think it is a good idea to review it. I made this back of an envelope sketch:
Left subplot is the same figure as in the book: c | Where is the explanatory effect of common variance among covariates accounted for in regression procedures?
Even though you say that the geometry of this is fairly clear to you, I think it is a good idea to review it. I made this back of an envelope sketch:
Left subplot is the same figure as in the book: consider two ... | Where is the explanatory effect of common variance among covariates accounted for in regression proc
Even though you say that the geometry of this is fairly clear to you, I think it is a good idea to review it. I made this back of an envelope sketch:
Left subplot is the same figure as in the book: c |
35,706 | Where is the explanatory effect of common variance among covariates accounted for in regression procedures? | The GS procedure would start with $X_1$ and then move to orthogonalizing $X_2$. Since $X_1$ and $X_2$ share $X$ the result would practically be zero in your example. But the common element $X$ remains, because we started with $X_1$, and $X_1$ still has $X$.
Since $X_1$ and $X_2$ share common $X$, we would get that the... | Where is the explanatory effect of common variance among covariates accounted for in regression proc | The GS procedure would start with $X_1$ and then move to orthogonalizing $X_2$. Since $X_1$ and $X_2$ share $X$ the result would practically be zero in your example. But the common element $X$ remains | Where is the explanatory effect of common variance among covariates accounted for in regression procedures?
The GS procedure would start with $X_1$ and then move to orthogonalizing $X_2$. Since $X_1$ and $X_2$ share $X$ the result would practically be zero in your example. But the common element $X$ remains, because we... | Where is the explanatory effect of common variance among covariates accounted for in regression proc
The GS procedure would start with $X_1$ and then move to orthogonalizing $X_2$. Since $X_1$ and $X_2$ share $X$ the result would practically be zero in your example. But the common element $X$ remains |
35,707 | Prediction Intervals with Heteroscedasticity | It would depend on the nature of the heteroskedasticity. If you wanted a prediction interval, you usually need a parametric specification like:
$$
y_i \sim N(\mathbf{x}_i'\beta,\sigma_i(\mathbf{x}_i,\mathbf{z}_i ))
$$
i.e. $y_i$ is normally distributed with mean $\mathbf{x}_i'\beta$, and standard deviation $\sigma_i(\... | Prediction Intervals with Heteroscedasticity | It would depend on the nature of the heteroskedasticity. If you wanted a prediction interval, you usually need a parametric specification like:
$$
y_i \sim N(\mathbf{x}_i'\beta,\sigma_i(\mathbf{x}_i, | Prediction Intervals with Heteroscedasticity
It would depend on the nature of the heteroskedasticity. If you wanted a prediction interval, you usually need a parametric specification like:
$$
y_i \sim N(\mathbf{x}_i'\beta,\sigma_i(\mathbf{x}_i,\mathbf{z}_i ))
$$
i.e. $y_i$ is normally distributed with mean $\mathbf{x}... | Prediction Intervals with Heteroscedasticity
It would depend on the nature of the heteroskedasticity. If you wanted a prediction interval, you usually need a parametric specification like:
$$
y_i \sim N(\mathbf{x}_i'\beta,\sigma_i(\mathbf{x}_i, |
35,708 | Prediction Intervals with Heteroscedasticity | Nonparametric quantile regression gives a very general approach that allows for both heteroscedasticity and nonlinearity. See section 9: http://www.econ.uiuc.edu/~roger/research/rq/vig.pdf
UPDATE:
A reasonable approximation for a 90% prediction interval is the space between the 5th-percentile regression curve and the... | Prediction Intervals with Heteroscedasticity | Nonparametric quantile regression gives a very general approach that allows for both heteroscedasticity and nonlinearity. See section 9: http://www.econ.uiuc.edu/~roger/research/rq/vig.pdf
UPDATE:
A | Prediction Intervals with Heteroscedasticity
Nonparametric quantile regression gives a very general approach that allows for both heteroscedasticity and nonlinearity. See section 9: http://www.econ.uiuc.edu/~roger/research/rq/vig.pdf
UPDATE:
A reasonable approximation for a 90% prediction interval is the space betwee... | Prediction Intervals with Heteroscedasticity
Nonparametric quantile regression gives a very general approach that allows for both heteroscedasticity and nonlinearity. See section 9: http://www.econ.uiuc.edu/~roger/research/rq/vig.pdf
UPDATE:
A |
35,709 | Prediction Intervals with Heteroscedasticity | If the regression of your response on your explanatory variable is a straight line and your variance increases with the explanatory variable, a weighted regression model is needed with or (if your nonconstant variance is more extreme) as your weight. This weights your variance by your x value, so that there's a propo... | Prediction Intervals with Heteroscedasticity | If the regression of your response on your explanatory variable is a straight line and your variance increases with the explanatory variable, a weighted regression model is needed with or (if your n | Prediction Intervals with Heteroscedasticity
If the regression of your response on your explanatory variable is a straight line and your variance increases with the explanatory variable, a weighted regression model is needed with or (if your nonconstant variance is more extreme) as your weight. This weights your vari... | Prediction Intervals with Heteroscedasticity
If the regression of your response on your explanatory variable is a straight line and your variance increases with the explanatory variable, a weighted regression model is needed with or (if your n |
35,710 | Test for significant excess of significant p-values across multiple comparisons | There are a number of methods for combining $p$-values which could be considered.
Birnbaum in his paper
"Combining independent tests of significance" available
here
points out the problem
is poorly specified.
This may
account for the number of methods available
and their differing behaviour.
The null hypothesis $H_0$ i... | Test for significant excess of significant p-values across multiple comparisons | There are a number of methods for combining $p$-values which could be considered.
Birnbaum in his paper
"Combining independent tests of significance" available
here
points out the problem
is poorly sp | Test for significant excess of significant p-values across multiple comparisons
There are a number of methods for combining $p$-values which could be considered.
Birnbaum in his paper
"Combining independent tests of significance" available
here
points out the problem
is poorly specified.
This may
account for the number... | Test for significant excess of significant p-values across multiple comparisons
There are a number of methods for combining $p$-values which could be considered.
Birnbaum in his paper
"Combining independent tests of significance" available
here
points out the problem
is poorly sp |
35,711 | Test for significant excess of significant p-values across multiple comparisons | About 10 years ago Bradley Efron wrote a number of papers on the subject. I think in one of them he also used the permutation approach, but the main idea was to estimate the null distribution from the data parametrically. You can find the corresponding R package instructions here. | Test for significant excess of significant p-values across multiple comparisons | About 10 years ago Bradley Efron wrote a number of papers on the subject. I think in one of them he also used the permutation approach, but the main idea was to estimate the null distribution from the | Test for significant excess of significant p-values across multiple comparisons
About 10 years ago Bradley Efron wrote a number of papers on the subject. I think in one of them he also used the permutation approach, but the main idea was to estimate the null distribution from the data parametrically. You can find the c... | Test for significant excess of significant p-values across multiple comparisons
About 10 years ago Bradley Efron wrote a number of papers on the subject. I think in one of them he also used the permutation approach, but the main idea was to estimate the null distribution from the |
35,712 | Does correlation imply mutual information? | Mutual information is zero if and only if $p(x,y) = p(x) p(y)$ and this condition implies that correlation is zero. So, if correlation is non-zero, then mutual information need to be non-zero. | Does correlation imply mutual information? | Mutual information is zero if and only if $p(x,y) = p(x) p(y)$ and this condition implies that correlation is zero. So, if correlation is non-zero, then mutual information need to be non-zero. | Does correlation imply mutual information?
Mutual information is zero if and only if $p(x,y) = p(x) p(y)$ and this condition implies that correlation is zero. So, if correlation is non-zero, then mutual information need to be non-zero. | Does correlation imply mutual information?
Mutual information is zero if and only if $p(x,y) = p(x) p(y)$ and this condition implies that correlation is zero. So, if correlation is non-zero, then mutual information need to be non-zero. |
35,713 | Sum of squared Poisson probability masses | Don't hesitate to use WolframAlpha to get the sum of a series. Or do you need a mathematical proof ?
This gives $\exp(-2\lambda)I_0(2\lambda)$.
The link to the documentation of the Bessel function $I_0$ is this one.
Actually the proof here would just mean the series representation of $I_0$.
If you want to use R to ev... | Sum of squared Poisson probability masses | Don't hesitate to use WolframAlpha to get the sum of a series. Or do you need a mathematical proof ?
This gives $\exp(-2\lambda)I_0(2\lambda)$.
The link to the documentation of the Bessel function $ | Sum of squared Poisson probability masses
Don't hesitate to use WolframAlpha to get the sum of a series. Or do you need a mathematical proof ?
This gives $\exp(-2\lambda)I_0(2\lambda)$.
The link to the documentation of the Bessel function $I_0$ is this one.
Actually the proof here would just mean the series represent... | Sum of squared Poisson probability masses
Don't hesitate to use WolframAlpha to get the sum of a series. Or do you need a mathematical proof ?
This gives $\exp(-2\lambda)I_0(2\lambda)$.
The link to the documentation of the Bessel function $ |
35,714 | Relationship between correlation and linear dependency | whuber's much more detailed answer appeared while I was composing this answer of mine (which essentially uses the same argument).
Let $X$ and $Y$ denote two random variables with finite variances
$\sigma_X^2$ and $\sigma_Y^2$ respectively and correlation coefficient
$\rho = \pm 1$. Then,
\begin{align}\operatorname{va... | Relationship between correlation and linear dependency | whuber's much more detailed answer appeared while I was composing this answer of mine (which essentially uses the same argument).
Let $X$ and $Y$ denote two random variables with finite variances
$\si | Relationship between correlation and linear dependency
whuber's much more detailed answer appeared while I was composing this answer of mine (which essentially uses the same argument).
Let $X$ and $Y$ denote two random variables with finite variances
$\sigma_X^2$ and $\sigma_Y^2$ respectively and correlation coefficien... | Relationship between correlation and linear dependency
whuber's much more detailed answer appeared while I was composing this answer of mine (which essentially uses the same argument).
Let $X$ and $Y$ denote two random variables with finite variances
$\si |
35,715 | Relationship between correlation and linear dependency | Let the pair of (random) variables be $(X_1,X_2)$. Since their correlation coefficient exists, each has a finite variance $\sigma^2_i$ and a finite mean $\mu_i$. The standardized variables are $Z_i = (X_i - \mu_i)/\sigma_i$. In particular their second moments are unity:
$$\mathbb{E}(Z_i^2) = 1.$$
By definition, the ... | Relationship between correlation and linear dependency | Let the pair of (random) variables be $(X_1,X_2)$. Since their correlation coefficient exists, each has a finite variance $\sigma^2_i$ and a finite mean $\mu_i$. The standardized variables are $Z_i | Relationship between correlation and linear dependency
Let the pair of (random) variables be $(X_1,X_2)$. Since their correlation coefficient exists, each has a finite variance $\sigma^2_i$ and a finite mean $\mu_i$. The standardized variables are $Z_i = (X_i - \mu_i)/\sigma_i$. In particular their second moments ar... | Relationship between correlation and linear dependency
Let the pair of (random) variables be $(X_1,X_2)$. Since their correlation coefficient exists, each has a finite variance $\sigma^2_i$ and a finite mean $\mu_i$. The standardized variables are $Z_i |
35,716 | Data visualization for missing data | I would honestly simply leave data points without information empty. In R:
foo <- structure(c(10,NA,NA,67,38),.Names=paste0("Day",1:5))
plot(foo,xaxt="n",xlab="",ylab="",pch=19,type="o",
ylim=c(0,max(foo,na.rm=TRUE)))
axis(1,seq_along(foo),names(foo))
Anything else is defensible if it reflects information you have... | Data visualization for missing data | I would honestly simply leave data points without information empty. In R:
foo <- structure(c(10,NA,NA,67,38),.Names=paste0("Day",1:5))
plot(foo,xaxt="n",xlab="",ylab="",pch=19,type="o",
ylim=c(0,ma | Data visualization for missing data
I would honestly simply leave data points without information empty. In R:
foo <- structure(c(10,NA,NA,67,38),.Names=paste0("Day",1:5))
plot(foo,xaxt="n",xlab="",ylab="",pch=19,type="o",
ylim=c(0,max(foo,na.rm=TRUE)))
axis(1,seq_along(foo),names(foo))
Anything else is defensible... | Data visualization for missing data
I would honestly simply leave data points without information empty. In R:
foo <- structure(c(10,NA,NA,67,38),.Names=paste0("Day",1:5))
plot(foo,xaxt="n",xlab="",ylab="",pch=19,type="o",
ylim=c(0,ma |
35,717 | Fit regression model from a fan-shaped relation, in R | Here's two fan-shaped plots generated by different methods:
(Click here for a larger version.)
These in turn suggest two different approaches for modelling data that looks more or less like this:
Take logs, and fit a linear model with the coefficient restricted to 1 (also called an offset)
divide $y$ by $x$ and then ... | Fit regression model from a fan-shaped relation, in R | Here's two fan-shaped plots generated by different methods:
(Click here for a larger version.)
These in turn suggest two different approaches for modelling data that looks more or less like this:
Ta | Fit regression model from a fan-shaped relation, in R
Here's two fan-shaped plots generated by different methods:
(Click here for a larger version.)
These in turn suggest two different approaches for modelling data that looks more or less like this:
Take logs, and fit a linear model with the coefficient restricted to... | Fit regression model from a fan-shaped relation, in R
Here's two fan-shaped plots generated by different methods:
(Click here for a larger version.)
These in turn suggest two different approaches for modelling data that looks more or less like this:
Ta |
35,718 | Simulate from a dynamic mixture of distributions | As pointed out by Dougal, the shape of your target density$$h_\beta(r)\propto (1-w_{m,\tau}(r))f_{\beta_0}(r)+w_{m,\tau}(r) g_{\epsilon,\sigma}(r)
$$is open to accept-reject simulation since
$$(1-w_{m,\tau}(r))f_{\beta_0}(r)+w_{m,\tau}(r) g_{\epsilon,\sigma}(r)
\le f_{\beta_0}(r)+g_{\epsilon,\sigma}(r)=2\left\{\frac{1}... | Simulate from a dynamic mixture of distributions | As pointed out by Dougal, the shape of your target density$$h_\beta(r)\propto (1-w_{m,\tau}(r))f_{\beta_0}(r)+w_{m,\tau}(r) g_{\epsilon,\sigma}(r)
$$is open to accept-reject simulation since
$$(1-w_{m | Simulate from a dynamic mixture of distributions
As pointed out by Dougal, the shape of your target density$$h_\beta(r)\propto (1-w_{m,\tau}(r))f_{\beta_0}(r)+w_{m,\tau}(r) g_{\epsilon,\sigma}(r)
$$is open to accept-reject simulation since
$$(1-w_{m,\tau}(r))f_{\beta_0}(r)+w_{m,\tau}(r) g_{\epsilon,\sigma}(r)
\le f_{\b... | Simulate from a dynamic mixture of distributions
As pointed out by Dougal, the shape of your target density$$h_\beta(r)\propto (1-w_{m,\tau}(r))f_{\beta_0}(r)+w_{m,\tau}(r) g_{\epsilon,\sigma}(r)
$$is open to accept-reject simulation since
$$(1-w_{m |
35,719 | Simulate from a dynamic mixture of distributions | I suggest that you investigate Probabilistic Programming. Basically, you write programs that operate on probability distributions rather than (random) variables. This makes it easy to define functions that are dynamic mixtures of distributions. While full-featured Probabilistic Programming systems support Bayesian s... | Simulate from a dynamic mixture of distributions | I suggest that you investigate Probabilistic Programming. Basically, you write programs that operate on probability distributions rather than (random) variables. This makes it easy to define functio | Simulate from a dynamic mixture of distributions
I suggest that you investigate Probabilistic Programming. Basically, you write programs that operate on probability distributions rather than (random) variables. This makes it easy to define functions that are dynamic mixtures of distributions. While full-featured Pro... | Simulate from a dynamic mixture of distributions
I suggest that you investigate Probabilistic Programming. Basically, you write programs that operate on probability distributions rather than (random) variables. This makes it easy to define functio |
35,720 | Why does Lucene IDF have a seemingly additional +1? | All TF-IDF weighting schemes are just heuristic methods to give more weight to unusual terms. I'm not sure that TF-IDF schemes generally have a solid statistical basis behind them (see reference 1), except for the observation that TF-IDF tends to produce better results than simple word counts. Since the quality of the ... | Why does Lucene IDF have a seemingly additional +1? | All TF-IDF weighting schemes are just heuristic methods to give more weight to unusual terms. I'm not sure that TF-IDF schemes generally have a solid statistical basis behind them (see reference 1), e | Why does Lucene IDF have a seemingly additional +1?
All TF-IDF weighting schemes are just heuristic methods to give more weight to unusual terms. I'm not sure that TF-IDF schemes generally have a solid statistical basis behind them (see reference 1), except for the observation that TF-IDF tends to produce better result... | Why does Lucene IDF have a seemingly additional +1?
All TF-IDF weighting schemes are just heuristic methods to give more weight to unusual terms. I'm not sure that TF-IDF schemes generally have a solid statistical basis behind them (see reference 1), e |
35,721 | Who conjectured that every correlation is caused by causal mechanisms? | This conjecture is called Reichenbach's Principle of Common Cause (RPCC), as it was first made precise by Hans Reichenbach (in 1956; imprecise versions have been around for much longer). The Stanford Encyclopedia of Philosophy has a good discussion and plenty of references.
Tangent: A friend recently asked me this exac... | Who conjectured that every correlation is caused by causal mechanisms? | This conjecture is called Reichenbach's Principle of Common Cause (RPCC), as it was first made precise by Hans Reichenbach (in 1956; imprecise versions have been around for much longer). The Stanford | Who conjectured that every correlation is caused by causal mechanisms?
This conjecture is called Reichenbach's Principle of Common Cause (RPCC), as it was first made precise by Hans Reichenbach (in 1956; imprecise versions have been around for much longer). The Stanford Encyclopedia of Philosophy has a good discussion ... | Who conjectured that every correlation is caused by causal mechanisms?
This conjecture is called Reichenbach's Principle of Common Cause (RPCC), as it was first made precise by Hans Reichenbach (in 1956; imprecise versions have been around for much longer). The Stanford |
35,722 | How to use Random Forest for categorical variables with missing value | Off the top of my head, I would say that this shouldn't be an issue. The rf package in R implements random forests using CARTs. One of the nicest thing about trees is how they are "natively" capable of dealing with categorical and missing variables. Here is the package documentation; you can download the package itself... | How to use Random Forest for categorical variables with missing value | Off the top of my head, I would say that this shouldn't be an issue. The rf package in R implements random forests using CARTs. One of the nicest thing about trees is how they are "natively" capable o | How to use Random Forest for categorical variables with missing value
Off the top of my head, I would say that this shouldn't be an issue. The rf package in R implements random forests using CARTs. One of the nicest thing about trees is how they are "natively" capable of dealing with categorical and missing variables. ... | How to use Random Forest for categorical variables with missing value
Off the top of my head, I would say that this shouldn't be an issue. The rf package in R implements random forests using CARTs. One of the nicest thing about trees is how they are "natively" capable o |
35,723 | How to use Random Forest for categorical variables with missing value | The R randomForest package includes functions for doing a rough imputation of missing values and then iterativelly improving this imputation based on case proximity in RF runs.
There are a bunch of other methods that have been proposed as ways rf's and decision trees can handle missing values:
1) Leave them out when sp... | How to use Random Forest for categorical variables with missing value | The R randomForest package includes functions for doing a rough imputation of missing values and then iterativelly improving this imputation based on case proximity in RF runs.
There are a bunch of ot | How to use Random Forest for categorical variables with missing value
The R randomForest package includes functions for doing a rough imputation of missing values and then iterativelly improving this imputation based on case proximity in RF runs.
There are a bunch of other methods that have been proposed as ways rf's a... | How to use Random Forest for categorical variables with missing value
The R randomForest package includes functions for doing a rough imputation of missing values and then iterativelly improving this imputation based on case proximity in RF runs.
There are a bunch of ot |
35,724 | How to use Random Forest for categorical variables with missing value | You can simply introduce a new level for each categorical variable which represents missing data. Then you would simply replace the missing fields with this new category. | How to use Random Forest for categorical variables with missing value | You can simply introduce a new level for each categorical variable which represents missing data. Then you would simply replace the missing fields with this new category. | How to use Random Forest for categorical variables with missing value
You can simply introduce a new level for each categorical variable which represents missing data. Then you would simply replace the missing fields with this new category. | How to use Random Forest for categorical variables with missing value
You can simply introduce a new level for each categorical variable which represents missing data. Then you would simply replace the missing fields with this new category. |
35,725 | De-normalizing Google Trends data? | Since the normalization consists in
$$ \mathbf{z} = \frac{\mathbf{x}}{\max(\mathbf{x})}, $$
where $\mathbf{x}$ is the vector of search volumes, and $\max(\mathbf{x})$ is the maximal element of $\mathbf{x}$, if you want de-normalized data, you should multiply each element of the normalized vector times the maximal eleme... | De-normalizing Google Trends data? | Since the normalization consists in
$$ \mathbf{z} = \frac{\mathbf{x}}{\max(\mathbf{x})}, $$
where $\mathbf{x}$ is the vector of search volumes, and $\max(\mathbf{x})$ is the maximal element of $\mathb | De-normalizing Google Trends data?
Since the normalization consists in
$$ \mathbf{z} = \frac{\mathbf{x}}{\max(\mathbf{x})}, $$
where $\mathbf{x}$ is the vector of search volumes, and $\max(\mathbf{x})$ is the maximal element of $\mathbf{x}$, if you want de-normalized data, you should multiply each element of the normal... | De-normalizing Google Trends data?
Since the normalization consists in
$$ \mathbf{z} = \frac{\mathbf{x}}{\max(\mathbf{x})}, $$
where $\mathbf{x}$ is the vector of search volumes, and $\max(\mathbf{x})$ is the maximal element of $\mathb |
35,726 | De-normalizing Google Trends data? | De-normalizing Google Trends data can be very useful, but it is tricky, due to rounding errors: when comparing 2 queries of vastly different search volume, the time series for the less frequent query could appear to be 0 everywhere.
To solve this problem, we have developed a method called Google Trends Anchor Bank. It'... | De-normalizing Google Trends data? | De-normalizing Google Trends data can be very useful, but it is tricky, due to rounding errors: when comparing 2 queries of vastly different search volume, the time series for the less frequent query | De-normalizing Google Trends data?
De-normalizing Google Trends data can be very useful, but it is tricky, due to rounding errors: when comparing 2 queries of vastly different search volume, the time series for the less frequent query could appear to be 0 everywhere.
To solve this problem, we have developed a method ca... | De-normalizing Google Trends data?
De-normalizing Google Trends data can be very useful, but it is tricky, due to rounding errors: when comparing 2 queries of vastly different search volume, the time series for the less frequent query |
35,727 | Approaches for generating synthetic survey data with dependent answers? | Here I use a latent variable approach. This readily extends to the continuous/categorical case.
The idea is to treat a continuous variable (the latent variable) as laying behind the ordered categories that are actually observed (by splitting up the continuous variable at breakpoints).
So for the two variables that are ... | Approaches for generating synthetic survey data with dependent answers? | Here I use a latent variable approach. This readily extends to the continuous/categorical case.
The idea is to treat a continuous variable (the latent variable) as laying behind the ordered categories | Approaches for generating synthetic survey data with dependent answers?
Here I use a latent variable approach. This readily extends to the continuous/categorical case.
The idea is to treat a continuous variable (the latent variable) as laying behind the ordered categories that are actually observed (by splitting up the... | Approaches for generating synthetic survey data with dependent answers?
Here I use a latent variable approach. This readily extends to the continuous/categorical case.
The idea is to treat a continuous variable (the latent variable) as laying behind the ordered categories |
35,728 | Approaches for generating synthetic survey data with dependent answers? | Are your variables quantitative or categorical variables ?
In an article we recently wrote, we wanted to simulate three quantitative anwers to a survey : $z$ and $u$ had to be independant, and $X$ had to be correlated to both $z$ and $u$, so we generated them like this :
$\begin{align*}
u &\sim \mathcal{U}[a,b] \\
z &\... | Approaches for generating synthetic survey data with dependent answers? | Are your variables quantitative or categorical variables ?
In an article we recently wrote, we wanted to simulate three quantitative anwers to a survey : $z$ and $u$ had to be independant, and $X$ had | Approaches for generating synthetic survey data with dependent answers?
Are your variables quantitative or categorical variables ?
In an article we recently wrote, we wanted to simulate three quantitative anwers to a survey : $z$ and $u$ had to be independant, and $X$ had to be correlated to both $z$ and $u$, so we gen... | Approaches for generating synthetic survey data with dependent answers?
Are your variables quantitative or categorical variables ?
In an article we recently wrote, we wanted to simulate three quantitative anwers to a survey : $z$ and $u$ had to be independant, and $X$ had |
35,729 | Why don't we train neural networks to maximize linear correlation instead of error? | Because that would be a completely different objective altogether. Note that unlike MSE, Pearson correlation is maximal iff there is a linear relationship between both variables. This means that
The network would "think" it has correctly learned its inputs if its output is roughly proportional to the dependent variab... | Why don't we train neural networks to maximize linear correlation instead of error? | Because that would be a completely different objective altogether. Note that unlike MSE, Pearson correlation is maximal iff there is a linear relationship between both variables. This means that
The | Why don't we train neural networks to maximize linear correlation instead of error?
Because that would be a completely different objective altogether. Note that unlike MSE, Pearson correlation is maximal iff there is a linear relationship between both variables. This means that
The network would "think" it has correc... | Why don't we train neural networks to maximize linear correlation instead of error?
Because that would be a completely different objective altogether. Note that unlike MSE, Pearson correlation is maximal iff there is a linear relationship between both variables. This means that
The |
35,730 | Why don't we train neural networks to maximize linear correlation instead of error? | It's more like a comment, though I can't comment yet.
I'd suspect that minimizing RMSE respective to a normalized input is (roughly?) equivalent to maximizing the Pearson correlation coefficient, but the latter is more computationally expensive. | Why don't we train neural networks to maximize linear correlation instead of error? | It's more like a comment, though I can't comment yet.
I'd suspect that minimizing RMSE respective to a normalized input is (roughly?) equivalent to maximizing the Pearson correlation coefficient, but | Why don't we train neural networks to maximize linear correlation instead of error?
It's more like a comment, though I can't comment yet.
I'd suspect that minimizing RMSE respective to a normalized input is (roughly?) equivalent to maximizing the Pearson correlation coefficient, but the latter is more computationally e... | Why don't we train neural networks to maximize linear correlation instead of error?
It's more like a comment, though I can't comment yet.
I'd suspect that minimizing RMSE respective to a normalized input is (roughly?) equivalent to maximizing the Pearson correlation coefficient, but |
35,731 | Estimating Size of a Set based on two Overlapping Subsets | This sounds like the basic "capture-recapture" problem, sometimes called "mark and recapture".
You have a population of unknown size $N$; imagine them to be indistinguishable balls in an urn (all white, say). You take a sample of size $n$ randomly from the population, and mark them (paint them black say), return them ... | Estimating Size of a Set based on two Overlapping Subsets | This sounds like the basic "capture-recapture" problem, sometimes called "mark and recapture".
You have a population of unknown size $N$; imagine them to be indistinguishable balls in an urn (all whi | Estimating Size of a Set based on two Overlapping Subsets
This sounds like the basic "capture-recapture" problem, sometimes called "mark and recapture".
You have a population of unknown size $N$; imagine them to be indistinguishable balls in an urn (all white, say). You take a sample of size $n$ randomly from the popu... | Estimating Size of a Set based on two Overlapping Subsets
This sounds like the basic "capture-recapture" problem, sometimes called "mark and recapture".
You have a population of unknown size $N$; imagine them to be indistinguishable balls in an urn (all whi |
35,732 | What deviance is glmnet using to compare values of $\lambda$? | I just wanted to add to the input, but don't at the moment have a concise answer and it's too long for a comment. Hopefully this gives more insight.
It seems that the function of interest is in the unpacked glmnet library, and is called
cv.lognet.R It's hard to explicitly trace everything, as much is in S3/S4 code, bu... | What deviance is glmnet using to compare values of $\lambda$? | I just wanted to add to the input, but don't at the moment have a concise answer and it's too long for a comment. Hopefully this gives more insight.
It seems that the function of interest is in the un | What deviance is glmnet using to compare values of $\lambda$?
I just wanted to add to the input, but don't at the moment have a concise answer and it's too long for a comment. Hopefully this gives more insight.
It seems that the function of interest is in the unpacked glmnet library, and is called
cv.lognet.R It's har... | What deviance is glmnet using to compare values of $\lambda$?
I just wanted to add to the input, but don't at the moment have a concise answer and it's too long for a comment. Hopefully this gives more insight.
It seems that the function of interest is in the un |
35,733 | What deviance is glmnet using to compare values of $\lambda$? | So I visited the CRAN site and downloaded what I think is the source of the glmnet package. In ./glmnet/R/plot.cv.glmnet.R it seems that you'd find the source code you're after. It's pretty brief so I'll paste here but it's probably best if you check it out yourself to be sure that it is indeed the code that is running... | What deviance is glmnet using to compare values of $\lambda$? | So I visited the CRAN site and downloaded what I think is the source of the glmnet package. In ./glmnet/R/plot.cv.glmnet.R it seems that you'd find the source code you're after. It's pretty brief so I | What deviance is glmnet using to compare values of $\lambda$?
So I visited the CRAN site and downloaded what I think is the source of the glmnet package. In ./glmnet/R/plot.cv.glmnet.R it seems that you'd find the source code you're after. It's pretty brief so I'll paste here but it's probably best if you check it out ... | What deviance is glmnet using to compare values of $\lambda$?
So I visited the CRAN site and downloaded what I think is the source of the glmnet package. In ./glmnet/R/plot.cv.glmnet.R it seems that you'd find the source code you're after. It's pretty brief so I |
35,734 | Is a negative OOB score possible with scikit-learn's RandomForestRegressor? | RandomForestRegressor's oob_score_ attribute is the score of out-of-bag samples. scikit-learn uses "score" to mean something like "measure of how good a model is", which is different for different models. For RandomForestRegressor (as for most regression models), it's the coefficient of determination, as can be seen by... | Is a negative OOB score possible with scikit-learn's RandomForestRegressor? | RandomForestRegressor's oob_score_ attribute is the score of out-of-bag samples. scikit-learn uses "score" to mean something like "measure of how good a model is", which is different for different mod | Is a negative OOB score possible with scikit-learn's RandomForestRegressor?
RandomForestRegressor's oob_score_ attribute is the score of out-of-bag samples. scikit-learn uses "score" to mean something like "measure of how good a model is", which is different for different models. For RandomForestRegressor (as for most ... | Is a negative OOB score possible with scikit-learn's RandomForestRegressor?
RandomForestRegressor's oob_score_ attribute is the score of out-of-bag samples. scikit-learn uses "score" to mean something like "measure of how good a model is", which is different for different mod |
35,735 | Relationship between skew and kurtosis in a sample | A discussion on the limits of the sample skewness and kurtosis is available here. The author gives proper references to the original proofs, and the cited results are:
$$
|g_1| \le \frac{n-2}{\sqrt{n-1}} = \sqrt{n-1} - \frac{1}{\sqrt{n-1}}
$$
$$
b_2 = g_2 + 3 \le \frac{n^2-3n+3}{n-1} = n -2 + \frac1{n-1}
$$
So for $n=1... | Relationship between skew and kurtosis in a sample | A discussion on the limits of the sample skewness and kurtosis is available here. The author gives proper references to the original proofs, and the cited results are:
$$
|g_1| \le \frac{n-2}{\sqrt{n- | Relationship between skew and kurtosis in a sample
A discussion on the limits of the sample skewness and kurtosis is available here. The author gives proper references to the original proofs, and the cited results are:
$$
|g_1| \le \frac{n-2}{\sqrt{n-1}} = \sqrt{n-1} - \frac{1}{\sqrt{n-1}}
$$
$$
b_2 = g_2 + 3 \le \frac... | Relationship between skew and kurtosis in a sample
A discussion on the limits of the sample skewness and kurtosis is available here. The author gives proper references to the original proofs, and the cited results are:
$$
|g_1| \le \frac{n-2}{\sqrt{n- |
35,736 | Relationship between skew and kurtosis in a sample | Some broad discussion on how to understand the problem in the absence of sample definitions.
Since the quoted relationship applies to distributions, if you treat the ecdf as the cdf of a distribution, and apply those population definitions you gave, the relationship must still hold. That is, if you use $n$ denominators... | Relationship between skew and kurtosis in a sample | Some broad discussion on how to understand the problem in the absence of sample definitions.
Since the quoted relationship applies to distributions, if you treat the ecdf as the cdf of a distribution, | Relationship between skew and kurtosis in a sample
Some broad discussion on how to understand the problem in the absence of sample definitions.
Since the quoted relationship applies to distributions, if you treat the ecdf as the cdf of a distribution, and apply those population definitions you gave, the relationship mu... | Relationship between skew and kurtosis in a sample
Some broad discussion on how to understand the problem in the absence of sample definitions.
Since the quoted relationship applies to distributions, if you treat the ecdf as the cdf of a distribution, |
35,737 | Manually calculating p-value for t-test: How to avoid values bigger than $1$? | You can make use of abs in the numerator (so it's always >0) and keep the lower.tail=FALSE. | Manually calculating p-value for t-test: How to avoid values bigger than $1$? | You can make use of abs in the numerator (so it's always >0) and keep the lower.tail=FALSE. | Manually calculating p-value for t-test: How to avoid values bigger than $1$?
You can make use of abs in the numerator (so it's always >0) and keep the lower.tail=FALSE. | Manually calculating p-value for t-test: How to avoid values bigger than $1$?
You can make use of abs in the numerator (so it's always >0) and keep the lower.tail=FALSE. |
35,738 | Manually calculating p-value for t-test: How to avoid values bigger than $1$? | Glen_b is absolutely right about the abs, however, I have found that in certain data sets the values would require -abs to have the desired effect. I'm not able to explain why, but I'll leave these line of code here, incase anyone who is having a similar problem finds this thread.
t.value <- betacoeff/standard error... | Manually calculating p-value for t-test: How to avoid values bigger than $1$? | Glen_b is absolutely right about the abs, however, I have found that in certain data sets the values would require -abs to have the desired effect. I'm not able to explain why, but I'll leave these li | Manually calculating p-value for t-test: How to avoid values bigger than $1$?
Glen_b is absolutely right about the abs, however, I have found that in certain data sets the values would require -abs to have the desired effect. I'm not able to explain why, but I'll leave these line of code here, incase anyone who is havi... | Manually calculating p-value for t-test: How to avoid values bigger than $1$?
Glen_b is absolutely right about the abs, however, I have found that in certain data sets the values would require -abs to have the desired effect. I'm not able to explain why, but I'll leave these li |
35,739 | Understanding the error term | $e$ is the population error (the part of $Y$ not explained by the linear combination of $X$ and $\beta$), while $\hat{e}$ are the residuals (the sample part of $Y$ not explained by $X$ and $\hat{\beta}$). Linear regression assumes $e \overset{\rm iid}{\sim} N(0, \sigma^2)$ with $\sigma^2$ constant, and we should check ... | Understanding the error term | $e$ is the population error (the part of $Y$ not explained by the linear combination of $X$ and $\beta$), while $\hat{e}$ are the residuals (the sample part of $Y$ not explained by $X$ and $\hat{\beta | Understanding the error term
$e$ is the population error (the part of $Y$ not explained by the linear combination of $X$ and $\beta$), while $\hat{e}$ are the residuals (the sample part of $Y$ not explained by $X$ and $\hat{\beta}$). Linear regression assumes $e \overset{\rm iid}{\sim} N(0, \sigma^2)$ with $\sigma^2$ c... | Understanding the error term
$e$ is the population error (the part of $Y$ not explained by the linear combination of $X$ and $\beta$), while $\hat{e}$ are the residuals (the sample part of $Y$ not explained by $X$ and $\hat{\beta |
35,740 | Tuning alpha parameter in LASSO linear model in scikitlearn | First: trying to set alpha to find a pre-specified number of important features isn't a good idea. Whether a feature is predictive of the response is a property of the data, not your model. So you want your model to tell you how many features are important, not the other way around. If you try to mess with your alpha u... | Tuning alpha parameter in LASSO linear model in scikitlearn | First: trying to set alpha to find a pre-specified number of important features isn't a good idea. Whether a feature is predictive of the response is a property of the data, not your model. So you wan | Tuning alpha parameter in LASSO linear model in scikitlearn
First: trying to set alpha to find a pre-specified number of important features isn't a good idea. Whether a feature is predictive of the response is a property of the data, not your model. So you want your model to tell you how many features are important, no... | Tuning alpha parameter in LASSO linear model in scikitlearn
First: trying to set alpha to find a pre-specified number of important features isn't a good idea. Whether a feature is predictive of the response is a property of the data, not your model. So you wan |
35,741 | Tuning alpha parameter in LASSO linear model in scikitlearn | You could try applying the Elastic Net Regression some times. It combines the Lasso and Ridge regression methods in order to give your feature selection a 'human touch'. This is quite helpful in optimizing your features while preserving the intuition from features in your data. | Tuning alpha parameter in LASSO linear model in scikitlearn | You could try applying the Elastic Net Regression some times. It combines the Lasso and Ridge regression methods in order to give your feature selection a 'human touch'. This is quite helpful in optim | Tuning alpha parameter in LASSO linear model in scikitlearn
You could try applying the Elastic Net Regression some times. It combines the Lasso and Ridge regression methods in order to give your feature selection a 'human touch'. This is quite helpful in optimizing your features while preserving the intuition from feat... | Tuning alpha parameter in LASSO linear model in scikitlearn
You could try applying the Elastic Net Regression some times. It combines the Lasso and Ridge regression methods in order to give your feature selection a 'human touch'. This is quite helpful in optim |
35,742 | Time series regression with lagged dependent and independent variables | First, you should decide on using a univariate or a multivariate model. It seems reasonable to think that oil price and unemployment are causal for the air travel demand and not the other way around. Thus, in line with one of the answers to this post, you may address your study in a univariate setting. If the previous ... | Time series regression with lagged dependent and independent variables | First, you should decide on using a univariate or a multivariate model. It seems reasonable to think that oil price and unemployment are causal for the air travel demand and not the other way around. | Time series regression with lagged dependent and independent variables
First, you should decide on using a univariate or a multivariate model. It seems reasonable to think that oil price and unemployment are causal for the air travel demand and not the other way around. Thus, in line with one of the answers to this pos... | Time series regression with lagged dependent and independent variables
First, you should decide on using a univariate or a multivariate model. It seems reasonable to think that oil price and unemployment are causal for the air travel demand and not the other way around. |
35,743 | Weighted Kendall tau rank correlation coefficient | I don't have commenting privileges, so I will attempt an answer here. Perhaps your original question is unclear, but here are answers depending on your exact meaning:
"I want to penalise R2 more as the differences in position is towards the head than tail. Thus, along with the ranking, I also want to take into consider... | Weighted Kendall tau rank correlation coefficient | I don't have commenting privileges, so I will attempt an answer here. Perhaps your original question is unclear, but here are answers depending on your exact meaning:
"I want to penalise R2 more as th | Weighted Kendall tau rank correlation coefficient
I don't have commenting privileges, so I will attempt an answer here. Perhaps your original question is unclear, but here are answers depending on your exact meaning:
"I want to penalise R2 more as the differences in position is towards the head than tail. Thus, along w... | Weighted Kendall tau rank correlation coefficient
I don't have commenting privileges, so I will attempt an answer here. Perhaps your original question is unclear, but here are answers depending on your exact meaning:
"I want to penalise R2 more as th |
35,744 | Weighted Kendall tau rank correlation coefficient | A positional weighted kendall-tau (a.k.a Kemeny) metric would do the work. This is a generalization of the original metric with assigning weights on possible swaps on consecutive positions (hence an infinite class).
A simple example would be assigning weights to a swap between 1st and 2nd alternatives, 2nd and 3rd, so... | Weighted Kendall tau rank correlation coefficient | A positional weighted kendall-tau (a.k.a Kemeny) metric would do the work. This is a generalization of the original metric with assigning weights on possible swaps on consecutive positions (hence an i | Weighted Kendall tau rank correlation coefficient
A positional weighted kendall-tau (a.k.a Kemeny) metric would do the work. This is a generalization of the original metric with assigning weights on possible swaps on consecutive positions (hence an infinite class).
A simple example would be assigning weights to a swap... | Weighted Kendall tau rank correlation coefficient
A positional weighted kendall-tau (a.k.a Kemeny) metric would do the work. This is a generalization of the original metric with assigning weights on possible swaps on consecutive positions (hence an i |
35,745 | Weighted Kendall tau rank correlation coefficient | I don't know if it is possible with Kendall tau, but some ranking measures such as Discounted cumulative gain naturally penalize more inversions towards some extreme of the list. | Weighted Kendall tau rank correlation coefficient | I don't know if it is possible with Kendall tau, but some ranking measures such as Discounted cumulative gain naturally penalize more inversions towards some extreme of the list. | Weighted Kendall tau rank correlation coefficient
I don't know if it is possible with Kendall tau, but some ranking measures such as Discounted cumulative gain naturally penalize more inversions towards some extreme of the list. | Weighted Kendall tau rank correlation coefficient
I don't know if it is possible with Kendall tau, but some ranking measures such as Discounted cumulative gain naturally penalize more inversions towards some extreme of the list. |
35,746 | Benchmark datasets for testing multiple regression or multivariate regression model? | See NIST's Statistical Reference Datasets. These include data chosen or designed to present numerical challenges to regression algorithms. The Longley data, with highly collinear predictors, is perhaps the most famous example. | Benchmark datasets for testing multiple regression or multivariate regression model? | See NIST's Statistical Reference Datasets. These include data chosen or designed to present numerical challenges to regression algorithms. The Longley data, with highly collinear predictors, is perhap | Benchmark datasets for testing multiple regression or multivariate regression model?
See NIST's Statistical Reference Datasets. These include data chosen or designed to present numerical challenges to regression algorithms. The Longley data, with highly collinear predictors, is perhaps the most famous example. | Benchmark datasets for testing multiple regression or multivariate regression model?
See NIST's Statistical Reference Datasets. These include data chosen or designed to present numerical challenges to regression algorithms. The Longley data, with highly collinear predictors, is perhap |
35,747 | Benchmark datasets for testing multiple regression or multivariate regression model? | Generate some random data yourself in whatever language you're using, that follow the assumptions of your model, e.g., for linear regression generate $X$, then $\beta$, then do $y = X\beta + \epsilon$ where $\epsilon$ is normally distributed with mean zero and sd of say 1. See if you can recover the correct $\beta$ whe... | Benchmark datasets for testing multiple regression or multivariate regression model? | Generate some random data yourself in whatever language you're using, that follow the assumptions of your model, e.g., for linear regression generate $X$, then $\beta$, then do $y = X\beta + \epsilon$ | Benchmark datasets for testing multiple regression or multivariate regression model?
Generate some random data yourself in whatever language you're using, that follow the assumptions of your model, e.g., for linear regression generate $X$, then $\beta$, then do $y = X\beta + \epsilon$ where $\epsilon$ is normally distr... | Benchmark datasets for testing multiple regression or multivariate regression model?
Generate some random data yourself in whatever language you're using, that follow the assumptions of your model, e.g., for linear regression generate $X$, then $\beta$, then do $y = X\beta + \epsilon$ |
35,748 | Different p-values for fixed effects in summary() of glmer() and likelihood ratio test comparison in R | It looks like you are seeing the difference between Wald p-values (based on the curvature of the log-likelihood surface at the maximum likelihood estimate) and likelihood ratio test p-values (based on comparisons between the full and reduced models).
take a look at tpr <- profile(a25,which="beta_"); lattice::xyplot(tp... | Different p-values for fixed effects in summary() of glmer() and likelihood ratio test comparison in | It looks like you are seeing the difference between Wald p-values (based on the curvature of the log-likelihood surface at the maximum likelihood estimate) and likelihood ratio test p-values (based on | Different p-values for fixed effects in summary() of glmer() and likelihood ratio test comparison in R
It looks like you are seeing the difference between Wald p-values (based on the curvature of the log-likelihood surface at the maximum likelihood estimate) and likelihood ratio test p-values (based on comparisons betw... | Different p-values for fixed effects in summary() of glmer() and likelihood ratio test comparison in
It looks like you are seeing the difference between Wald p-values (based on the curvature of the log-likelihood surface at the maximum likelihood estimate) and likelihood ratio test p-values (based on |
35,749 | Poisson process and the memoryless property | Memorylessness is a property of the following form:
$$\Pr(X>m+n \mid X > m)=\Pr(X>n)\ .$$
This property holds for $X_1=\ \text{time to the next event in a Poisson process}\ $, but it doesn't hold for $X_k=\ \text{time to the}\, k^\text{th}\, \text{event in a Poisson process}\ $ when $k>1$.
As for how to show it, you co... | Poisson process and the memoryless property | Memorylessness is a property of the following form:
$$\Pr(X>m+n \mid X > m)=\Pr(X>n)\ .$$
This property holds for $X_1=\ \text{time to the next event in a Poisson process}\ $, but it doesn't hold for | Poisson process and the memoryless property
Memorylessness is a property of the following form:
$$\Pr(X>m+n \mid X > m)=\Pr(X>n)\ .$$
This property holds for $X_1=\ \text{time to the next event in a Poisson process}\ $, but it doesn't hold for $X_k=\ \text{time to the}\, k^\text{th}\, \text{event in a Poisson process}\... | Poisson process and the memoryless property
Memorylessness is a property of the following form:
$$\Pr(X>m+n \mid X > m)=\Pr(X>n)\ .$$
This property holds for $X_1=\ \text{time to the next event in a Poisson process}\ $, but it doesn't hold for |
35,750 | Logistic-Regression: Prior correction at test time | For any distribution with over binary variable $C$ and continuous variable $x$:
\begin{align}
p(C_1|x) &= \frac{p(x|C_1)p(C_1)}{p(x)}\\
&= \frac{p(x|C_1)p(C_1)}{p(x|C_1)p(C_1) + p(x|C_2)p(C_2)}\\
&= \frac{1}{1 + \frac{p(x|C_2)p(C_2)}{p(x|C_1)p(C_1)}}\\
&= \frac{1}{1 + \exp\left(\ln\frac{p(x|C_2)p(C_2)}{p(x|C_1)p(C_1)}\... | Logistic-Regression: Prior correction at test time | For any distribution with over binary variable $C$ and continuous variable $x$:
\begin{align}
p(C_1|x) &= \frac{p(x|C_1)p(C_1)}{p(x)}\\
&= \frac{p(x|C_1)p(C_1)}{p(x|C_1)p(C_1) + p(x|C_2)p(C_2)}\\
&= \ | Logistic-Regression: Prior correction at test time
For any distribution with over binary variable $C$ and continuous variable $x$:
\begin{align}
p(C_1|x) &= \frac{p(x|C_1)p(C_1)}{p(x)}\\
&= \frac{p(x|C_1)p(C_1)}{p(x|C_1)p(C_1) + p(x|C_2)p(C_2)}\\
&= \frac{1}{1 + \frac{p(x|C_2)p(C_2)}{p(x|C_1)p(C_1)}}\\
&= \frac{1}{1 + ... | Logistic-Regression: Prior correction at test time
For any distribution with over binary variable $C$ and continuous variable $x$:
\begin{align}
p(C_1|x) &= \frac{p(x|C_1)p(C_1)}{p(x)}\\
&= \frac{p(x|C_1)p(C_1)}{p(x|C_1)p(C_1) + p(x|C_2)p(C_2)}\\
&= \ |
35,751 | Maximum likelihood estimator for $\theta$ and $E[X]$ | Let $X_1,\dots,X_n$ be a random sample from density $f(x_i)=(\theta/x_i^2)\,I_{(\theta,\infty)}(x_i)$, for $\theta>0$. Since $I_{(\theta,\infty)}(x_i)=I_{(0, x_i)}(\theta)$, writing $x=(x_1,\dots,x_n)$, the likelihood function is
$$
L_x(\theta) = \frac{\theta^n}{\prod_{i=1}^n x_i^2} I_{(0,x_{(1)})}(\theta) \, , \qqua... | Maximum likelihood estimator for $\theta$ and $E[X]$ | Let $X_1,\dots,X_n$ be a random sample from density $f(x_i)=(\theta/x_i^2)\,I_{(\theta,\infty)}(x_i)$, for $\theta>0$. Since $I_{(\theta,\infty)}(x_i)=I_{(0, x_i)}(\theta)$, writing $x=(x_1,\dots,x_n) | Maximum likelihood estimator for $\theta$ and $E[X]$
Let $X_1,\dots,X_n$ be a random sample from density $f(x_i)=(\theta/x_i^2)\,I_{(\theta,\infty)}(x_i)$, for $\theta>0$. Since $I_{(\theta,\infty)}(x_i)=I_{(0, x_i)}(\theta)$, writing $x=(x_1,\dots,x_n)$, the likelihood function is
$$
L_x(\theta) = \frac{\theta^n}{\p... | Maximum likelihood estimator for $\theta$ and $E[X]$
Let $X_1,\dots,X_n$ be a random sample from density $f(x_i)=(\theta/x_i^2)\,I_{(\theta,\infty)}(x_i)$, for $\theta>0$. Since $I_{(\theta,\infty)}(x_i)=I_{(0, x_i)}(\theta)$, writing $x=(x_1,\dots,x_n) |
35,752 | Maximum likelihood estimator for $\theta$ and $E[X]$ | One cannot provide an estimator for a distribution moment that is not finite. Here we have a case of a distribution that does not have a finite expected value. The question that usually comes next is "then what does the sample mean from an i.i.d. sample estimates in such a case?" The answer is that the sample mean is ... | Maximum likelihood estimator for $\theta$ and $E[X]$ | One cannot provide an estimator for a distribution moment that is not finite. Here we have a case of a distribution that does not have a finite expected value. The question that usually comes next is | Maximum likelihood estimator for $\theta$ and $E[X]$
One cannot provide an estimator for a distribution moment that is not finite. Here we have a case of a distribution that does not have a finite expected value. The question that usually comes next is "then what does the sample mean from an i.i.d. sample estimates in... | Maximum likelihood estimator for $\theta$ and $E[X]$
One cannot provide an estimator for a distribution moment that is not finite. Here we have a case of a distribution that does not have a finite expected value. The question that usually comes next is |
35,753 | Why is power analysis with logistic regression so liberal compared to chi squared? | The two tests (logistic regression and chi-square) are equivalent and a power analysis should give the same answer.
You are assuming that a value of 0.15 for f2 and w are the same effect size, they're not. A small value of w is 0.1, a small value of f2 is 0.02.
cohen.ES(test=c("chisq"), size=c("small"))
cohen.ES(test=c... | Why is power analysis with logistic regression so liberal compared to chi squared? | The two tests (logistic regression and chi-square) are equivalent and a power analysis should give the same answer.
You are assuming that a value of 0.15 for f2 and w are the same effect size, they're | Why is power analysis with logistic regression so liberal compared to chi squared?
The two tests (logistic regression and chi-square) are equivalent and a power analysis should give the same answer.
You are assuming that a value of 0.15 for f2 and w are the same effect size, they're not. A small value of w is 0.1, a sm... | Why is power analysis with logistic regression so liberal compared to chi squared?
The two tests (logistic regression and chi-square) are equivalent and a power analysis should give the same answer.
You are assuming that a value of 0.15 for f2 and w are the same effect size, they're |
35,754 | Difference between random effect and random intercept model | A random intercept model estimates separate intercepts for each unit of each level at which the intercept is permitted to vary. This is one kind of random effect model. Another kind of random effect model also includes random slopes, and estimates separate slopes (i.e. coefficients, betas, effects, etc. depending on yo... | Difference between random effect and random intercept model | A random intercept model estimates separate intercepts for each unit of each level at which the intercept is permitted to vary. This is one kind of random effect model. Another kind of random effect m | Difference between random effect and random intercept model
A random intercept model estimates separate intercepts for each unit of each level at which the intercept is permitted to vary. This is one kind of random effect model. Another kind of random effect model also includes random slopes, and estimates separate slo... | Difference between random effect and random intercept model
A random intercept model estimates separate intercepts for each unit of each level at which the intercept is permitted to vary. This is one kind of random effect model. Another kind of random effect m |
35,755 | Is p-value also the false discovery rate? | Your false discovery rate not only depends on the p-value threshold, but also on the truth. In fact, if your null hypothesis is in reality wrong it is impossible for you to make a false discovery.
Maybe it's helpful to think of it like that: the p-value threshold is the probability of making false discoveries when ther... | Is p-value also the false discovery rate? | Your false discovery rate not only depends on the p-value threshold, but also on the truth. In fact, if your null hypothesis is in reality wrong it is impossible for you to make a false discovery.
May | Is p-value also the false discovery rate?
Your false discovery rate not only depends on the p-value threshold, but also on the truth. In fact, if your null hypothesis is in reality wrong it is impossible for you to make a false discovery.
Maybe it's helpful to think of it like that: the p-value threshold is the probabi... | Is p-value also the false discovery rate?
Your false discovery rate not only depends on the p-value threshold, but also on the truth. In fact, if your null hypothesis is in reality wrong it is impossible for you to make a false discovery.
May |
35,756 | Is p-value also the false discovery rate? | The difference between P values and false positive rate (or false discovery rate) is explained, clearly I hope, in http://rsos.royalsocietypublishing.org/content/1/3/140216
Although that paper uses the term False Discovery Rate, I now prefer False Positive Rate, becuse the former term is often used in the context of co... | Is p-value also the false discovery rate? | The difference between P values and false positive rate (or false discovery rate) is explained, clearly I hope, in http://rsos.royalsocietypublishing.org/content/1/3/140216
Although that paper uses th | Is p-value also the false discovery rate?
The difference between P values and false positive rate (or false discovery rate) is explained, clearly I hope, in http://rsos.royalsocietypublishing.org/content/1/3/140216
Although that paper uses the term False Discovery Rate, I now prefer False Positive Rate, becuse the form... | Is p-value also the false discovery rate?
The difference between P values and false positive rate (or false discovery rate) is explained, clearly I hope, in http://rsos.royalsocietypublishing.org/content/1/3/140216
Although that paper uses th |
35,757 | Missing at Random Data in GEE | ML estimation based on complete cases is not considered efficient and can be horribly biased. Likelihood-based complete case estimation is consistent in general only if the data is MCAR. If data is MAR then you can use something like EM or data augmentation to get efficient likelihood-based estimates. The appropriate l... | Missing at Random Data in GEE | ML estimation based on complete cases is not considered efficient and can be horribly biased. Likelihood-based complete case estimation is consistent in general only if the data is MCAR. If data is MA | Missing at Random Data in GEE
ML estimation based on complete cases is not considered efficient and can be horribly biased. Likelihood-based complete case estimation is consistent in general only if the data is MCAR. If data is MAR then you can use something like EM or data augmentation to get efficient likelihood-base... | Missing at Random Data in GEE
ML estimation based on complete cases is not considered efficient and can be horribly biased. Likelihood-based complete case estimation is consistent in general only if the data is MCAR. If data is MA |
35,758 | Missing at Random Data in GEE | The OP's question, if I am understanding it correctly, is one that still nags me. I'll add my intuition in hopes that others will chime in and provide a resolution. I realize this post is 8 years old, but I don't think it was answered satisfactorily.
It seems guy overlooked your earlier assumption concerning the fact... | Missing at Random Data in GEE | The OP's question, if I am understanding it correctly, is one that still nags me. I'll add my intuition in hopes that others will chime in and provide a resolution. I realize this post is 8 years ol | Missing at Random Data in GEE
The OP's question, if I am understanding it correctly, is one that still nags me. I'll add my intuition in hopes that others will chime in and provide a resolution. I realize this post is 8 years old, but I don't think it was answered satisfactorily.
It seems guy overlooked your earlier ... | Missing at Random Data in GEE
The OP's question, if I am understanding it correctly, is one that still nags me. I'll add my intuition in hopes that others will chime in and provide a resolution. I realize this post is 8 years ol |
35,759 | Check if sample is representative of a larger sample | You could test whether several statistics that are descriptive of a distribution are the same in the subsample and the remaining sample. For example you could conduct tests for:
mean difference
median difference
stochastic dominance
different variance
shape
While you are at it, since you are interested in similarity,... | Check if sample is representative of a larger sample | You could test whether several statistics that are descriptive of a distribution are the same in the subsample and the remaining sample. For example you could conduct tests for:
mean difference
media | Check if sample is representative of a larger sample
You could test whether several statistics that are descriptive of a distribution are the same in the subsample and the remaining sample. For example you could conduct tests for:
mean difference
median difference
stochastic dominance
different variance
shape
While y... | Check if sample is representative of a larger sample
You could test whether several statistics that are descriptive of a distribution are the same in the subsample and the remaining sample. For example you could conduct tests for:
mean difference
media |
35,760 | Check if sample is representative of a larger sample | Since you want to compare the entire distributions, I'd recommend the two sample Kolmogorov-Smirnov test.
More information can be found here:
http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test | Check if sample is representative of a larger sample | Since you want to compare the entire distributions, I'd recommend the two sample Kolmogorov-Smirnov test.
More information can be found here:
http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_ | Check if sample is representative of a larger sample
Since you want to compare the entire distributions, I'd recommend the two sample Kolmogorov-Smirnov test.
More information can be found here:
http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test | Check if sample is representative of a larger sample
Since you want to compare the entire distributions, I'd recommend the two sample Kolmogorov-Smirnov test.
More information can be found here:
http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_ |
35,761 | Understanding the minimization of mean squared error function | Concerning your first question, adding and subtracting is a trick in statistics which is often used to more easily work with certain expressions. By adding and subtracting you do not change your equation but it makes it possible to group certain terms to obtain the result more easily.
For your second question, to make ... | Understanding the minimization of mean squared error function | Concerning your first question, adding and subtracting is a trick in statistics which is often used to more easily work with certain expressions. By adding and subtracting you do not change your equat | Understanding the minimization of mean squared error function
Concerning your first question, adding and subtracting is a trick in statistics which is often used to more easily work with certain expressions. By adding and subtracting you do not change your equation but it makes it possible to group certain terms to obt... | Understanding the minimization of mean squared error function
Concerning your first question, adding and subtracting is a trick in statistics which is often used to more easily work with certain expressions. By adding and subtracting you do not change your equat |
35,762 | Understanding the minimization of mean squared error function | For your second question, you want to show that
$$E\left[ (Y-E(Y|X)(f(X)-E(Y|X))\right]=0.$$
Now, if we look at the first term of the product, if we didn't have a conditional expectation, we would have
$$E(Y-E(Y))=E(Y)-E(Y)=0.$$
But by the Law of Total expectation, we know that
$$E(W)=E(E(W|Z)),$$
so you can actually ... | Understanding the minimization of mean squared error function | For your second question, you want to show that
$$E\left[ (Y-E(Y|X)(f(X)-E(Y|X))\right]=0.$$
Now, if we look at the first term of the product, if we didn't have a conditional expectation, we would ha | Understanding the minimization of mean squared error function
For your second question, you want to show that
$$E\left[ (Y-E(Y|X)(f(X)-E(Y|X))\right]=0.$$
Now, if we look at the first term of the product, if we didn't have a conditional expectation, we would have
$$E(Y-E(Y))=E(Y)-E(Y)=0.$$
But by the Law of Total expe... | Understanding the minimization of mean squared error function
For your second question, you want to show that
$$E\left[ (Y-E(Y|X)(f(X)-E(Y|X))\right]=0.$$
Now, if we look at the first term of the product, if we didn't have a conditional expectation, we would ha |
35,763 | Order of items in a questionnaire | Order certainly can matter. As a simple example, suppose I have two items on my questionnaire, which I could give in two different orders.
(a) Rate your happiness (Very Unhappy, Unhappy, Neutral, Happy, Very Happy)
(b) Are you in a relationship with another person (Yes, No)
If I ask question (b) first, it will like... | Order of items in a questionnaire | Order certainly can matter. As a simple example, suppose I have two items on my questionnaire, which I could give in two different orders.
(a) Rate your happiness (Very Unhappy, Unhappy, Neutral, H | Order of items in a questionnaire
Order certainly can matter. As a simple example, suppose I have two items on my questionnaire, which I could give in two different orders.
(a) Rate your happiness (Very Unhappy, Unhappy, Neutral, Happy, Very Happy)
(b) Are you in a relationship with another person (Yes, No)
If I as... | Order of items in a questionnaire
Order certainly can matter. As a simple example, suppose I have two items on my questionnaire, which I could give in two different orders.
(a) Rate your happiness (Very Unhappy, Unhappy, Neutral, H |
35,764 | Order of items in a questionnaire | It depends on the nature of the questionnaire. For instance, I've read that the first few items in lists that participants rank (e.g., from most to least favorite/true/important/etc.) tend to be ranked higher, presumably due to serial position effects. However, I'm not sure where I read that, and in searching for the r... | Order of items in a questionnaire | It depends on the nature of the questionnaire. For instance, I've read that the first few items in lists that participants rank (e.g., from most to least favorite/true/important/etc.) tend to be ranke | Order of items in a questionnaire
It depends on the nature of the questionnaire. For instance, I've read that the first few items in lists that participants rank (e.g., from most to least favorite/true/important/etc.) tend to be ranked higher, presumably due to serial position effects. However, I'm not sure where I rea... | Order of items in a questionnaire
It depends on the nature of the questionnaire. For instance, I've read that the first few items in lists that participants rank (e.g., from most to least favorite/true/important/etc.) tend to be ranke |
35,765 | Interpret clustering plotted in the first two principal components | Principal components are combinations of features. For example, say you have demographic data consisting of three features: height, weight and income. Then, if height and weight are highly correlated, it might be useful to combine them into a single feature. Principal component analysis (PCA) does this via a weighted l... | Interpret clustering plotted in the first two principal components | Principal components are combinations of features. For example, say you have demographic data consisting of three features: height, weight and income. Then, if height and weight are highly correlated, | Interpret clustering plotted in the first two principal components
Principal components are combinations of features. For example, say you have demographic data consisting of three features: height, weight and income. Then, if height and weight are highly correlated, it might be useful to combine them into a single fea... | Interpret clustering plotted in the first two principal components
Principal components are combinations of features. For example, say you have demographic data consisting of three features: height, weight and income. Then, if height and weight are highly correlated, |
35,766 | What is wrong with this chi-squared calculation? | Your R code thinks you have a 2x2 contingency table for the chi-squared test, whereas your 'by hand' version treats two of your values as the expected values with which to compare the first two values. You need to decide which setup is correct and use it consistently both times.
Here is your R version:
> test ... | What is wrong with this chi-squared calculation? | Your R code thinks you have a 2x2 contingency table for the chi-squared test, whereas your 'by hand' version treats two of your values as the expected values with which to compare the first two values | What is wrong with this chi-squared calculation?
Your R code thinks you have a 2x2 contingency table for the chi-squared test, whereas your 'by hand' version treats two of your values as the expected values with which to compare the first two values. You need to decide which setup is correct and use it consistently bot... | What is wrong with this chi-squared calculation?
Your R code thinks you have a 2x2 contingency table for the chi-squared test, whereas your 'by hand' version treats two of your values as the expected values with which to compare the first two values |
35,767 | Star Coordinates vs. principal component analysis | PCA and "star coordinates" do different things. Because star coordinates standardize all the values, a fair comparison would apply PCA to a correlation matrix (rather than the covariance matrix), which is another way of standardizing the values.
PCA identifies a coordinate system adapted to the shape of the data, whi... | Star Coordinates vs. principal component analysis | PCA and "star coordinates" do different things. Because star coordinates standardize all the values, a fair comparison would apply PCA to a correlation matrix (rather than the covariance matrix), whi | Star Coordinates vs. principal component analysis
PCA and "star coordinates" do different things. Because star coordinates standardize all the values, a fair comparison would apply PCA to a correlation matrix (rather than the covariance matrix), which is another way of standardizing the values.
PCA identifies a coord... | Star Coordinates vs. principal component analysis
PCA and "star coordinates" do different things. Because star coordinates standardize all the values, a fair comparison would apply PCA to a correlation matrix (rather than the covariance matrix), whi |
35,768 | Standard error of proportion that takes into account population size | If you're randomly sampling without replacement from a finite population, you're not in a binomial sampling situation, but a hypergeometric one.
When you're in a binomial situation with population proportion $\pi$, the variance of the count, $X$ is $n\pi(1-\pi)$ and so the variance of the sample proportion $p=X/n$ is $... | Standard error of proportion that takes into account population size | If you're randomly sampling without replacement from a finite population, you're not in a binomial sampling situation, but a hypergeometric one.
When you're in a binomial situation with population pro | Standard error of proportion that takes into account population size
If you're randomly sampling without replacement from a finite population, you're not in a binomial sampling situation, but a hypergeometric one.
When you're in a binomial situation with population proportion $\pi$, the variance of the count, $X$ is $n... | Standard error of proportion that takes into account population size
If you're randomly sampling without replacement from a finite population, you're not in a binomial sampling situation, but a hypergeometric one.
When you're in a binomial situation with population pro |
35,769 | How to compare dbscan clusters / choose epsilon parameter | Inertia is only a sensible measure for spherical clusters. I.e. not for DBSCAN.
Similar reasonings apply for most internal measures: most are designed around centroid-based cluster models, not arbitrarily shaped clusters.
For DBSCAN, a sensible measure would be density-connectedness. But that needs the same parameters ... | How to compare dbscan clusters / choose epsilon parameter | Inertia is only a sensible measure for spherical clusters. I.e. not for DBSCAN.
Similar reasonings apply for most internal measures: most are designed around centroid-based cluster models, not arbitra | How to compare dbscan clusters / choose epsilon parameter
Inertia is only a sensible measure for spherical clusters. I.e. not for DBSCAN.
Similar reasonings apply for most internal measures: most are designed around centroid-based cluster models, not arbitrarily shaped clusters.
For DBSCAN, a sensible measure would be ... | How to compare dbscan clusters / choose epsilon parameter
Inertia is only a sensible measure for spherical clusters. I.e. not for DBSCAN.
Similar reasonings apply for most internal measures: most are designed around centroid-based cluster models, not arbitra |
35,770 | Unbalanced distribution of sample size between groups in logistic regression: should one worry? | You are right that logistic regression does not make any assumptions about the distribution of your independent variable. What will occur as a result of your situation is that you will have less power than if you had equal $n$s. However, reducing the $n$ in the Rich group will only lessen your power further. Rather,... | Unbalanced distribution of sample size between groups in logistic regression: should one worry? | You are right that logistic regression does not make any assumptions about the distribution of your independent variable. What will occur as a result of your situation is that you will have less powe | Unbalanced distribution of sample size between groups in logistic regression: should one worry?
You are right that logistic regression does not make any assumptions about the distribution of your independent variable. What will occur as a result of your situation is that you will have less power than if you had equal ... | Unbalanced distribution of sample size between groups in logistic regression: should one worry?
You are right that logistic regression does not make any assumptions about the distribution of your independent variable. What will occur as a result of your situation is that you will have less powe |
35,771 | Interpreting coefficients of first differences of logarithms | For $small$ changes, you can interpret logged differences as percentage changes after multiplying by 100.
For example, $y_t=9$ and $y_{t-1}=8$. Then $\ln 9 - \ln 8=.118$ or 11.8%, which is the logarithmic approximation to the actual 12.5% increase. Note that I had to multiply by 100 here. For $y_t=9$ and $y_{t-1}=8.5$ ... | Interpreting coefficients of first differences of logarithms | For $small$ changes, you can interpret logged differences as percentage changes after multiplying by 100.
For example, $y_t=9$ and $y_{t-1}=8$. Then $\ln 9 - \ln 8=.118$ or 11.8%, which is the logarit | Interpreting coefficients of first differences of logarithms
For $small$ changes, you can interpret logged differences as percentage changes after multiplying by 100.
For example, $y_t=9$ and $y_{t-1}=8$. Then $\ln 9 - \ln 8=.118$ or 11.8%, which is the logarithmic approximation to the actual 12.5% increase. Note that ... | Interpreting coefficients of first differences of logarithms
For $small$ changes, you can interpret logged differences as percentage changes after multiplying by 100.
For example, $y_t=9$ and $y_{t-1}=8$. Then $\ln 9 - \ln 8=.118$ or 11.8%, which is the logarit |
35,772 | Differences between Dwass-Steel-Critchlow-Fligner and Mann-Whitney U-test for a post-hoc pairwise analysis | There are absolutely differences.
The Mann-Whitney U test (i.e. the rank sum test) is not appropriate as a post hoc test following the omnibus Kruskal-Wallis nonparametric analog to the one-way ANOVA for two reasons:
The rank sum test uses different ranks than those employed in the Kruskal-Wallis test (i.e. in both te... | Differences between Dwass-Steel-Critchlow-Fligner and Mann-Whitney U-test for a post-hoc pairwise an | There are absolutely differences.
The Mann-Whitney U test (i.e. the rank sum test) is not appropriate as a post hoc test following the omnibus Kruskal-Wallis nonparametric analog to the one-way ANOVA | Differences between Dwass-Steel-Critchlow-Fligner and Mann-Whitney U-test for a post-hoc pairwise analysis
There are absolutely differences.
The Mann-Whitney U test (i.e. the rank sum test) is not appropriate as a post hoc test following the omnibus Kruskal-Wallis nonparametric analog to the one-way ANOVA for two reaso... | Differences between Dwass-Steel-Critchlow-Fligner and Mann-Whitney U-test for a post-hoc pairwise an
There are absolutely differences.
The Mann-Whitney U test (i.e. the rank sum test) is not appropriate as a post hoc test following the omnibus Kruskal-Wallis nonparametric analog to the one-way ANOVA |
35,773 | How should I explain the lack of ERROR in a repeated measures ANOVA table using REML? | You solve a "classical ANOVA" (linear model) by means of least squares, this is, partitioning the sums of squares (among explicative factors) and minimizing the residual sum of squares (unexplained variation). An ANOVA table resumes that partition into all components in the model.
In a linear mixed model you are solvin... | How should I explain the lack of ERROR in a repeated measures ANOVA table using REML? | You solve a "classical ANOVA" (linear model) by means of least squares, this is, partitioning the sums of squares (among explicative factors) and minimizing the residual sum of squares (unexplained va | How should I explain the lack of ERROR in a repeated measures ANOVA table using REML?
You solve a "classical ANOVA" (linear model) by means of least squares, this is, partitioning the sums of squares (among explicative factors) and minimizing the residual sum of squares (unexplained variation). An ANOVA table resumes t... | How should I explain the lack of ERROR in a repeated measures ANOVA table using REML?
You solve a "classical ANOVA" (linear model) by means of least squares, this is, partitioning the sums of squares (among explicative factors) and minimizing the residual sum of squares (unexplained va |
35,774 | How should I explain the lack of ERROR in a repeated measures ANOVA table using REML? | ANOVA is a strange word, because it means many different things. When people fit a general linear model with categorical predictors, they often call it ANOVA, and they get sums of squares (including error sums of squares).
From ?anova
When given a single argument it produces a table which tests whether the model terms... | How should I explain the lack of ERROR in a repeated measures ANOVA table using REML? | ANOVA is a strange word, because it means many different things. When people fit a general linear model with categorical predictors, they often call it ANOVA, and they get sums of squares (including e | How should I explain the lack of ERROR in a repeated measures ANOVA table using REML?
ANOVA is a strange word, because it means many different things. When people fit a general linear model with categorical predictors, they often call it ANOVA, and they get sums of squares (including error sums of squares).
From ?anov... | How should I explain the lack of ERROR in a repeated measures ANOVA table using REML?
ANOVA is a strange word, because it means many different things. When people fit a general linear model with categorical predictors, they often call it ANOVA, and they get sums of squares (including e |
35,775 | What is a "good fit" Brier score and Harrell's C Index | Prior CV postings on the matter of GOF measures in generalized linear models:
Find out pseudo R square value for a Logistic Regression analysis
Which pseudo-$R^2$ measure is the one to report for logistic regression (Cox & Snell or Nagelkerke)?
Addressing model uncertainty
Compare classifiers based on AUROC or accuracy... | What is a "good fit" Brier score and Harrell's C Index | Prior CV postings on the matter of GOF measures in generalized linear models:
Find out pseudo R square value for a Logistic Regression analysis
Which pseudo-$R^2$ measure is the one to report for logi | What is a "good fit" Brier score and Harrell's C Index
Prior CV postings on the matter of GOF measures in generalized linear models:
Find out pseudo R square value for a Logistic Regression analysis
Which pseudo-$R^2$ measure is the one to report for logistic regression (Cox & Snell or Nagelkerke)?
Addressing model unc... | What is a "good fit" Brier score and Harrell's C Index
Prior CV postings on the matter of GOF measures in generalized linear models:
Find out pseudo R square value for a Logistic Regression analysis
Which pseudo-$R^2$ measure is the one to report for logi |
35,776 | What is a "good fit" Brier score and Harrell's C Index | It is easier (but still not very easy) to find an acceptable Brier score. In general it's all relative. A model is useful insofar as it is better than alternatives. Now with pure calibration accuracy you can sometimes judge a model to be inadequate no matter the comparitor. | What is a "good fit" Brier score and Harrell's C Index | It is easier (but still not very easy) to find an acceptable Brier score. In general it's all relative. A model is useful insofar as it is better than alternatives. Now with pure calibration accura | What is a "good fit" Brier score and Harrell's C Index
It is easier (but still not very easy) to find an acceptable Brier score. In general it's all relative. A model is useful insofar as it is better than alternatives. Now with pure calibration accuracy you can sometimes judge a model to be inadequate no matter the... | What is a "good fit" Brier score and Harrell's C Index
It is easier (but still not very easy) to find an acceptable Brier score. In general it's all relative. A model is useful insofar as it is better than alternatives. Now with pure calibration accura |
35,777 | Two different formulas for AICc | I wish I understood the paper better, but if you look at Hurvich & Tsai (1989) equation 3, they are defining the AIC itself as:
$$
\textrm{AIC} = n(\log\hat{\sigma}^2 + 1) + 2\left(m + 1\right)
$$
Which, naïvely implies $k = m+1$ and then the Hurvich & Tsai and Anderson et al post 1999 are actually one and the same as
... | Two different formulas for AICc | I wish I understood the paper better, but if you look at Hurvich & Tsai (1989) equation 3, they are defining the AIC itself as:
$$
\textrm{AIC} = n(\log\hat{\sigma}^2 + 1) + 2\left(m + 1\right)
$$
Whi | Two different formulas for AICc
I wish I understood the paper better, but if you look at Hurvich & Tsai (1989) equation 3, they are defining the AIC itself as:
$$
\textrm{AIC} = n(\log\hat{\sigma}^2 + 1) + 2\left(m + 1\right)
$$
Which, naïvely implies $k = m+1$ and then the Hurvich & Tsai and Anderson et al post 1999 a... | Two different formulas for AICc
I wish I understood the paper better, but if you look at Hurvich & Tsai (1989) equation 3, they are defining the AIC itself as:
$$
\textrm{AIC} = n(\log\hat{\sigma}^2 + 1) + 2\left(m + 1\right)
$$
Whi |
35,778 | What is a better way to construct a confidence interval for the probability of success in binomial distributions? | The wikipedia page on binomial distributions has several measures of confidence intervals. In R, they, and others, are implemented in the binom.confint command in the binom package. There are costs and benefits to them all. You should look into them further and select the one you like the best.
Now that I've given th... | What is a better way to construct a confidence interval for the probability of success in binomial d | The wikipedia page on binomial distributions has several measures of confidence intervals. In R, they, and others, are implemented in the binom.confint command in the binom package. There are costs a | What is a better way to construct a confidence interval for the probability of success in binomial distributions?
The wikipedia page on binomial distributions has several measures of confidence intervals. In R, they, and others, are implemented in the binom.confint command in the binom package. There are costs and ben... | What is a better way to construct a confidence interval for the probability of success in binomial d
The wikipedia page on binomial distributions has several measures of confidence intervals. In R, they, and others, are implemented in the binom.confint command in the binom package. There are costs a |
35,779 | What is a better way to construct a confidence interval for the probability of success in binomial distributions? | There's a neat little article published decades ago in JAMA entitled "If nothing goes wrong, is everything all right?". The authors considered the possibilities of a binomial parameter being in a variety of "locations": and derived the probabilities of zero outcomes out of N integer instances under varying sample sizes... | What is a better way to construct a confidence interval for the probability of success in binomial d | There's a neat little article published decades ago in JAMA entitled "If nothing goes wrong, is everything all right?". The authors considered the possibilities of a binomial parameter being in a vari | What is a better way to construct a confidence interval for the probability of success in binomial distributions?
There's a neat little article published decades ago in JAMA entitled "If nothing goes wrong, is everything all right?". The authors considered the possibilities of a binomial parameter being in a variety of... | What is a better way to construct a confidence interval for the probability of success in binomial d
There's a neat little article published decades ago in JAMA entitled "If nothing goes wrong, is everything all right?". The authors considered the possibilities of a binomial parameter being in a vari |
35,780 | Why is dependence a problem? | The p-value for the t-test is computed under the assumption that all observations are independent. Computing probabilities (such as the p-value) is much more difficult when you're dealing with dependent variables, and it is not always easy to see mathematically where things go wrong with the test in the presence of dep... | Why is dependence a problem? | The p-value for the t-test is computed under the assumption that all observations are independent. Computing probabilities (such as the p-value) is much more difficult when you're dealing with depende | Why is dependence a problem?
The p-value for the t-test is computed under the assumption that all observations are independent. Computing probabilities (such as the p-value) is much more difficult when you're dealing with dependent variables, and it is not always easy to see mathematically where things go wrong with th... | Why is dependence a problem?
The p-value for the t-test is computed under the assumption that all observations are independent. Computing probabilities (such as the p-value) is much more difficult when you're dealing with depende |
35,781 | Why is dependence a problem? | The problem would be that comparing the two schools this way mixes university level effects with classroom level effects. A mixed model would let you disentangle these. If you aren't interested in disentangling them, you should still take account of the clustered sampling (although many people fail to do this).
@Nico '... | Why is dependence a problem? | The problem would be that comparing the two schools this way mixes university level effects with classroom level effects. A mixed model would let you disentangle these. If you aren't interested in dis | Why is dependence a problem?
The problem would be that comparing the two schools this way mixes university level effects with classroom level effects. A mixed model would let you disentangle these. If you aren't interested in disentangling them, you should still take account of the clustered sampling (although many peo... | Why is dependence a problem?
The problem would be that comparing the two schools this way mixes university level effects with classroom level effects. A mixed model would let you disentangle these. If you aren't interested in dis |
35,782 | Why is dependence a problem? | There is nothing wrong with the test you described because you took a sample from both schools in a fair way. Dependent observations come into play when there is another variable on which the samples depend. I.e., in one of the schools only one class has shown up and you decided to take results from 50 people within th... | Why is dependence a problem? | There is nothing wrong with the test you described because you took a sample from both schools in a fair way. Dependent observations come into play when there is another variable on which the samples | Why is dependence a problem?
There is nothing wrong with the test you described because you took a sample from both schools in a fair way. Dependent observations come into play when there is another variable on which the samples depend. I.e., in one of the schools only one class has shown up and you decided to take res... | Why is dependence a problem?
There is nothing wrong with the test you described because you took a sample from both schools in a fair way. Dependent observations come into play when there is another variable on which the samples |
35,783 | Estimate multinomial probit model with mlogit (R package) | The run with probit=TRUE has not converged to a good answer. See the line in the output that starts with 'last step could not find higher value' and compare the same section in the logit model output. The other reason it takes so long to fit the probit model is that the software is approximating a high dimensional inte... | Estimate multinomial probit model with mlogit (R package) | The run with probit=TRUE has not converged to a good answer. See the line in the output that starts with 'last step could not find higher value' and compare the same section in the logit model output. | Estimate multinomial probit model with mlogit (R package)
The run with probit=TRUE has not converged to a good answer. See the line in the output that starts with 'last step could not find higher value' and compare the same section in the logit model output. The other reason it takes so long to fit the probit model is ... | Estimate multinomial probit model with mlogit (R package)
The run with probit=TRUE has not converged to a good answer. See the line in the output that starts with 'last step could not find higher value' and compare the same section in the logit model output. |
35,784 | Estimate multinomial probit model with mlogit (R package) | Probit models often take longer to fit because the likelihood function is calculated by simulation or quadrature. The logit likelihood has a closed form solution that makes it fast.
Also, the Probit likelihood function is not globally convex, so the algorithm can converge to local maxima. You need to try different star... | Estimate multinomial probit model with mlogit (R package) | Probit models often take longer to fit because the likelihood function is calculated by simulation or quadrature. The logit likelihood has a closed form solution that makes it fast.
Also, the Probit l | Estimate multinomial probit model with mlogit (R package)
Probit models often take longer to fit because the likelihood function is calculated by simulation or quadrature. The logit likelihood has a closed form solution that makes it fast.
Also, the Probit likelihood function is not globally convex, so the algorithm ca... | Estimate multinomial probit model with mlogit (R package)
Probit models often take longer to fit because the likelihood function is calculated by simulation or quadrature. The logit likelihood has a closed form solution that makes it fast.
Also, the Probit l |
35,785 | ML with fastest classification speed | Support Vector Machines classify new vectors by comparing them against the set of support vectors. Depending on what parameters you used and the cost function, this set of support vectors might be large. For more than two classes, the number of SVMs needed increases as well, further reducing performance. For better run... | ML with fastest classification speed | Support Vector Machines classify new vectors by comparing them against the set of support vectors. Depending on what parameters you used and the cost function, this set of support vectors might be lar | ML with fastest classification speed
Support Vector Machines classify new vectors by comparing them against the set of support vectors. Depending on what parameters you used and the cost function, this set of support vectors might be large. For more than two classes, the number of SVMs needed increases as well, further... | ML with fastest classification speed
Support Vector Machines classify new vectors by comparing them against the set of support vectors. Depending on what parameters you used and the cost function, this set of support vectors might be lar |
35,786 | ML with fastest classification speed | I would recommend trying Random Ferns -- they are easy to implement, fast to train and even faster to predict, and due to ensemble structure you can easily control their speed/quality balance. Oh, and they are trivially parallel.
They may have problems with accuracy and memory consuption, though; but this depends on th... | ML with fastest classification speed | I would recommend trying Random Ferns -- they are easy to implement, fast to train and even faster to predict, and due to ensemble structure you can easily control their speed/quality balance. Oh, and | ML with fastest classification speed
I would recommend trying Random Ferns -- they are easy to implement, fast to train and even faster to predict, and due to ensemble structure you can easily control their speed/quality balance. Oh, and they are trivially parallel.
They may have problems with accuracy and memory consu... | ML with fastest classification speed
I would recommend trying Random Ferns -- they are easy to implement, fast to train and even faster to predict, and due to ensemble structure you can easily control their speed/quality balance. Oh, and |
35,787 | Profile likelihood confidence intervals | Very good question.
In this link it is explained that SAS uses a numerical approximation (which basically consists of a modification of the Newton-Raphson algorithm)
Setting this option to both produces two sets of CL, based on the Wald test and on the profile-likelihood approach. (Venzon, D. J. and Moolgavkar, S. H.... | Profile likelihood confidence intervals | Very good question.
In this link it is explained that SAS uses a numerical approximation (which basically consists of a modification of the Newton-Raphson algorithm)
Setting this option to both prod | Profile likelihood confidence intervals
Very good question.
In this link it is explained that SAS uses a numerical approximation (which basically consists of a modification of the Newton-Raphson algorithm)
Setting this option to both produces two sets of CL, based on the Wald test and on the profile-likelihood approa... | Profile likelihood confidence intervals
Very good question.
In this link it is explained that SAS uses a numerical approximation (which basically consists of a modification of the Newton-Raphson algorithm)
Setting this option to both prod |
35,788 | Pocket algorithm for training perceptrons | It's discussed a little more fully in the neural networks book of Rojas, which is available from his website. I believe the book also contains a reference to the original paper which introduced the algorithm.
http://www.inf.fu-berlin.de/inst/ag-ki/rojas_home/pmwiki/pmwiki.php?n=Books.NeuralNetworksBook
Edit: yes, here ... | Pocket algorithm for training perceptrons | It's discussed a little more fully in the neural networks book of Rojas, which is available from his website. I believe the book also contains a reference to the original paper which introduced the al | Pocket algorithm for training perceptrons
It's discussed a little more fully in the neural networks book of Rojas, which is available from his website. I believe the book also contains a reference to the original paper which introduced the algorithm.
http://www.inf.fu-berlin.de/inst/ag-ki/rojas_home/pmwiki/pmwiki.php?n... | Pocket algorithm for training perceptrons
It's discussed a little more fully in the neural networks book of Rojas, which is available from his website. I believe the book also contains a reference to the original paper which introduced the al |
35,789 | Pocket algorithm for training perceptrons | Basically the pocket algorithm is a perceptron learning algorithm with a memory which keeps the result of the iteration. You can consider the pocket algorithm something similar to:
def pocket(training_list, max_iteration):
w = randomVector()
best_error = error(w)
for i in range(0, max_iteration):
x=... | Pocket algorithm for training perceptrons | Basically the pocket algorithm is a perceptron learning algorithm with a memory which keeps the result of the iteration. You can consider the pocket algorithm something similar to:
def pocket(training | Pocket algorithm for training perceptrons
Basically the pocket algorithm is a perceptron learning algorithm with a memory which keeps the result of the iteration. You can consider the pocket algorithm something similar to:
def pocket(training_list, max_iteration):
w = randomVector()
best_error = error(w)
fo... | Pocket algorithm for training perceptrons
Basically the pocket algorithm is a perceptron learning algorithm with a memory which keeps the result of the iteration. You can consider the pocket algorithm something similar to:
def pocket(training |
35,790 | Pocket algorithm for training perceptrons | I have found the blog very helpful to understand Pocket Algorithm. I am giving excerpt from that blog.
Pocket Learning Algorithm
The idea is straightforward: this algorithm keeps the best result seen so far in its pocket (that is why it is called Pocket Learning Algorithm). The best result means the number of misclassi... | Pocket algorithm for training perceptrons | I have found the blog very helpful to understand Pocket Algorithm. I am giving excerpt from that blog.
Pocket Learning Algorithm
The idea is straightforward: this algorithm keeps the best result seen | Pocket algorithm for training perceptrons
I have found the blog very helpful to understand Pocket Algorithm. I am giving excerpt from that blog.
Pocket Learning Algorithm
The idea is straightforward: this algorithm keeps the best result seen so far in its pocket (that is why it is called Pocket Learning Algorithm). The... | Pocket algorithm for training perceptrons
I have found the blog very helpful to understand Pocket Algorithm. I am giving excerpt from that blog.
Pocket Learning Algorithm
The idea is straightforward: this algorithm keeps the best result seen |
35,791 | how to calculate partial dependence when I have 4 predictors? | Suppose that we have a data set $X = [x_s \, x_c] \in \mathbb R^{n \times p}$ where $x_s$ is a matrix of variables we want to know the partial dependencies for and $x_c$ is a matrix of the remaining predictors. Let $y \in \mathbb R$ be a vector of responses (i.e. a regression problem). Suppose that $y = f(x) + \epsilon... | how to calculate partial dependence when I have 4 predictors? | Suppose that we have a data set $X = [x_s \, x_c] \in \mathbb R^{n \times p}$ where $x_s$ is a matrix of variables we want to know the partial dependencies for and $x_c$ is a matrix of the remaining p | how to calculate partial dependence when I have 4 predictors?
Suppose that we have a data set $X = [x_s \, x_c] \in \mathbb R^{n \times p}$ where $x_s$ is a matrix of variables we want to know the partial dependencies for and $x_c$ is a matrix of the remaining predictors. Let $y \in \mathbb R$ be a vector of responses ... | how to calculate partial dependence when I have 4 predictors?
Suppose that we have a data set $X = [x_s \, x_c] \in \mathbb R^{n \times p}$ where $x_s$ is a matrix of variables we want to know the partial dependencies for and $x_c$ is a matrix of the remaining p |
35,792 | Sampling with or without replacement? | From finite population perspective, the difference in variances of the sample means or totals obtained via sampling with replacement (SRSWR) and sampling without replacement (SRSWOR) is captured by the finite population correction (FPC):
$$
\mathbb{V}_{\rm SRSWOR}[\bar y] = \Bigl( 1 - \frac{n}{N}\Bigr) \mathbb{V}_{\rm... | Sampling with or without replacement? | From finite population perspective, the difference in variances of the sample means or totals obtained via sampling with replacement (SRSWR) and sampling without replacement (SRSWOR) is captured by th | Sampling with or without replacement?
From finite population perspective, the difference in variances of the sample means or totals obtained via sampling with replacement (SRSWR) and sampling without replacement (SRSWOR) is captured by the finite population correction (FPC):
$$
\mathbb{V}_{\rm SRSWOR}[\bar y] = \Bigl( ... | Sampling with or without replacement?
From finite population perspective, the difference in variances of the sample means or totals obtained via sampling with replacement (SRSWR) and sampling without replacement (SRSWOR) is captured by th |
35,793 | Sampling with or without replacement? | the answer is very simple, the difference between Replace=T and Replace=F. When we draw random records or rows from a sample. When we add the argument Replace=T, meaning, suppose we draw 5 records randomly from a sample. After drawing those records, we replace those back to sample for next draw. And in case of Replace=... | Sampling with or without replacement? | the answer is very simple, the difference between Replace=T and Replace=F. When we draw random records or rows from a sample. When we add the argument Replace=T, meaning, suppose we draw 5 records ran | Sampling with or without replacement?
the answer is very simple, the difference between Replace=T and Replace=F. When we draw random records or rows from a sample. When we add the argument Replace=T, meaning, suppose we draw 5 records randomly from a sample. After drawing those records, we replace those back to sample ... | Sampling with or without replacement?
the answer is very simple, the difference between Replace=T and Replace=F. When we draw random records or rows from a sample. When we add the argument Replace=T, meaning, suppose we draw 5 records ran |
35,794 | Does Pearson correlation require removal of bivariate or univariate outliers? | You will have to remove both. But that will not be enough. You will also have to remove those observations that are outlying on any projections of your data along any direction in $\mathbb{R}^2$. This is because of so-called multivariate outliers.
It is possible for outliers to depart significantly from the pattern of ... | Does Pearson correlation require removal of bivariate or univariate outliers? | You will have to remove both. But that will not be enough. You will also have to remove those observations that are outlying on any projections of your data along any direction in $\mathbb{R}^2$. This | Does Pearson correlation require removal of bivariate or univariate outliers?
You will have to remove both. But that will not be enough. You will also have to remove those observations that are outlying on any projections of your data along any direction in $\mathbb{R}^2$. This is because of so-called multivariate outl... | Does Pearson correlation require removal of bivariate or univariate outliers?
You will have to remove both. But that will not be enough. You will also have to remove those observations that are outlying on any projections of your data along any direction in $\mathbb{R}^2$. This |
35,795 | How to validate & diagnose a gamma GLM in R? | -Look at Chapter 6 or Section 6.3.4 in the book "Statistical Models in S" by Chambers and Hastie. Also you many want to check the package boot and function "glm.diag.plots" (Diagnostics plots for generalized linear models). Here are some code with gamma family and the plots from the help file.
library(boot)
data(leuk,... | How to validate & diagnose a gamma GLM in R? | -Look at Chapter 6 or Section 6.3.4 in the book "Statistical Models in S" by Chambers and Hastie. Also you many want to check the package boot and function "glm.diag.plots" (Diagnostics plots for gen | How to validate & diagnose a gamma GLM in R?
-Look at Chapter 6 or Section 6.3.4 in the book "Statistical Models in S" by Chambers and Hastie. Also you many want to check the package boot and function "glm.diag.plots" (Diagnostics plots for generalized linear models). Here are some code with gamma family and the plots... | How to validate & diagnose a gamma GLM in R?
-Look at Chapter 6 or Section 6.3.4 in the book "Statistical Models in S" by Chambers and Hastie. Also you many want to check the package boot and function "glm.diag.plots" (Diagnostics plots for gen |
35,796 | Algebra for data confidence | [I note that there's some lack of clarity in the question; confidence intervals apply to things like parameters, as well as means or other functions of parameters; if we're talking about intervals for data that would be other kinds of interval (prediction intervals, tolerance intervals and so on). I'll proceed as if we... | Algebra for data confidence | [I note that there's some lack of clarity in the question; confidence intervals apply to things like parameters, as well as means or other functions of parameters; if we're talking about intervals for | Algebra for data confidence
[I note that there's some lack of clarity in the question; confidence intervals apply to things like parameters, as well as means or other functions of parameters; if we're talking about intervals for data that would be other kinds of interval (prediction intervals, tolerance intervals and s... | Algebra for data confidence
[I note that there's some lack of clarity in the question; confidence intervals apply to things like parameters, as well as means or other functions of parameters; if we're talking about intervals for |
35,797 | Algebra for data confidence | I don't know if I would describe it as a special algebra per se, but the essential idea you are getting at is the Central Limit Theorem. The CLT is, in fact, one of the cornerstones of statistics. Although we usually discuss the CLT in terms of the mean, there is an obvious connection between the mean of a set of num... | Algebra for data confidence | I don't know if I would describe it as a special algebra per se, but the essential idea you are getting at is the Central Limit Theorem. The CLT is, in fact, one of the cornerstones of statistics. A | Algebra for data confidence
I don't know if I would describe it as a special algebra per se, but the essential idea you are getting at is the Central Limit Theorem. The CLT is, in fact, one of the cornerstones of statistics. Although we usually discuss the CLT in terms of the mean, there is an obvious connection betw... | Algebra for data confidence
I don't know if I would describe it as a special algebra per se, but the essential idea you are getting at is the Central Limit Theorem. The CLT is, in fact, one of the cornerstones of statistics. A |
35,798 | Clear description of PCA using SVD of covariance matrix | What are dimensions of $U$, $S$ and $V^T$?
Since $\Sigma$ is a M by M matrix, the three matrices $U$, $S$, $V^T$ wil be all M by M matrices. Because applying SVD on a N by M matrix, you will get $U_{N{\times}N}$, $S_{N{\times}M}$, and $V^T_{M{\times}M}$. You can verify that in matlab. When you truncate the singular va... | Clear description of PCA using SVD of covariance matrix | What are dimensions of $U$, $S$ and $V^T$?
Since $\Sigma$ is a M by M matrix, the three matrices $U$, $S$, $V^T$ wil be all M by M matrices. Because applying SVD on a N by M matrix, you will get $U_{ | Clear description of PCA using SVD of covariance matrix
What are dimensions of $U$, $S$ and $V^T$?
Since $\Sigma$ is a M by M matrix, the three matrices $U$, $S$, $V^T$ wil be all M by M matrices. Because applying SVD on a N by M matrix, you will get $U_{N{\times}N}$, $S_{N{\times}M}$, and $V^T_{M{\times}M}$. You can ... | Clear description of PCA using SVD of covariance matrix
What are dimensions of $U$, $S$ and $V^T$?
Since $\Sigma$ is a M by M matrix, the three matrices $U$, $S$, $V^T$ wil be all M by M matrices. Because applying SVD on a N by M matrix, you will get $U_{ |
35,799 | p-value as a distance? | A specific case, where the p-values are generated from $\chi ^2$ tests over frequency tables were used as similarities and multidimensional scaling was applied in this paper:
http://www.biomedcentral.com/content/pdf/1748-7188-1-10.pdf | p-value as a distance? | A specific case, where the p-values are generated from $\chi ^2$ tests over frequency tables were used as similarities and multidimensional scaling was applied in this paper:
http://www.biomedcentral | p-value as a distance?
A specific case, where the p-values are generated from $\chi ^2$ tests over frequency tables were used as similarities and multidimensional scaling was applied in this paper:
http://www.biomedcentral.com/content/pdf/1748-7188-1-10.pdf | p-value as a distance?
A specific case, where the p-values are generated from $\chi ^2$ tests over frequency tables were used as similarities and multidimensional scaling was applied in this paper:
http://www.biomedcentral |
35,800 | p-value as a distance? | If all the "true distances" are 0, then the p-values will follow a uniform distribution and would just be random, incorrect distances.
If the true distances are not 0 then you still have scaling issues where a test statisic may be more meaningful. P-values of 0.9 and 0.6 are not very different in interpretation while ... | p-value as a distance? | If all the "true distances" are 0, then the p-values will follow a uniform distribution and would just be random, incorrect distances.
If the true distances are not 0 then you still have scaling issue | p-value as a distance?
If all the "true distances" are 0, then the p-values will follow a uniform distribution and would just be random, incorrect distances.
If the true distances are not 0 then you still have scaling issues where a test statisic may be more meaningful. P-values of 0.9 and 0.6 are not very different i... | p-value as a distance?
If all the "true distances" are 0, then the p-values will follow a uniform distribution and would just be random, incorrect distances.
If the true distances are not 0 then you still have scaling issue |
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