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 |
|---|---|---|---|---|---|---|
36,701 | The right distance for the clustering. Maybe Mahalanobis? | The distance measure you use for cluster analysis should depend on your data. For example, in Ecology we frequently use data on species presence/absence/abundance of ecological communities, and use distance (i.e., similarity) measures such as the Sorensen and Bray-Curtis measures.
There should not be anything specifica... | The right distance for the clustering. Maybe Mahalanobis? | The distance measure you use for cluster analysis should depend on your data. For example, in Ecology we frequently use data on species presence/absence/abundance of ecological communities, and use di | The right distance for the clustering. Maybe Mahalanobis?
The distance measure you use for cluster analysis should depend on your data. For example, in Ecology we frequently use data on species presence/absence/abundance of ecological communities, and use distance (i.e., similarity) measures such as the Sorensen and Br... | The right distance for the clustering. Maybe Mahalanobis?
The distance measure you use for cluster analysis should depend on your data. For example, in Ecology we frequently use data on species presence/absence/abundance of ecological communities, and use di |
36,702 | The right distance for the clustering. Maybe Mahalanobis? | Maybe have a look at correlation clustering, which is meant to find clusters that have a non-spherical shape.
If you want to give Mahalanobis a try, note that Gaussian Mixture Model EM clustering does use Mahalanobis distance. | The right distance for the clustering. Maybe Mahalanobis? | Maybe have a look at correlation clustering, which is meant to find clusters that have a non-spherical shape.
If you want to give Mahalanobis a try, note that Gaussian Mixture Model EM clustering doe | The right distance for the clustering. Maybe Mahalanobis?
Maybe have a look at correlation clustering, which is meant to find clusters that have a non-spherical shape.
If you want to give Mahalanobis a try, note that Gaussian Mixture Model EM clustering does use Mahalanobis distance. | The right distance for the clustering. Maybe Mahalanobis?
Maybe have a look at correlation clustering, which is meant to find clusters that have a non-spherical shape.
If you want to give Mahalanobis a try, note that Gaussian Mixture Model EM clustering doe |
36,703 | About linear combinations of independent Brownian motions | The sum of two independent normal random variables is normal. Therefore, for a given fixed $t$,
$$
\frac{(B(t)+W(t))-(B(0)+W(0))}{\sqrt{2}} \sim \mathcal N(0,\sqrt{t}) \>,
$$
i.e., a normal distribution with mean zero and standard deviation $\sqrt{t}$; here the starting values are known.
Furthermore, independence of ... | About linear combinations of independent Brownian motions | The sum of two independent normal random variables is normal. Therefore, for a given fixed $t$,
$$
\frac{(B(t)+W(t))-(B(0)+W(0))}{\sqrt{2}} \sim \mathcal N(0,\sqrt{t}) \>,
$$
i.e., a normal distribut | About linear combinations of independent Brownian motions
The sum of two independent normal random variables is normal. Therefore, for a given fixed $t$,
$$
\frac{(B(t)+W(t))-(B(0)+W(0))}{\sqrt{2}} \sim \mathcal N(0,\sqrt{t}) \>,
$$
i.e., a normal distribution with mean zero and standard deviation $\sqrt{t}$; here the... | About linear combinations of independent Brownian motions
The sum of two independent normal random variables is normal. Therefore, for a given fixed $t$,
$$
\frac{(B(t)+W(t))-(B(0)+W(0))}{\sqrt{2}} \sim \mathcal N(0,\sqrt{t}) \>,
$$
i.e., a normal distribut |
36,704 | Jeffreys prior for continuous uniform distribution | I think the other answer is wrong, so will give a detailed development here. First, let $X_1, \dotsc, X_n$ be iid uniform on the interval $(0,\theta)$. Then the likelihood function can be written as
$$
L(\theta)= \theta^{-n} \cdot \mathbb{1}(\theta \ge T)
$$ where $T=\max(X_1, \dotsc, X_n)$ is the sufficient statis... | Jeffreys prior for continuous uniform distribution | I think the other answer is wrong, so will give a detailed development here. First, let $X_1, \dotsc, X_n$ be iid uniform on the interval $(0,\theta)$. Then the likelihood function can be written as
| Jeffreys prior for continuous uniform distribution
I think the other answer is wrong, so will give a detailed development here. First, let $X_1, \dotsc, X_n$ be iid uniform on the interval $(0,\theta)$. Then the likelihood function can be written as
$$
L(\theta)= \theta^{-n} \cdot \mathbb{1}(\theta \ge T)
$$ where ... | Jeffreys prior for continuous uniform distribution
I think the other answer is wrong, so will give a detailed development here. First, let $X_1, \dotsc, X_n$ be iid uniform on the interval $(0,\theta)$. Then the likelihood function can be written as
|
36,705 | Jeffreys prior for continuous uniform distribution | The Jeffreys prior for $\theta$ doesn't depend upon the indicator function, although of course the posterior will. The square root of the second derivative of the log likelihood function is all you need:
$p(\theta) = \left(-\frac{\text{d}^2(\log \theta)}{\text{d}\theta^2}\right)^{1/2}$
When moving on to the posterior... | Jeffreys prior for continuous uniform distribution | The Jeffreys prior for $\theta$ doesn't depend upon the indicator function, although of course the posterior will. The square root of the second derivative of the log likelihood function is all you n | Jeffreys prior for continuous uniform distribution
The Jeffreys prior for $\theta$ doesn't depend upon the indicator function, although of course the posterior will. The square root of the second derivative of the log likelihood function is all you need:
$p(\theta) = \left(-\frac{\text{d}^2(\log \theta)}{\text{d}\the... | Jeffreys prior for continuous uniform distribution
The Jeffreys prior for $\theta$ doesn't depend upon the indicator function, although of course the posterior will. The square root of the second derivative of the log likelihood function is all you n |
36,706 | How to figure out what numbers often appear together in a dataset? | This question calls for a modification of the solution to a sequence counting problem: as noted in comments, it requests a cross-tabulation of co-occurrences of values.
I will illustrate a naive but effective modification with R code. First, let's introduce a small sample dataset to work with. It's in the usual matri... | How to figure out what numbers often appear together in a dataset? | This question calls for a modification of the solution to a sequence counting problem: as noted in comments, it requests a cross-tabulation of co-occurrences of values.
I will illustrate a naive but e | How to figure out what numbers often appear together in a dataset?
This question calls for a modification of the solution to a sequence counting problem: as noted in comments, it requests a cross-tabulation of co-occurrences of values.
I will illustrate a naive but effective modification with R code. First, let's intr... | How to figure out what numbers often appear together in a dataset?
This question calls for a modification of the solution to a sequence counting problem: as noted in comments, it requests a cross-tabulation of co-occurrences of values.
I will illustrate a naive but e |
36,707 | How to figure out what numbers often appear together in a dataset? | You are not looking for clustering.
Instead, you are looking for frequent itemset mining. There are dozens of algorithms for this, the most widely known probably are APRIORI, FP-Growth and Eclat. | How to figure out what numbers often appear together in a dataset? | You are not looking for clustering.
Instead, you are looking for frequent itemset mining. There are dozens of algorithms for this, the most widely known probably are APRIORI, FP-Growth and Eclat. | How to figure out what numbers often appear together in a dataset?
You are not looking for clustering.
Instead, you are looking for frequent itemset mining. There are dozens of algorithms for this, the most widely known probably are APRIORI, FP-Growth and Eclat. | How to figure out what numbers often appear together in a dataset?
You are not looking for clustering.
Instead, you are looking for frequent itemset mining. There are dozens of algorithms for this, the most widely known probably are APRIORI, FP-Growth and Eclat. |
36,708 | How to figure out what numbers often appear together in a dataset? | I use a simple Excel spreadsheet and load all the drawings and then do a data sort. When you do a data sort you can learn quickly which numbers will never and have never played together. I've also written Macros that can run pairs and 3 pairs. | How to figure out what numbers often appear together in a dataset? | I use a simple Excel spreadsheet and load all the drawings and then do a data sort. When you do a data sort you can learn quickly which numbers will never and have never played together. I've also w | How to figure out what numbers often appear together in a dataset?
I use a simple Excel spreadsheet and load all the drawings and then do a data sort. When you do a data sort you can learn quickly which numbers will never and have never played together. I've also written Macros that can run pairs and 3 pairs. | How to figure out what numbers often appear together in a dataset?
I use a simple Excel spreadsheet and load all the drawings and then do a data sort. When you do a data sort you can learn quickly which numbers will never and have never played together. I've also w |
36,709 | Missing data at random | You can't tell, absolutely, at least, not from statistics.
You can compare the cases that are missing to those that are not missing on any variables that are present in both, but there still could be other things that aren't in the data set. For a simple example, suppose your data set consists only of two variables "ra... | Missing data at random | You can't tell, absolutely, at least, not from statistics.
You can compare the cases that are missing to those that are not missing on any variables that are present in both, but there still could be | Missing data at random
You can't tell, absolutely, at least, not from statistics.
You can compare the cases that are missing to those that are not missing on any variables that are present in both, but there still could be other things that aren't in the data set. For a simple example, suppose your data set consists on... | Missing data at random
You can't tell, absolutely, at least, not from statistics.
You can compare the cases that are missing to those that are not missing on any variables that are present in both, but there still could be |
36,710 | Derivation of the Satterthwaite appproximation | Background: Understanding the method of moments (MoM) in a basic way
Motivation for the method: The (strong) Law of Large Numbers (LLN) gives us reason to think that (at least for large samples), a sample expectation will be close to the population expectation (note that the LLN applies to higher moments by taking $Z=X... | Derivation of the Satterthwaite appproximation | Background: Understanding the method of moments (MoM) in a basic way
Motivation for the method: The (strong) Law of Large Numbers (LLN) gives us reason to think that (at least for large samples), a sa | Derivation of the Satterthwaite appproximation
Background: Understanding the method of moments (MoM) in a basic way
Motivation for the method: The (strong) Law of Large Numbers (LLN) gives us reason to think that (at least for large samples), a sample expectation will be close to the population expectation (note that t... | Derivation of the Satterthwaite appproximation
Background: Understanding the method of moments (MoM) in a basic way
Motivation for the method: The (strong) Law of Large Numbers (LLN) gives us reason to think that (at least for large samples), a sa |
36,711 | Derivation of the Satterthwaite appproximation | As pointed out patiently by Glen_b above, since $X_{i}$ is an independent random sample, we have $$E(\sum a_{i}Y_{i})=\sum a_{i}E(Y_{i})=\sum a_{i} Y_{i}$$where the last equation $$E(Y_{i})=Y_{i}$$ follows from the fact that from the definition of method of moments we have $$E(X)=\frac{\sum X_{i}}{n}=\overline{X}=X \te... | Derivation of the Satterthwaite appproximation | As pointed out patiently by Glen_b above, since $X_{i}$ is an independent random sample, we have $$E(\sum a_{i}Y_{i})=\sum a_{i}E(Y_{i})=\sum a_{i} Y_{i}$$where the last equation $$E(Y_{i})=Y_{i}$$ fo | Derivation of the Satterthwaite appproximation
As pointed out patiently by Glen_b above, since $X_{i}$ is an independent random sample, we have $$E(\sum a_{i}Y_{i})=\sum a_{i}E(Y_{i})=\sum a_{i} Y_{i}$$where the last equation $$E(Y_{i})=Y_{i}$$ follows from the fact that from the definition of method of moments we have... | Derivation of the Satterthwaite appproximation
As pointed out patiently by Glen_b above, since $X_{i}$ is an independent random sample, we have $$E(\sum a_{i}Y_{i})=\sum a_{i}E(Y_{i})=\sum a_{i} Y_{i}$$where the last equation $$E(Y_{i})=Y_{i}$$ fo |
36,712 | Adverse results of clustering criteria | The question you should ask yourself is this: what do you want to achieve.
All these criteria are nothing but heuristics. You judge the result of one mathematical optimization technique by yet another mathematical function. This does not actually measure if the result is good, but just whether the data fits to certain ... | Adverse results of clustering criteria | The question you should ask yourself is this: what do you want to achieve.
All these criteria are nothing but heuristics. You judge the result of one mathematical optimization technique by yet another | Adverse results of clustering criteria
The question you should ask yourself is this: what do you want to achieve.
All these criteria are nothing but heuristics. You judge the result of one mathematical optimization technique by yet another mathematical function. This does not actually measure if the result is good, but... | Adverse results of clustering criteria
The question you should ask yourself is this: what do you want to achieve.
All these criteria are nothing but heuristics. You judge the result of one mathematical optimization technique by yet another |
36,713 | Adverse results of clustering criteria | Longitude and latitude are angles which define points on a sphere so you should probably be looking at the Great Circle Distance or other geodesic distances between points rather than the Euclidean distance.
Also as has been mentioned, certain explicitly model-based clustering algorithms like mixture models and implici... | Adverse results of clustering criteria | Longitude and latitude are angles which define points on a sphere so you should probably be looking at the Great Circle Distance or other geodesic distances between points rather than the Euclidean di | Adverse results of clustering criteria
Longitude and latitude are angles which define points on a sphere so you should probably be looking at the Great Circle Distance or other geodesic distances between points rather than the Euclidean distance.
Also as has been mentioned, certain explicitly model-based clustering alg... | Adverse results of clustering criteria
Longitude and latitude are angles which define points on a sphere so you should probably be looking at the Great Circle Distance or other geodesic distances between points rather than the Euclidean di |
36,714 | Difference between independent and non-informative censoring | The first set of definitions seem right to me.
Your adviser's definition two seems to be a conflation of independent and non-informative censoring assumptions. I haven't seen non-informative censoring defined before with reference to the covariate profile.
The following text is from "Survival analysis: A self-learning ... | Difference between independent and non-informative censoring | The first set of definitions seem right to me.
Your adviser's definition two seems to be a conflation of independent and non-informative censoring assumptions. I haven't seen non-informative censoring | Difference between independent and non-informative censoring
The first set of definitions seem right to me.
Your adviser's definition two seems to be a conflation of independent and non-informative censoring assumptions. I haven't seen non-informative censoring defined before with reference to the covariate profile.
Th... | Difference between independent and non-informative censoring
The first set of definitions seem right to me.
Your adviser's definition two seems to be a conflation of independent and non-informative censoring assumptions. I haven't seen non-informative censoring |
36,715 | How to use rpart's result in prediction | fit = rpart(formula, data =, method =, control=)
fitVariablesUsed <- names(fit[,1:20])
preds <- predict(fit, data = newdata[,c(fitVariablesUsed)], type = c("prob"))
this will return a probability matrix for each of the observations. Meaning it will give a probability that the observation is in class 1, class2, etc.
m... | How to use rpart's result in prediction | fit = rpart(formula, data =, method =, control=)
fitVariablesUsed <- names(fit[,1:20])
preds <- predict(fit, data = newdata[,c(fitVariablesUsed)], type = c("prob"))
this will return a probability mat | How to use rpart's result in prediction
fit = rpart(formula, data =, method =, control=)
fitVariablesUsed <- names(fit[,1:20])
preds <- predict(fit, data = newdata[,c(fitVariablesUsed)], type = c("prob"))
this will return a probability matrix for each of the observations. Meaning it will give a probability that the o... | How to use rpart's result in prediction
fit = rpart(formula, data =, method =, control=)
fitVariablesUsed <- names(fit[,1:20])
preds <- predict(fit, data = newdata[,c(fitVariablesUsed)], type = c("prob"))
this will return a probability mat |
36,716 | How to use rpart's result in prediction | To make a prediction based on a different dataframe than the one used to train your model (e.g. the test dataframe), you should use the newdata parameter to predict() rather than data, because data is not a real parameter (documentation).
predict(output_of_rpart, type=, newdata=testDataFrame) | How to use rpart's result in prediction | To make a prediction based on a different dataframe than the one used to train your model (e.g. the test dataframe), you should use the newdata parameter to predict() rather than data, because data is | How to use rpart's result in prediction
To make a prediction based on a different dataframe than the one used to train your model (e.g. the test dataframe), you should use the newdata parameter to predict() rather than data, because data is not a real parameter (documentation).
predict(output_of_rpart, type=, newdata=t... | How to use rpart's result in prediction
To make a prediction based on a different dataframe than the one used to train your model (e.g. the test dataframe), you should use the newdata parameter to predict() rather than data, because data is |
36,717 | What is the fastest unsupervised feature learning algorithm? | K-means is pretty fast, as is PCA. If you use a sparse SVD library (like the irlba package for R) you can approximate PCA pretty quickly on large datasets.
I think there's some pretty fast algorithms for online (also known as sequential) k-means. | What is the fastest unsupervised feature learning algorithm? | K-means is pretty fast, as is PCA. If you use a sparse SVD library (like the irlba package for R) you can approximate PCA pretty quickly on large datasets.
I think there's some pretty fast algorithms | What is the fastest unsupervised feature learning algorithm?
K-means is pretty fast, as is PCA. If you use a sparse SVD library (like the irlba package for R) you can approximate PCA pretty quickly on large datasets.
I think there's some pretty fast algorithms for online (also known as sequential) k-means. | What is the fastest unsupervised feature learning algorithm?
K-means is pretty fast, as is PCA. If you use a sparse SVD library (like the irlba package for R) you can approximate PCA pretty quickly on large datasets.
I think there's some pretty fast algorithms |
36,718 | What is the fastest unsupervised feature learning algorithm? | One thing to consider is the MDA, the Marginalized Denoising Autoencoder. It trains orders of magnitude faster than an SdA and may be the solution that you're looking for. [1][2] I personally am more interested in the latter paper as learning non-linear representations is important in domains which have highly non-line... | What is the fastest unsupervised feature learning algorithm? | One thing to consider is the MDA, the Marginalized Denoising Autoencoder. It trains orders of magnitude faster than an SdA and may be the solution that you're looking for. [1][2] I personally am more | What is the fastest unsupervised feature learning algorithm?
One thing to consider is the MDA, the Marginalized Denoising Autoencoder. It trains orders of magnitude faster than an SdA and may be the solution that you're looking for. [1][2] I personally am more interested in the latter paper as learning non-linear repre... | What is the fastest unsupervised feature learning algorithm?
One thing to consider is the MDA, the Marginalized Denoising Autoencoder. It trains orders of magnitude faster than an SdA and may be the solution that you're looking for. [1][2] I personally am more |
36,719 | Why isn't the Dantzig selector popular in applied statistics? | The $\ell_\infty$ loss term is VERY sensitive to outliers.
Most (all?) of the theory for the Dantzig selector is under the assumption of normal / Gaussian errors. With this error distribution, there isn't much difference between $\ell_2$ loss and $\ell_\infty$ loss. However, with real data, we would like to be less s... | Why isn't the Dantzig selector popular in applied statistics? | The $\ell_\infty$ loss term is VERY sensitive to outliers.
Most (all?) of the theory for the Dantzig selector is under the assumption of normal / Gaussian errors. With this error distribution, there | Why isn't the Dantzig selector popular in applied statistics?
The $\ell_\infty$ loss term is VERY sensitive to outliers.
Most (all?) of the theory for the Dantzig selector is under the assumption of normal / Gaussian errors. With this error distribution, there isn't much difference between $\ell_2$ loss and $\ell_\inf... | Why isn't the Dantzig selector popular in applied statistics?
The $\ell_\infty$ loss term is VERY sensitive to outliers.
Most (all?) of the theory for the Dantzig selector is under the assumption of normal / Gaussian errors. With this error distribution, there |
36,720 | High level interpretation of Cramer-Rao bound and Fisher information matrix | I think you are correct in your interpretations. The below is an informal response to your points.
If an unbiased estimator achieves the CRB, then it is the optimal estimator out of the class of unbiased estimators for the parameter.
Because their estimator achieves the CRB, the greater the FIM then the more certain ... | High level interpretation of Cramer-Rao bound and Fisher information matrix | I think you are correct in your interpretations. The below is an informal response to your points.
If an unbiased estimator achieves the CRB, then it is the optimal estimator out of the class of unb | High level interpretation of Cramer-Rao bound and Fisher information matrix
I think you are correct in your interpretations. The below is an informal response to your points.
If an unbiased estimator achieves the CRB, then it is the optimal estimator out of the class of unbiased estimators for the parameter.
Because ... | High level interpretation of Cramer-Rao bound and Fisher information matrix
I think you are correct in your interpretations. The below is an informal response to your points.
If an unbiased estimator achieves the CRB, then it is the optimal estimator out of the class of unb |
36,721 | Smoothing algorithm for irregular time interval | The simplest algorithm is the median filter. You can find an C++ implementation in
the R package robfilter. That implementation also include an 'online' version
that only uses past data and implements some algorithmic short-cuts.
Of course you will still have to set the "width" argument yourself, but this is the co... | Smoothing algorithm for irregular time interval | The simplest algorithm is the median filter. You can find an C++ implementation in
the R package robfilter. That implementation also include an 'online' version
that only uses past data and implemen | Smoothing algorithm for irregular time interval
The simplest algorithm is the median filter. You can find an C++ implementation in
the R package robfilter. That implementation also include an 'online' version
that only uses past data and implements some algorithmic short-cuts.
Of course you will still have to set t... | Smoothing algorithm for irregular time interval
The simplest algorithm is the median filter. You can find an C++ implementation in
the R package robfilter. That implementation also include an 'online' version
that only uses past data and implemen |
36,722 | Smoothing algorithm for irregular time interval | I think what you want is a median filter: "Median filtering is very widely used in digital image processing because, under certain conditions, it preserves edges while removing noise". | Smoothing algorithm for irregular time interval | I think what you want is a median filter: "Median filtering is very widely used in digital image processing because, under certain conditions, it preserves edges while removing noise". | Smoothing algorithm for irregular time interval
I think what you want is a median filter: "Median filtering is very widely used in digital image processing because, under certain conditions, it preserves edges while removing noise". | Smoothing algorithm for irregular time interval
I think what you want is a median filter: "Median filtering is very widely used in digital image processing because, under certain conditions, it preserves edges while removing noise". |
36,723 | Correct interpretation of Lmer output | I address your interpretations 1 and 2 in order:
1) How you interpret factors depends on which level of the factor is the reference category. The fact that the model calls it Type2 suggests to me that Type1 is the reference, and that the parameter represents how the estimate changes when Type == 2. Thus, I disagree wit... | Correct interpretation of Lmer output | I address your interpretations 1 and 2 in order:
1) How you interpret factors depends on which level of the factor is the reference category. The fact that the model calls it Type2 suggests to me that | Correct interpretation of Lmer output
I address your interpretations 1 and 2 in order:
1) How you interpret factors depends on which level of the factor is the reference category. The fact that the model calls it Type2 suggests to me that Type1 is the reference, and that the parameter represents how the estimate change... | Correct interpretation of Lmer output
I address your interpretations 1 and 2 in order:
1) How you interpret factors depends on which level of the factor is the reference category. The fact that the model calls it Type2 suggests to me that |
36,724 | Why are the Lagrange multipliers sparse for SVMs? | The Lagrange multipliers in the context of SVMs are typically denoted $\alpha_i$. The fact that one often observes that most $\alpha_i=0$ is a direct consequence of the Karush-Kuhn-Tucker (KKT) dual complementarity conditions:
Since $y_i(\mathbf{w}^T\mathbf{x}_i+b) = 1$ iff $\mathbf{x}_i$ is on the SVM decision bounda... | Why are the Lagrange multipliers sparse for SVMs? | The Lagrange multipliers in the context of SVMs are typically denoted $\alpha_i$. The fact that one often observes that most $\alpha_i=0$ is a direct consequence of the Karush-Kuhn-Tucker (KKT) dual c | Why are the Lagrange multipliers sparse for SVMs?
The Lagrange multipliers in the context of SVMs are typically denoted $\alpha_i$. The fact that one often observes that most $\alpha_i=0$ is a direct consequence of the Karush-Kuhn-Tucker (KKT) dual complementarity conditions:
Since $y_i(\mathbf{w}^T\mathbf{x}_i+b) = 1... | Why are the Lagrange multipliers sparse for SVMs?
The Lagrange multipliers in the context of SVMs are typically denoted $\alpha_i$. The fact that one often observes that most $\alpha_i=0$ is a direct consequence of the Karush-Kuhn-Tucker (KKT) dual c |
36,725 | Analyzing changes in a repeated categorical measure | If you used a simple multinomial model without explicitly including the time dependency, I don't think your approach works well.
Luckily, researchers in psychometrics have developed a number of sophisticated tools for measurement of change based on items (like survey questions). The key idea is to decompose the change... | Analyzing changes in a repeated categorical measure | If you used a simple multinomial model without explicitly including the time dependency, I don't think your approach works well.
Luckily, researchers in psychometrics have developed a number of sophi | Analyzing changes in a repeated categorical measure
If you used a simple multinomial model without explicitly including the time dependency, I don't think your approach works well.
Luckily, researchers in psychometrics have developed a number of sophisticated tools for measurement of change based on items (like survey... | Analyzing changes in a repeated categorical measure
If you used a simple multinomial model without explicitly including the time dependency, I don't think your approach works well.
Luckily, researchers in psychometrics have developed a number of sophi |
36,726 | VIF values and interactions in multiple regression | I go with Penguin_Knight. You will check interaction term also for VIF but you can ignore high values of VIFs here when you use interaction. You can further check for the detailed overview here:
http://www.statisticalhorizons.com/multicollinearity | VIF values and interactions in multiple regression | I go with Penguin_Knight. You will check interaction term also for VIF but you can ignore high values of VIFs here when you use interaction. You can further check for the detailed overview here:
http | VIF values and interactions in multiple regression
I go with Penguin_Knight. You will check interaction term also for VIF but you can ignore high values of VIFs here when you use interaction. You can further check for the detailed overview here:
http://www.statisticalhorizons.com/multicollinearity | VIF values and interactions in multiple regression
I go with Penguin_Knight. You will check interaction term also for VIF but you can ignore high values of VIFs here when you use interaction. You can further check for the detailed overview here:
http |
36,727 | Regsubsets with leaps fails | Did you instruct regsubsets to do a forward selection? The default is "exhaustive", I believe.
In any case, the collinearities will still cause trouble. Any time regsubsets considers a collection of variables that are too collinear (i.e. the design matrix is practically singular), it will fail.
"Best subset" methods ca... | Regsubsets with leaps fails | Did you instruct regsubsets to do a forward selection? The default is "exhaustive", I believe.
In any case, the collinearities will still cause trouble. Any time regsubsets considers a collection of v | Regsubsets with leaps fails
Did you instruct regsubsets to do a forward selection? The default is "exhaustive", I believe.
In any case, the collinearities will still cause trouble. Any time regsubsets considers a collection of variables that are too collinear (i.e. the design matrix is practically singular), it will fa... | Regsubsets with leaps fails
Did you instruct regsubsets to do a forward selection? The default is "exhaustive", I believe.
In any case, the collinearities will still cause trouble. Any time regsubsets considers a collection of v |
36,728 | Non-parametric alternative for 2-way ANOVA [duplicate] | The problem you have in analyzing these data is that interactions don't really make sense when you have non-parametric tests. Non-parametric tests consider data to be ranks - that is we know if something is higher or lower, but we don't know the magnitude.
An interaction says does the magnitude of the effect of X1 d... | Non-parametric alternative for 2-way ANOVA [duplicate] | The problem you have in analyzing these data is that interactions don't really make sense when you have non-parametric tests. Non-parametric tests consider data to be ranks - that is we know if somet | Non-parametric alternative for 2-way ANOVA [duplicate]
The problem you have in analyzing these data is that interactions don't really make sense when you have non-parametric tests. Non-parametric tests consider data to be ranks - that is we know if something is higher or lower, but we don't know the magnitude.
An in... | Non-parametric alternative for 2-way ANOVA [duplicate]
The problem you have in analyzing these data is that interactions don't really make sense when you have non-parametric tests. Non-parametric tests consider data to be ranks - that is we know if somet |
36,729 | Non-parametric alternative for 2-way ANOVA [duplicate] | The only method that I know of that has support in the literature for the interaction test is the use of a transformation of the raw data to normal scores, such as the ranking procedure by Van der Waerden and by Blom. Both are available in SAS under proc rank. | Non-parametric alternative for 2-way ANOVA [duplicate] | The only method that I know of that has support in the literature for the interaction test is the use of a transformation of the raw data to normal scores, such as the ranking procedure by Van der Wae | Non-parametric alternative for 2-way ANOVA [duplicate]
The only method that I know of that has support in the literature for the interaction test is the use of a transformation of the raw data to normal scores, such as the ranking procedure by Van der Waerden and by Blom. Both are available in SAS under proc rank. | Non-parametric alternative for 2-way ANOVA [duplicate]
The only method that I know of that has support in the literature for the interaction test is the use of a transformation of the raw data to normal scores, such as the ranking procedure by Van der Wae |
36,730 | Regarding precision and recall for the highly unbalanced validation data set [duplicate] | I work in biomedical text classification, where this sort of situation happens all the time. You're exactly right--precision and recall aren't all that informative for highly-skewed data. I tend to use AUC as my performance metric, as it's not sensitive to class distribution. | Regarding precision and recall for the highly unbalanced validation data set [duplicate] | I work in biomedical text classification, where this sort of situation happens all the time. You're exactly right--precision and recall aren't all that informative for highly-skewed data. I tend to us | Regarding precision and recall for the highly unbalanced validation data set [duplicate]
I work in biomedical text classification, where this sort of situation happens all the time. You're exactly right--precision and recall aren't all that informative for highly-skewed data. I tend to use AUC as my performance metric,... | Regarding precision and recall for the highly unbalanced validation data set [duplicate]
I work in biomedical text classification, where this sort of situation happens all the time. You're exactly right--precision and recall aren't all that informative for highly-skewed data. I tend to us |
36,731 | Regarding precision and recall for the highly unbalanced validation data set [duplicate] | You could introduce a cost function, consistent with your application, with values for TP, FP, TN, FN and optimise your predictors for that. | Regarding precision and recall for the highly unbalanced validation data set [duplicate] | You could introduce a cost function, consistent with your application, with values for TP, FP, TN, FN and optimise your predictors for that. | Regarding precision and recall for the highly unbalanced validation data set [duplicate]
You could introduce a cost function, consistent with your application, with values for TP, FP, TN, FN and optimise your predictors for that. | Regarding precision and recall for the highly unbalanced validation data set [duplicate]
You could introduce a cost function, consistent with your application, with values for TP, FP, TN, FN and optimise your predictors for that. |
36,732 | Regarding precision and recall for the highly unbalanced validation data set [duplicate] | I think you need to be clearer what you mean when you say "Not valid": in the sense that they summarise the contingency table, they are valid, but they are biased in the case of highly imbalanced data. One alternate measure you can look at, which tends to be more stable across class balance, is the mean of true positiv... | Regarding precision and recall for the highly unbalanced validation data set [duplicate] | I think you need to be clearer what you mean when you say "Not valid": in the sense that they summarise the contingency table, they are valid, but they are biased in the case of highly imbalanced data | Regarding precision and recall for the highly unbalanced validation data set [duplicate]
I think you need to be clearer what you mean when you say "Not valid": in the sense that they summarise the contingency table, they are valid, but they are biased in the case of highly imbalanced data. One alternate measure you can... | Regarding precision and recall for the highly unbalanced validation data set [duplicate]
I think you need to be clearer what you mean when you say "Not valid": in the sense that they summarise the contingency table, they are valid, but they are biased in the case of highly imbalanced data |
36,733 | A re-formalization of a conjugate prior? | It is an interesting remark that I have not seen explicitly spelled out, however the parameter space for conjugate priors is often chosen in the opposite way, namely the largest possible set that keeps the sampling distribution well defined. See Brown's Fundamentals of Statistical Exponential Families (1986). | A re-formalization of a conjugate prior? | It is an interesting remark that I have not seen explicitly spelled out, however the parameter space for conjugate priors is often chosen in the opposite way, namely the largest possible set that keep | A re-formalization of a conjugate prior?
It is an interesting remark that I have not seen explicitly spelled out, however the parameter space for conjugate priors is often chosen in the opposite way, namely the largest possible set that keeps the sampling distribution well defined. See Brown's Fundamentals of Statistic... | A re-formalization of a conjugate prior?
It is an interesting remark that I have not seen explicitly spelled out, however the parameter space for conjugate priors is often chosen in the opposite way, namely the largest possible set that keep |
36,734 | Can I prove a curvilinear relationship when the linear independent variable is not significant | No, it is not essential that both the linear and quadratic terms be significant. Only the quadratic term need be significant.
In fact, it is important to note that the linear term takes on a somewhat different interpretation in the context of a model that also includes the quadratic term. In such a model, the linear te... | Can I prove a curvilinear relationship when the linear independent variable is not significant | No, it is not essential that both the linear and quadratic terms be significant. Only the quadratic term need be significant.
In fact, it is important to note that the linear term takes on a somewhat | Can I prove a curvilinear relationship when the linear independent variable is not significant
No, it is not essential that both the linear and quadratic terms be significant. Only the quadratic term need be significant.
In fact, it is important to note that the linear term takes on a somewhat different interpretation ... | Can I prove a curvilinear relationship when the linear independent variable is not significant
No, it is not essential that both the linear and quadratic terms be significant. Only the quadratic term need be significant.
In fact, it is important to note that the linear term takes on a somewhat |
36,735 | Can I prove a curvilinear relationship when the linear independent variable is not significant | Think about what significance means. A relationship of the form you suggest can be characterized as
$Y = a_1X^2+a_2X+b$
and empirically estimated as $\hat{Y}=\alpha_1\hat{X}^2+\alpha_2\hat{X}+\beta+\epsilon$.
What does the significance of an estimate - say, $\alpha_2$ - mean? The significance is Pr(data|H0), and given... | Can I prove a curvilinear relationship when the linear independent variable is not significant | Think about what significance means. A relationship of the form you suggest can be characterized as
$Y = a_1X^2+a_2X+b$
and empirically estimated as $\hat{Y}=\alpha_1\hat{X}^2+\alpha_2\hat{X}+\beta+\ | Can I prove a curvilinear relationship when the linear independent variable is not significant
Think about what significance means. A relationship of the form you suggest can be characterized as
$Y = a_1X^2+a_2X+b$
and empirically estimated as $\hat{Y}=\alpha_1\hat{X}^2+\alpha_2\hat{X}+\beta+\epsilon$.
What does the s... | Can I prove a curvilinear relationship when the linear independent variable is not significant
Think about what significance means. A relationship of the form you suggest can be characterized as
$Y = a_1X^2+a_2X+b$
and empirically estimated as $\hat{Y}=\alpha_1\hat{X}^2+\alpha_2\hat{X}+\beta+\ |
36,736 | Can I prove a curvilinear relationship when the linear independent variable is not significant | It is actually not essential that either term be significant, but you never prove anything with just a model.
The given estimates of coefficients are estimates, and they provide evidence. A large coefficient on the quadratic term provides a lot of evidence, a small coefficient provides a little evidence, of a curvilin... | Can I prove a curvilinear relationship when the linear independent variable is not significant | It is actually not essential that either term be significant, but you never prove anything with just a model.
The given estimates of coefficients are estimates, and they provide evidence. A large coe | Can I prove a curvilinear relationship when the linear independent variable is not significant
It is actually not essential that either term be significant, but you never prove anything with just a model.
The given estimates of coefficients are estimates, and they provide evidence. A large coefficient on the quadratic... | Can I prove a curvilinear relationship when the linear independent variable is not significant
It is actually not essential that either term be significant, but you never prove anything with just a model.
The given estimates of coefficients are estimates, and they provide evidence. A large coe |
36,737 | Can I prove a curvilinear relationship when the linear independent variable is not significant | As noted, the significance of the curvilinear term stands by itself, regardless of the significance of the linear term in the regression. If the linear term is near zero, then the curve is a U or inverted U if it is significant. If both terms are significant, the resulting line is more like a hill with an accelerating... | Can I prove a curvilinear relationship when the linear independent variable is not significant | As noted, the significance of the curvilinear term stands by itself, regardless of the significance of the linear term in the regression. If the linear term is near zero, then the curve is a U or inve | Can I prove a curvilinear relationship when the linear independent variable is not significant
As noted, the significance of the curvilinear term stands by itself, regardless of the significance of the linear term in the regression. If the linear term is near zero, then the curve is a U or inverted U if it is significa... | Can I prove a curvilinear relationship when the linear independent variable is not significant
As noted, the significance of the curvilinear term stands by itself, regardless of the significance of the linear term in the regression. If the linear term is near zero, then the curve is a U or inve |
36,738 | Terminology for different types of epidemiological variable | Let us assume we're talking about a particular categorical variable. Lets say a "residence" variable that indicates if someone lives in a private home, an apartment, a dorm or group living space, a nursing home, a prison, or other.
For your first example, I don't know that I'd call the variable anything. I'd probably e... | Terminology for different types of epidemiological variable | Let us assume we're talking about a particular categorical variable. Lets say a "residence" variable that indicates if someone lives in a private home, an apartment, a dorm or group living space, a nu | Terminology for different types of epidemiological variable
Let us assume we're talking about a particular categorical variable. Lets say a "residence" variable that indicates if someone lives in a private home, an apartment, a dorm or group living space, a nursing home, a prison, or other.
For your first example, I do... | Terminology for different types of epidemiological variable
Let us assume we're talking about a particular categorical variable. Lets say a "residence" variable that indicates if someone lives in a private home, an apartment, a dorm or group living space, a nu |
36,739 | Terminology for different types of epidemiological variable | For the first question, there is no particular term for X. Exclusion criteria is a term used to refer to rules used to exclude patients from being enrolled in the trial. There may be an analogy here to the process of excluding data when a mathematical condition exists but it is a different situation and I have never ... | Terminology for different types of epidemiological variable | For the first question, there is no particular term for X. Exclusion criteria is a term used to refer to rules used to exclude patients from being enrolled in the trial. There may be an analogy here | Terminology for different types of epidemiological variable
For the first question, there is no particular term for X. Exclusion criteria is a term used to refer to rules used to exclude patients from being enrolled in the trial. There may be an analogy here to the process of excluding data when a mathematical condit... | Terminology for different types of epidemiological variable
For the first question, there is no particular term for X. Exclusion criteria is a term used to refer to rules used to exclude patients from being enrolled in the trial. There may be an analogy here |
36,740 | Using $\chi^2$ to compare two Markov transition matrices | It looks as though you would like to use the Pearson $\chi^2$ test to assess whether a sample $x_1,...,x_n$ that is taken from a first-order chain with transition probabilities given by $M$ is well fit by the second order chain with transition probabilities given by $M^2$.
The notation you are using is a little confusi... | Using $\chi^2$ to compare two Markov transition matrices | It looks as though you would like to use the Pearson $\chi^2$ test to assess whether a sample $x_1,...,x_n$ that is taken from a first-order chain with transition probabilities given by $M$ is well fi | Using $\chi^2$ to compare two Markov transition matrices
It looks as though you would like to use the Pearson $\chi^2$ test to assess whether a sample $x_1,...,x_n$ that is taken from a first-order chain with transition probabilities given by $M$ is well fit by the second order chain with transition probabilities given... | Using $\chi^2$ to compare two Markov transition matrices
It looks as though you would like to use the Pearson $\chi^2$ test to assess whether a sample $x_1,...,x_n$ that is taken from a first-order chain with transition probabilities given by $M$ is well fi |
36,741 | Part correlation and R squared | Your output shows strong suppressive activity. It can never be shown on a Venn diagram. A suppressor IV is a predictor which addition to the model raises $R^2$ greater than its own $r^2$ with the DV, because suppressor is correlated mostly with the error term in the model which lacks the supressor, rather than correlat... | Part correlation and R squared | Your output shows strong suppressive activity. It can never be shown on a Venn diagram. A suppressor IV is a predictor which addition to the model raises $R^2$ greater than its own $r^2$ with the DV, | Part correlation and R squared
Your output shows strong suppressive activity. It can never be shown on a Venn diagram. A suppressor IV is a predictor which addition to the model raises $R^2$ greater than its own $r^2$ with the DV, because suppressor is correlated mostly with the error term in the model which lacks the ... | Part correlation and R squared
Your output shows strong suppressive activity. It can never be shown on a Venn diagram. A suppressor IV is a predictor which addition to the model raises $R^2$ greater than its own $r^2$ with the DV, |
36,742 | OLS: $E[\epsilon_{it}^T\epsilon_{it}] \not= 0$ in 1st equation biases standard errors in 2nd equation? | In order to be sure you need to go into the details, this implies comparing the true variance covariance matrix with the one you get in the second ols stage.
The true one:
This can be obtained by replacing eq.2 into eq.1, pooled OLS follows, and from it, the true $\hat a , \hat b$ variance covariance matrix:
$Y_{it} =... | OLS: $E[\epsilon_{it}^T\epsilon_{it}] \not= 0$ in 1st equation biases standard errors in 2nd equatio | In order to be sure you need to go into the details, this implies comparing the true variance covariance matrix with the one you get in the second ols stage.
The true one:
This can be obtained by rep | OLS: $E[\epsilon_{it}^T\epsilon_{it}] \not= 0$ in 1st equation biases standard errors in 2nd equation?
In order to be sure you need to go into the details, this implies comparing the true variance covariance matrix with the one you get in the second ols stage.
The true one:
This can be obtained by replacing eq.2 into ... | OLS: $E[\epsilon_{it}^T\epsilon_{it}] \not= 0$ in 1st equation biases standard errors in 2nd equatio
In order to be sure you need to go into the details, this implies comparing the true variance covariance matrix with the one you get in the second ols stage.
The true one:
This can be obtained by rep |
36,743 | OLS: $E[\epsilon_{it}^T\epsilon_{it}] \not= 0$ in 1st equation biases standard errors in 2nd equation? | I am putting up another answer with more details.
In standard linear regression model (in matrix form):
$$Y=X\beta+\varepsilon$$
the OLS estimate is the following
$$\hat\beta=(X^TX)^{-1}X^TY.$$
Its variance then is
$$Var(\hat\beta)=(X^TX)^{-1}X^TVar(Y)X(X^TX)^{-1}.$$
The usual assumption for regression is that
$$Var(Y... | OLS: $E[\epsilon_{it}^T\epsilon_{it}] \not= 0$ in 1st equation biases standard errors in 2nd equatio | I am putting up another answer with more details.
In standard linear regression model (in matrix form):
$$Y=X\beta+\varepsilon$$
the OLS estimate is the following
$$\hat\beta=(X^TX)^{-1}X^TY.$$
Its v | OLS: $E[\epsilon_{it}^T\epsilon_{it}] \not= 0$ in 1st equation biases standard errors in 2nd equation?
I am putting up another answer with more details.
In standard linear regression model (in matrix form):
$$Y=X\beta+\varepsilon$$
the OLS estimate is the following
$$\hat\beta=(X^TX)^{-1}X^TY.$$
Its variance then is
$... | OLS: $E[\epsilon_{it}^T\epsilon_{it}] \not= 0$ in 1st equation biases standard errors in 2nd equatio
I am putting up another answer with more details.
In standard linear regression model (in matrix form):
$$Y=X\beta+\varepsilon$$
the OLS estimate is the following
$$\hat\beta=(X^TX)^{-1}X^TY.$$
Its v |
36,744 | OLS: $E[\epsilon_{it}^T\epsilon_{it}] \not= 0$ in 1st equation biases standard errors in 2nd equation? | I think the problem lies in definition of the second model. I think it is assumed that
$$\gamma_i=a+bZ_i+u_i$$
with the usual assumption that
$$cov(\gamma_i,\gamma_j|Z_1,...,Z_N)=0,$$
i.e. that the $\gamma_i$ are not correlated if we control for $Z_i$. Now when you substitute $\hat{\gamma}$ instead of $\gamma$, you ne... | OLS: $E[\epsilon_{it}^T\epsilon_{it}] \not= 0$ in 1st equation biases standard errors in 2nd equatio | I think the problem lies in definition of the second model. I think it is assumed that
$$\gamma_i=a+bZ_i+u_i$$
with the usual assumption that
$$cov(\gamma_i,\gamma_j|Z_1,...,Z_N)=0,$$
i.e. that the $ | OLS: $E[\epsilon_{it}^T\epsilon_{it}] \not= 0$ in 1st equation biases standard errors in 2nd equation?
I think the problem lies in definition of the second model. I think it is assumed that
$$\gamma_i=a+bZ_i+u_i$$
with the usual assumption that
$$cov(\gamma_i,\gamma_j|Z_1,...,Z_N)=0,$$
i.e. that the $\gamma_i$ are not... | OLS: $E[\epsilon_{it}^T\epsilon_{it}] \not= 0$ in 1st equation biases standard errors in 2nd equatio
I think the problem lies in definition of the second model. I think it is assumed that
$$\gamma_i=a+bZ_i+u_i$$
with the usual assumption that
$$cov(\gamma_i,\gamma_j|Z_1,...,Z_N)=0,$$
i.e. that the $ |
36,745 | What is the difference between Informative (IVM) and Relevance (RVM) vector machines | The RVM places an Automatic Relevance Determination (ARD) prior on the weights in a regularized regression/logistic regression setup. (The ARD prior is a just a weak gamma prior on the precision of a gaussian random variable). Marginalizing out the weights and maximizing the likelihood of the data with respect to the p... | What is the difference between Informative (IVM) and Relevance (RVM) vector machines | The RVM places an Automatic Relevance Determination (ARD) prior on the weights in a regularized regression/logistic regression setup. (The ARD prior is a just a weak gamma prior on the precision of a | What is the difference between Informative (IVM) and Relevance (RVM) vector machines
The RVM places an Automatic Relevance Determination (ARD) prior on the weights in a regularized regression/logistic regression setup. (The ARD prior is a just a weak gamma prior on the precision of a gaussian random variable). Marginal... | What is the difference between Informative (IVM) and Relevance (RVM) vector machines
The RVM places an Automatic Relevance Determination (ARD) prior on the weights in a regularized regression/logistic regression setup. (The ARD prior is a just a weak gamma prior on the precision of a |
36,746 | What is the difference between Informative (IVM) and Relevance (RVM) vector machines | Some of the distinctions I have identified so far were hidden in (one of) the original papers by Neil Lawrence. There are two versions of "A Sparse Bayesian Compression Scheme - The Informative Vector Machine" [Kernel Workshop at NIPS 2001], one on the Microsoft research site, and one on Laurence's site.
In the MS ver... | What is the difference between Informative (IVM) and Relevance (RVM) vector machines | Some of the distinctions I have identified so far were hidden in (one of) the original papers by Neil Lawrence. There are two versions of "A Sparse Bayesian Compression Scheme - The Informative Vector | What is the difference between Informative (IVM) and Relevance (RVM) vector machines
Some of the distinctions I have identified so far were hidden in (one of) the original papers by Neil Lawrence. There are two versions of "A Sparse Bayesian Compression Scheme - The Informative Vector Machine" [Kernel Workshop at NIPS ... | What is the difference between Informative (IVM) and Relevance (RVM) vector machines
Some of the distinctions I have identified so far were hidden in (one of) the original papers by Neil Lawrence. There are two versions of "A Sparse Bayesian Compression Scheme - The Informative Vector |
36,747 | A question about parameters of Gamma distribution in Bayesian econometrics | For anyone still struggling with Koops terrible notation: The problem is that Koop uses neither the scale nor the rate parametrization, but rather a "mean,degrees of freedom" parametrization (see Appendix, Def. B. 22).
The distribution of $h$ in a proper parametrization (shape, rate) is thus
$$
h \sim \text{Gamma}(shap... | A question about parameters of Gamma distribution in Bayesian econometrics | For anyone still struggling with Koops terrible notation: The problem is that Koop uses neither the scale nor the rate parametrization, but rather a "mean,degrees of freedom" parametrization (see Appe | A question about parameters of Gamma distribution in Bayesian econometrics
For anyone still struggling with Koops terrible notation: The problem is that Koop uses neither the scale nor the rate parametrization, but rather a "mean,degrees of freedom" parametrization (see Appendix, Def. B. 22).
The distribution of $h$ in... | A question about parameters of Gamma distribution in Bayesian econometrics
For anyone still struggling with Koops terrible notation: The problem is that Koop uses neither the scale nor the rate parametrization, but rather a "mean,degrees of freedom" parametrization (see Appe |
36,748 | A question about parameters of Gamma distribution in Bayesian econometrics | I think that the Wikipedia article is referring to a specific form of the gamma distribution known as $\chi^2$. Chi square is $\rm{Gamma}(\nu,1/2)$ and $s^2$ would be the constant that the $\chi^2$ random variable is multiplied by to get a random variable with the distribution of a variance estimate. That is $\alpha=... | A question about parameters of Gamma distribution in Bayesian econometrics | I think that the Wikipedia article is referring to a specific form of the gamma distribution known as $\chi^2$. Chi square is $\rm{Gamma}(\nu,1/2)$ and $s^2$ would be the constant that the $\chi^2$ r | A question about parameters of Gamma distribution in Bayesian econometrics
I think that the Wikipedia article is referring to a specific form of the gamma distribution known as $\chi^2$. Chi square is $\rm{Gamma}(\nu,1/2)$ and $s^2$ would be the constant that the $\chi^2$ random variable is multiplied by to get a rand... | A question about parameters of Gamma distribution in Bayesian econometrics
I think that the Wikipedia article is referring to a specific form of the gamma distribution known as $\chi^2$. Chi square is $\rm{Gamma}(\nu,1/2)$ and $s^2$ would be the constant that the $\chi^2$ r |
36,749 | A question about parameters of Gamma distribution in Bayesian econometrics | It is customary to impose (as a prior) either the gamma distribution to $h=\frac{1}{\sigma^2}$ or the inverse gamma distribution to $\sigma^2$. Then, the posteior will have a beautiful looking. I believe you can assign a gamma distribution to $\sigma^2$, and still all calculation to derive the marginal by integrating o... | A question about parameters of Gamma distribution in Bayesian econometrics | It is customary to impose (as a prior) either the gamma distribution to $h=\frac{1}{\sigma^2}$ or the inverse gamma distribution to $\sigma^2$. Then, the posteior will have a beautiful looking. I beli | A question about parameters of Gamma distribution in Bayesian econometrics
It is customary to impose (as a prior) either the gamma distribution to $h=\frac{1}{\sigma^2}$ or the inverse gamma distribution to $\sigma^2$. Then, the posteior will have a beautiful looking. I believe you can assign a gamma distribution to $\... | A question about parameters of Gamma distribution in Bayesian econometrics
It is customary to impose (as a prior) either the gamma distribution to $h=\frac{1}{\sigma^2}$ or the inverse gamma distribution to $\sigma^2$. Then, the posteior will have a beautiful looking. I beli |
36,750 | Something like Central Limit Theorem for variance and maybe even for covariance? | For finite populations, as the sample size increases, the variance of the sample variance decreases (the finite population correction). When the sample size is equal to the population size, the sample variance is no longer a random variable. For any finite population, there will not be an asymptotic distribution of the... | Something like Central Limit Theorem for variance and maybe even for covariance? | For finite populations, as the sample size increases, the variance of the sample variance decreases (the finite population correction). When the sample size is equal to the population size, the sample | Something like Central Limit Theorem for variance and maybe even for covariance?
For finite populations, as the sample size increases, the variance of the sample variance decreases (the finite population correction). When the sample size is equal to the population size, the sample variance is no longer a random variabl... | Something like Central Limit Theorem for variance and maybe even for covariance?
For finite populations, as the sample size increases, the variance of the sample variance decreases (the finite population correction). When the sample size is equal to the population size, the sample |
36,751 | Box-Cox transformation for mixed models | Taking a look at the web (e.g. google) always helps
http://www.sciencedirect.com/science/article/pii/S0378375804001235
http://onlinelibrary.wiley.com/doi/10.1111/j.1467-985X.2005.00391.x/abstract
Of course, linear Gaussian models with random effects is a huge topic. | Box-Cox transformation for mixed models | Taking a look at the web (e.g. google) always helps
http://www.sciencedirect.com/science/article/pii/S0378375804001235
http://onlinelibrary.wiley.com/doi/10.1111/j.1467-985X.2005.00391.x/abstract
Of c | Box-Cox transformation for mixed models
Taking a look at the web (e.g. google) always helps
http://www.sciencedirect.com/science/article/pii/S0378375804001235
http://onlinelibrary.wiley.com/doi/10.1111/j.1467-985X.2005.00391.x/abstract
Of course, linear Gaussian models with random effects is a huge topic. | Box-Cox transformation for mixed models
Taking a look at the web (e.g. google) always helps
http://www.sciencedirect.com/science/article/pii/S0378375804001235
http://onlinelibrary.wiley.com/doi/10.1111/j.1467-985X.2005.00391.x/abstract
Of c |
36,752 | Confused by MATLAB's implementation of ridge | This is a matlab program to validate what cardinal said, it is actually due to the centering and scaling
% Create A(10 by 3 matrix) and b(10 by 1 matrix)
A=rand(10,3);
b=rand(10,1);
lambda=0.01
% centering and scaling A
s=std(A,0,1);
s=repmat(s,10,1);
A=(A-repmat(mean(A),10,1))./s;
%check the result
X1=inv(A'*A+eye(3... | Confused by MATLAB's implementation of ridge | This is a matlab program to validate what cardinal said, it is actually due to the centering and scaling
% Create A(10 by 3 matrix) and b(10 by 1 matrix)
A=rand(10,3);
b=rand(10,1);
lambda=0.01
% cent | Confused by MATLAB's implementation of ridge
This is a matlab program to validate what cardinal said, it is actually due to the centering and scaling
% Create A(10 by 3 matrix) and b(10 by 1 matrix)
A=rand(10,3);
b=rand(10,1);
lambda=0.01
% centering and scaling A
s=std(A,0,1);
s=repmat(s,10,1);
A=(A-repmat(mean(A),10... | Confused by MATLAB's implementation of ridge
This is a matlab program to validate what cardinal said, it is actually due to the centering and scaling
% Create A(10 by 3 matrix) and b(10 by 1 matrix)
A=rand(10,3);
b=rand(10,1);
lambda=0.01
% cent |
36,753 | Confused by MATLAB's implementation of ridge | You should specialize the scale in ridge as 0, so it looks like x = ridge(A, b, lambda,0). In this case, the first row of x is constant and the rest are the coefficients. In other words, x(2:end,:) should be the same result as you got by using (1). This is clearly stated in the mathlab documentation. Hoping this helps. | Confused by MATLAB's implementation of ridge | You should specialize the scale in ridge as 0, so it looks like x = ridge(A, b, lambda,0). In this case, the first row of x is constant and the rest are the coefficients. In other words, x(2:end,:) sh | Confused by MATLAB's implementation of ridge
You should specialize the scale in ridge as 0, so it looks like x = ridge(A, b, lambda,0). In this case, the first row of x is constant and the rest are the coefficients. In other words, x(2:end,:) should be the same result as you got by using (1). This is clearly stated in ... | Confused by MATLAB's implementation of ridge
You should specialize the scale in ridge as 0, so it looks like x = ridge(A, b, lambda,0). In this case, the first row of x is constant and the rest are the coefficients. In other words, x(2:end,:) sh |
36,754 | Verifying neural network model performance | Just to make sure we are on the same page: You have a sequence of 1000 samples with 7 features each. There is a sequential pattern in there, which is why you process them with an RNN. At each timestep:
It depends. It might get better if you use different normalizations, hard to tell.
To me it just sounds like classif... | Verifying neural network model performance | Just to make sure we are on the same page: You have a sequence of 1000 samples with 7 features each. There is a sequential pattern in there, which is why you process them with an RNN. At each timestep | Verifying neural network model performance
Just to make sure we are on the same page: You have a sequence of 1000 samples with 7 features each. There is a sequential pattern in there, which is why you process them with an RNN. At each timestep:
It depends. It might get better if you use different normalizations, hard... | Verifying neural network model performance
Just to make sure we are on the same page: You have a sequence of 1000 samples with 7 features each. There is a sequential pattern in there, which is why you process them with an RNN. At each timestep |
36,755 | Associating a probability to disease propagation in regions of a map | Alright, first, I actually think your question is more suited for the new "Computational Science" site that should be coming into Public Beta through Area 51 soon. There are a number of issues behind the modeling of infectious diseases that are not really within the scope of a statistical analysis site.
Answering your ... | Associating a probability to disease propagation in regions of a map | Alright, first, I actually think your question is more suited for the new "Computational Science" site that should be coming into Public Beta through Area 51 soon. There are a number of issues behind | Associating a probability to disease propagation in regions of a map
Alright, first, I actually think your question is more suited for the new "Computational Science" site that should be coming into Public Beta through Area 51 soon. There are a number of issues behind the modeling of infectious diseases that are not re... | Associating a probability to disease propagation in regions of a map
Alright, first, I actually think your question is more suited for the new "Computational Science" site that should be coming into Public Beta through Area 51 soon. There are a number of issues behind |
36,756 | Associating a probability to disease propagation in regions of a map | Sounds like you want to do "Agent-based modelling" - if you are computing with the behaviour of individuals. [Personally I prefer the term 'simulation' to 'modelling' when it's not what a statistician would call a 'model'...]
I suspect the simplest example is just to have a finite time-step, and rates of transfer betwe... | Associating a probability to disease propagation in regions of a map | Sounds like you want to do "Agent-based modelling" - if you are computing with the behaviour of individuals. [Personally I prefer the term 'simulation' to 'modelling' when it's not what a statistician | Associating a probability to disease propagation in regions of a map
Sounds like you want to do "Agent-based modelling" - if you are computing with the behaviour of individuals. [Personally I prefer the term 'simulation' to 'modelling' when it's not what a statistician would call a 'model'...]
I suspect the simplest ex... | Associating a probability to disease propagation in regions of a map
Sounds like you want to do "Agent-based modelling" - if you are computing with the behaviour of individuals. [Personally I prefer the term 'simulation' to 'modelling' when it's not what a statistician |
36,757 | General approach for non-parametric two-way ANOVA | The proportional odds ordinal logistic model is a generalization of the Wilcoxon and Kruskal-Wallis tests that extend to multiple covariates, interactions, etc. It is a semiparametric method that only uses the ranks of Y. It handles continuous Y, creating k-1 intercepts where k is the number of unique Y values. | General approach for non-parametric two-way ANOVA | The proportional odds ordinal logistic model is a generalization of the Wilcoxon and Kruskal-Wallis tests that extend to multiple covariates, interactions, etc. It is a semiparametric method that onl | General approach for non-parametric two-way ANOVA
The proportional odds ordinal logistic model is a generalization of the Wilcoxon and Kruskal-Wallis tests that extend to multiple covariates, interactions, etc. It is a semiparametric method that only uses the ranks of Y. It handles continuous Y, creating k-1 intercep... | General approach for non-parametric two-way ANOVA
The proportional odds ordinal logistic model is a generalization of the Wilcoxon and Kruskal-Wallis tests that extend to multiple covariates, interactions, etc. It is a semiparametric method that onl |
36,758 | General approach for non-parametric two-way ANOVA | This sounds good to me. There are some issues to consider though:
In option 2, you need to make sure to correct the p-values in your wilcox tests for multiple hypothesis testing. The pairwise.wilcox.test function in R will do this for you.
In my experience, even though the bootstrap approach is very nice here, if oth... | General approach for non-parametric two-way ANOVA | This sounds good to me. There are some issues to consider though:
In option 2, you need to make sure to correct the p-values in your wilcox tests for multiple hypothesis testing. The pairwise.wilcox. | General approach for non-parametric two-way ANOVA
This sounds good to me. There are some issues to consider though:
In option 2, you need to make sure to correct the p-values in your wilcox tests for multiple hypothesis testing. The pairwise.wilcox.test function in R will do this for you.
In my experience, even thoug... | General approach for non-parametric two-way ANOVA
This sounds good to me. There are some issues to consider though:
In option 2, you need to make sure to correct the p-values in your wilcox tests for multiple hypothesis testing. The pairwise.wilcox. |
36,759 | Fit a robust regression line using an MM-estimator in R | By default, the documentation indicates that rlm uses psi=psi.huber weights. Thus, if you want to use Tukey's bisquare, you need to specify psi=psi.bisquare. The default settings are psi.bisquare(u, c = 4.685, deriv = 0), which you can change as desired. For instance, possibly something like
rlm(x ~ y, method="MM", psi... | Fit a robust regression line using an MM-estimator in R | By default, the documentation indicates that rlm uses psi=psi.huber weights. Thus, if you want to use Tukey's bisquare, you need to specify psi=psi.bisquare. The default settings are psi.bisquare(u, c | Fit a robust regression line using an MM-estimator in R
By default, the documentation indicates that rlm uses psi=psi.huber weights. Thus, if you want to use Tukey's bisquare, you need to specify psi=psi.bisquare. The default settings are psi.bisquare(u, c = 4.685, deriv = 0), which you can change as desired. For insta... | Fit a robust regression line using an MM-estimator in R
By default, the documentation indicates that rlm uses psi=psi.huber weights. Thus, if you want to use Tukey's bisquare, you need to specify psi=psi.bisquare. The default settings are psi.bisquare(u, c |
36,760 | Is Latin hypercube sampling effective in multiple dimensions? | I have split the issues described in your post into three questions below. A good reference for results on Latin Hypercube Sampling and other variance reduction techniques is this book chapter. Also, this book chapter provides information on some of the 'basics' of variance reduction.
Q0. What is variance reduction? Be... | Is Latin hypercube sampling effective in multiple dimensions? | I have split the issues described in your post into three questions below. A good reference for results on Latin Hypercube Sampling and other variance reduction techniques is this book chapter. Also, | Is Latin hypercube sampling effective in multiple dimensions?
I have split the issues described in your post into three questions below. A good reference for results on Latin Hypercube Sampling and other variance reduction techniques is this book chapter. Also, this book chapter provides information on some of the 'bas... | Is Latin hypercube sampling effective in multiple dimensions?
I have split the issues described in your post into three questions below. A good reference for results on Latin Hypercube Sampling and other variance reduction techniques is this book chapter. Also, |
36,761 | Is Latin hypercube sampling effective in multiple dimensions? | http://statweb.stanford.edu/~owen/mc/Ch-var-adv.pdf
This paper discusses the variance reduction of Latin Hypercube Sampling in multiple dimensions. LHS doesn't enforce uniformity when sampling in multiple dimensions because it simply samples in each dimension independently and then combines the dimensions randomly. Str... | Is Latin hypercube sampling effective in multiple dimensions? | http://statweb.stanford.edu/~owen/mc/Ch-var-adv.pdf
This paper discusses the variance reduction of Latin Hypercube Sampling in multiple dimensions. LHS doesn't enforce uniformity when sampling in mult | Is Latin hypercube sampling effective in multiple dimensions?
http://statweb.stanford.edu/~owen/mc/Ch-var-adv.pdf
This paper discusses the variance reduction of Latin Hypercube Sampling in multiple dimensions. LHS doesn't enforce uniformity when sampling in multiple dimensions because it simply samples in each dimensio... | Is Latin hypercube sampling effective in multiple dimensions?
http://statweb.stanford.edu/~owen/mc/Ch-var-adv.pdf
This paper discusses the variance reduction of Latin Hypercube Sampling in multiple dimensions. LHS doesn't enforce uniformity when sampling in mult |
36,762 | Is Latin hypercube sampling effective in multiple dimensions? | I want to comment on "additivity". LHS makes e.g. sure that X1 and X2 are distributed well (usually in (0,1)), so if a design depends only on one variable you will get a "perfect" histogram and strong variance reduction. For the integration of f=100*X1+X2 you will get good results too, but not for X1-X2! This differenc... | Is Latin hypercube sampling effective in multiple dimensions? | I want to comment on "additivity". LHS makes e.g. sure that X1 and X2 are distributed well (usually in (0,1)), so if a design depends only on one variable you will get a "perfect" histogram and strong | Is Latin hypercube sampling effective in multiple dimensions?
I want to comment on "additivity". LHS makes e.g. sure that X1 and X2 are distributed well (usually in (0,1)), so if a design depends only on one variable you will get a "perfect" histogram and strong variance reduction. For the integration of f=100*X1+X2 yo... | Is Latin hypercube sampling effective in multiple dimensions?
I want to comment on "additivity". LHS makes e.g. sure that X1 and X2 are distributed well (usually in (0,1)), so if a design depends only on one variable you will get a "perfect" histogram and strong |
36,763 | Predicting total number of bugs based on number of bugs revealed by each tester | This is a capture-recapture question, in this case with more than two visits, briefly discussed by Wikipedia and in more detail by the R vignette on the package Rcapture
Your assumptions of
different testers having different skills ($t$)
each bug being equally likely to be caught (not $h$)
the probability of a bug be... | Predicting total number of bugs based on number of bugs revealed by each tester | This is a capture-recapture question, in this case with more than two visits, briefly discussed by Wikipedia and in more detail by the R vignette on the package Rcapture
Your assumptions of
differen | Predicting total number of bugs based on number of bugs revealed by each tester
This is a capture-recapture question, in this case with more than two visits, briefly discussed by Wikipedia and in more detail by the R vignette on the package Rcapture
Your assumptions of
different testers having different skills ($t$)
... | Predicting total number of bugs based on number of bugs revealed by each tester
This is a capture-recapture question, in this case with more than two visits, briefly discussed by Wikipedia and in more detail by the R vignette on the package Rcapture
Your assumptions of
differen |
36,764 | Fourier data with non-integer periods, correcting for phase bias | The periodogram will estimate the periods. It will also handle noisy data and pick out multiple sinusoidal components of different period.
A quick and dirty Mathematica calculation is
data = N[Table[Sin[3.17*2*Pi*x/200], {x, 1, n}]];
welch = 1 - (2 (Range[n] - (n - 1)/2)/(n + 1))^2;
fData = Append[Abs[Fourier[welch da... | Fourier data with non-integer periods, correcting for phase bias | The periodogram will estimate the periods. It will also handle noisy data and pick out multiple sinusoidal components of different period.
A quick and dirty Mathematica calculation is
data = N[Table[ | Fourier data with non-integer periods, correcting for phase bias
The periodogram will estimate the periods. It will also handle noisy data and pick out multiple sinusoidal components of different period.
A quick and dirty Mathematica calculation is
data = N[Table[Sin[3.17*2*Pi*x/200], {x, 1, n}]];
welch = 1 - (2 (Rang... | Fourier data with non-integer periods, correcting for phase bias
The periodogram will estimate the periods. It will also handle noisy data and pick out multiple sinusoidal components of different period.
A quick and dirty Mathematica calculation is
data = N[Table[ |
36,765 | What article or book clearly states that one can't use protected t-tests in within subjects ANOVA? | I don't know of any paper that makes that explicit statement probably because it's not entirely true by itself.
You are correct that sphericity should be met. But, you've left the issue of sphericity vague in your question because "met" is ill defined and somewhat subjective. With only 4 levels you probably aren't ... | What article or book clearly states that one can't use protected t-tests in within subjects ANOVA? | I don't know of any paper that makes that explicit statement probably because it's not entirely true by itself.
You are correct that sphericity should be met. But, you've left the issue of spherici | What article or book clearly states that one can't use protected t-tests in within subjects ANOVA?
I don't know of any paper that makes that explicit statement probably because it's not entirely true by itself.
You are correct that sphericity should be met. But, you've left the issue of sphericity vague in your ques... | What article or book clearly states that one can't use protected t-tests in within subjects ANOVA?
I don't know of any paper that makes that explicit statement probably because it's not entirely true by itself.
You are correct that sphericity should be met. But, you've left the issue of spherici |
36,766 | Difference between loadings and correlations between observed variables and factor saved scores in factor analysis | I don't know R very well, so I can't track your code. But factor scores (unless the factors are simply principal components) are always approximate: exact scores cannot be computed because the uniqueness value for each case and variable is eternally unobservable. Thus, observed correlations between computed factor scor... | Difference between loadings and correlations between observed variables and factor saved scores in f | I don't know R very well, so I can't track your code. But factor scores (unless the factors are simply principal components) are always approximate: exact scores cannot be computed because the uniquen | Difference between loadings and correlations between observed variables and factor saved scores in factor analysis
I don't know R very well, so I can't track your code. But factor scores (unless the factors are simply principal components) are always approximate: exact scores cannot be computed because the uniqueness ... | Difference between loadings and correlations between observed variables and factor saved scores in f
I don't know R very well, so I can't track your code. But factor scores (unless the factors are simply principal components) are always approximate: exact scores cannot be computed because the uniquen |
36,767 | Difference between loadings and correlations between observed variables and factor saved scores in factor analysis | fa() uses the minres factoring method by default fm="minres".
The loadings correspond to the correlations only with the principal components factorization method. You can compute it with principal():
fa1 <- principal(X, nfactors = 3, rotate = 'none')
cor(X, fa1$scores)
PC1 PC2 PC3
[1,] ... | Difference between loadings and correlations between observed variables and factor saved scores in f | fa() uses the minres factoring method by default fm="minres".
The loadings correspond to the correlations only with the principal components factorization method. You can compute it with principal():
| Difference between loadings and correlations between observed variables and factor saved scores in factor analysis
fa() uses the minres factoring method by default fm="minres".
The loadings correspond to the correlations only with the principal components factorization method. You can compute it with principal():
fa1... | Difference between loadings and correlations between observed variables and factor saved scores in f
fa() uses the minres factoring method by default fm="minres".
The loadings correspond to the correlations only with the principal components factorization method. You can compute it with principal():
|
36,768 | Where can I read about the justification for the use of parametric probability distributions? | Nice question. I like Ben Bolker's descriptions from his book, Ecological Models and Data in R (preprint of the relevant chapter; the bestiary of distributions starts on page 19).
For each distribution, he has a few sentences to a page on where it comes from and what it's used for, plus some math and graphs. | Where can I read about the justification for the use of parametric probability distributions? | Nice question. I like Ben Bolker's descriptions from his book, Ecological Models and Data in R (preprint of the relevant chapter; the bestiary of distributions starts on page 19).
For each distributi | Where can I read about the justification for the use of parametric probability distributions?
Nice question. I like Ben Bolker's descriptions from his book, Ecological Models and Data in R (preprint of the relevant chapter; the bestiary of distributions starts on page 19).
For each distribution, he has a few sentences... | Where can I read about the justification for the use of parametric probability distributions?
Nice question. I like Ben Bolker's descriptions from his book, Ecological Models and Data in R (preprint of the relevant chapter; the bestiary of distributions starts on page 19).
For each distributi |
36,769 | Where can I read about the justification for the use of parametric probability distributions? | In some sense there is no such thing as a statistics without "parameters" and "models". It is an arbitrary labelling to some extent, depending on what you recognise as a "model" or "parameter". Parameters and models are basically ways of translating assumptions and knowledge about the real world into a mathematical s... | Where can I read about the justification for the use of parametric probability distributions? | In some sense there is no such thing as a statistics without "parameters" and "models". It is an arbitrary labelling to some extent, depending on what you recognise as a "model" or "parameter". Para | Where can I read about the justification for the use of parametric probability distributions?
In some sense there is no such thing as a statistics without "parameters" and "models". It is an arbitrary labelling to some extent, depending on what you recognise as a "model" or "parameter". Parameters and models are basi... | Where can I read about the justification for the use of parametric probability distributions?
In some sense there is no such thing as a statistics without "parameters" and "models". It is an arbitrary labelling to some extent, depending on what you recognise as a "model" or "parameter". Para |
36,770 | Where can I read about the justification for the use of parametric probability distributions? | A Bayesian way to introduce and motivate parametric models is through Exchangeability and De Finetti's Representation Theorem. There is some discussion in this question:
What is so cool about de Finetti's representation theorem?
A great introduction is given in the first chapter of Schervish's Theory of Statistics. All... | Where can I read about the justification for the use of parametric probability distributions? | A Bayesian way to introduce and motivate parametric models is through Exchangeability and De Finetti's Representation Theorem. There is some discussion in this question:
What is so cool about de Finet | Where can I read about the justification for the use of parametric probability distributions?
A Bayesian way to introduce and motivate parametric models is through Exchangeability and De Finetti's Representation Theorem. There is some discussion in this question:
What is so cool about de Finetti's representation theore... | Where can I read about the justification for the use of parametric probability distributions?
A Bayesian way to introduce and motivate parametric models is through Exchangeability and De Finetti's Representation Theorem. There is some discussion in this question:
What is so cool about de Finet |
36,771 | High quality publishing house for books in the field of statistics | Well, here is a list of the companies that paid to exhibit at the most recent (2011) Joint Statistical Meetings. This includes a lot of publishers. I am not sure why a major publisher would not be at the biggest statistical meeting in the world, or at least at the largest one to draw a lot of different teachers and r... | High quality publishing house for books in the field of statistics | Well, here is a list of the companies that paid to exhibit at the most recent (2011) Joint Statistical Meetings. This includes a lot of publishers. I am not sure why a major publisher would not be a | High quality publishing house for books in the field of statistics
Well, here is a list of the companies that paid to exhibit at the most recent (2011) Joint Statistical Meetings. This includes a lot of publishers. I am not sure why a major publisher would not be at the biggest statistical meeting in the world, or at... | High quality publishing house for books in the field of statistics
Well, here is a list of the companies that paid to exhibit at the most recent (2011) Joint Statistical Meetings. This includes a lot of publishers. I am not sure why a major publisher would not be a |
36,772 | High quality publishing house for books in the field of statistics | Another good one is Sage, which produces hundreds of small monographs in the Quantitative Applications in the Social Sciences series. | High quality publishing house for books in the field of statistics | Another good one is Sage, which produces hundreds of small monographs in the Quantitative Applications in the Social Sciences series. | High quality publishing house for books in the field of statistics
Another good one is Sage, which produces hundreds of small monographs in the Quantitative Applications in the Social Sciences series. | High quality publishing house for books in the field of statistics
Another good one is Sage, which produces hundreds of small monographs in the Quantitative Applications in the Social Sciences series. |
36,773 | How to derive Poisson distribution from gamma distribution? | I'm sure that Durrett's proof is nice. A straight forward solution to the question asked is as follows.
For $n \geq 1$
$$
\begin{array}{rcl}
P(N_t = n) & = & \int_0^t P(S_{n+1} > t \mid S_n = s) P(S_n \in ds) \\
& = & \int_0^t P(T_{n+1} > t-s) P(S_n \in ds) \\
& = & \int_0^t e^{-\lambda(t-s)} \frac{\lambda^n s^{n-... | How to derive Poisson distribution from gamma distribution? | I'm sure that Durrett's proof is nice. A straight forward solution to the question asked is as follows.
For $n \geq 1$
$$
\begin{array}{rcl}
P(N_t = n) & = & \int_0^t P(S_{n+1} > t \mid S_n = s) P( | How to derive Poisson distribution from gamma distribution?
I'm sure that Durrett's proof is nice. A straight forward solution to the question asked is as follows.
For $n \geq 1$
$$
\begin{array}{rcl}
P(N_t = n) & = & \int_0^t P(S_{n+1} > t \mid S_n = s) P(S_n \in ds) \\
& = & \int_0^t P(T_{n+1} > t-s) P(S_n \in ds... | How to derive Poisson distribution from gamma distribution?
I'm sure that Durrett's proof is nice. A straight forward solution to the question asked is as follows.
For $n \geq 1$
$$
\begin{array}{rcl}
P(N_t = n) & = & \int_0^t P(S_{n+1} > t \mid S_n = s) P( |
36,774 | Information on how value of k in k-fold cross-validation affects resulting accuracies | Not much of a "proof" but when k is small, you are removing a much larger chunk of your data, so you model has a much smaller amount of data to "learn from". For k=5 you are removing 20% of the data each time, whereas for k=200 you are only removing 0.5%. You model has a much better chance of picking up all the relev... | Information on how value of k in k-fold cross-validation affects resulting accuracies | Not much of a "proof" but when k is small, you are removing a much larger chunk of your data, so you model has a much smaller amount of data to "learn from". For k=5 you are removing 20% of the data | Information on how value of k in k-fold cross-validation affects resulting accuracies
Not much of a "proof" but when k is small, you are removing a much larger chunk of your data, so you model has a much smaller amount of data to "learn from". For k=5 you are removing 20% of the data each time, whereas for k=200 you a... | Information on how value of k in k-fold cross-validation affects resulting accuracies
Not much of a "proof" but when k is small, you are removing a much larger chunk of your data, so you model has a much smaller amount of data to "learn from". For k=5 you are removing 20% of the data |
36,775 | Should grades be assigned to students based on a normal distribution? | Why should grades be normally distributed?
Sometimes they are but if the grades are not normally distributed then the bell curve grading system, where the middle say 70% get C's, is probably not a good one to base grades off of. Although that grading is pretty harsh, few instructors would actually do it.
Use distribut... | Should grades be assigned to students based on a normal distribution? | Why should grades be normally distributed?
Sometimes they are but if the grades are not normally distributed then the bell curve grading system, where the middle say 70% get C's, is probably not a goo | Should grades be assigned to students based on a normal distribution?
Why should grades be normally distributed?
Sometimes they are but if the grades are not normally distributed then the bell curve grading system, where the middle say 70% get C's, is probably not a good one to base grades off of. Although that gradin... | Should grades be assigned to students based on a normal distribution?
Why should grades be normally distributed?
Sometimes they are but if the grades are not normally distributed then the bell curve grading system, where the middle say 70% get C's, is probably not a goo |
36,776 | Should grades be assigned to students based on a normal distribution? | 1.) Usually, grades are on an ordinal scale. So in a strict statistical sense, an overall grade should not be something like the mean grade, since adding such variables is not defined. The median grade however, does not clearly fit since it conveys the ranking between students in the same subject, not between subjects ... | Should grades be assigned to students based on a normal distribution? | 1.) Usually, grades are on an ordinal scale. So in a strict statistical sense, an overall grade should not be something like the mean grade, since adding such variables is not defined. The median grad | Should grades be assigned to students based on a normal distribution?
1.) Usually, grades are on an ordinal scale. So in a strict statistical sense, an overall grade should not be something like the mean grade, since adding such variables is not defined. The median grade however, does not clearly fit since it conveys t... | Should grades be assigned to students based on a normal distribution?
1.) Usually, grades are on an ordinal scale. So in a strict statistical sense, an overall grade should not be something like the mean grade, since adding such variables is not defined. The median grad |
36,777 | Chow test or not? | Your question is most interesting to me and it's solution has been my primary research for a number of years.
There are a number of ways that "a structural break" may occur.
If there is a change in the Intercept or a change in Trend in "the latter portion of the time series" then one would be better suited to perform ... | Chow test or not? | Your question is most interesting to me and it's solution has been my primary research for a number of years.
There are a number of ways that "a structural break" may occur.
If there is a change in t | Chow test or not?
Your question is most interesting to me and it's solution has been my primary research for a number of years.
There are a number of ways that "a structural break" may occur.
If there is a change in the Intercept or a change in Trend in "the latter portion of the time series" then one would be better ... | Chow test or not?
Your question is most interesting to me and it's solution has been my primary research for a number of years.
There are a number of ways that "a structural break" may occur.
If there is a change in t |
36,778 | Assessing multicollinearity of dichotomous predictor variables | I think you are trying to interpret P(A|B) and P(B|A) as if they should be the same thing. There is no reason for them to be equal, because of the product rule:
$$P(AB)=P(A|B)P(B)=P(B|A)P(A)$$
unless $P(B)=P(A)$ then $P(A|B) \neq P(B|A)$ in general. This explains the difference in the "yn" case. Unless you have a "b... | Assessing multicollinearity of dichotomous predictor variables | I think you are trying to interpret P(A|B) and P(B|A) as if they should be the same thing. There is no reason for them to be equal, because of the product rule:
$$P(AB)=P(A|B)P(B)=P(B|A)P(A)$$
unless | Assessing multicollinearity of dichotomous predictor variables
I think you are trying to interpret P(A|B) and P(B|A) as if they should be the same thing. There is no reason for them to be equal, because of the product rule:
$$P(AB)=P(A|B)P(B)=P(B|A)P(A)$$
unless $P(B)=P(A)$ then $P(A|B) \neq P(B|A)$ in general. This ... | Assessing multicollinearity of dichotomous predictor variables
I think you are trying to interpret P(A|B) and P(B|A) as if they should be the same thing. There is no reason for them to be equal, because of the product rule:
$$P(AB)=P(A|B)P(B)=P(B|A)P(A)$$
unless |
36,779 | Assessing multicollinearity of dichotomous predictor variables | Why are you worried about multicolinearity? The only reason that we need this assumption in regression is to ensure that we get unique estimates. Multicolinearity only matters for estimation when it is perfect---when one variable is an exact linear combination of the others.
If your experimentally-manipulated variables... | Assessing multicollinearity of dichotomous predictor variables | Why are you worried about multicolinearity? The only reason that we need this assumption in regression is to ensure that we get unique estimates. Multicolinearity only matters for estimation when it i | Assessing multicollinearity of dichotomous predictor variables
Why are you worried about multicolinearity? The only reason that we need this assumption in regression is to ensure that we get unique estimates. Multicolinearity only matters for estimation when it is perfect---when one variable is an exact linear combinat... | Assessing multicollinearity of dichotomous predictor variables
Why are you worried about multicolinearity? The only reason that we need this assumption in regression is to ensure that we get unique estimates. Multicolinearity only matters for estimation when it i |
36,780 | What to do following poor fit statistics for a confirmatory factor analysis? | I would probably do the following:
1) Split the data into two roughly equal segments.
2) Perform exploratory analyses on one of these and derive a new model
3) Test the model on the other half of the data.
This at least will be something that's not done all that often, which will make it a better fit for publication (s... | What to do following poor fit statistics for a confirmatory factor analysis? | I would probably do the following:
1) Split the data into two roughly equal segments.
2) Perform exploratory analyses on one of these and derive a new model
3) Test the model on the other half of the | What to do following poor fit statistics for a confirmatory factor analysis?
I would probably do the following:
1) Split the data into two roughly equal segments.
2) Perform exploratory analyses on one of these and derive a new model
3) Test the model on the other half of the data.
This at least will be something that'... | What to do following poor fit statistics for a confirmatory factor analysis?
I would probably do the following:
1) Split the data into two roughly equal segments.
2) Perform exploratory analyses on one of these and derive a new model
3) Test the model on the other half of the |
36,781 | What to do following poor fit statistics for a confirmatory factor analysis? | Instead of looking for statistical solutions that directly solve this problem, I would look for solutions that improve the diagnosis.
First, I'd compare the different samples used in the different studies.
Then, if you have the data, I'd look at the correlation patterns among the variables in the different samples. ... | What to do following poor fit statistics for a confirmatory factor analysis? | Instead of looking for statistical solutions that directly solve this problem, I would look for solutions that improve the diagnosis.
First, I'd compare the different samples used in the different s | What to do following poor fit statistics for a confirmatory factor analysis?
Instead of looking for statistical solutions that directly solve this problem, I would look for solutions that improve the diagnosis.
First, I'd compare the different samples used in the different studies.
Then, if you have the data, I'd loo... | What to do following poor fit statistics for a confirmatory factor analysis?
Instead of looking for statistical solutions that directly solve this problem, I would look for solutions that improve the diagnosis.
First, I'd compare the different samples used in the different s |
36,782 | Taking advantage of many pre-treatment measurements | This is not a complete answer, but just a few thoughts:
More pre-treatment measures should increase the reliability of your measurement of baseline differences. Increasing reliability of measuring baseline differences should increase your statistical power in detecting group differences (assuming a real effect exists)... | Taking advantage of many pre-treatment measurements | This is not a complete answer, but just a few thoughts:
More pre-treatment measures should increase the reliability of your measurement of baseline differences. Increasing reliability of measuring ba | Taking advantage of many pre-treatment measurements
This is not a complete answer, but just a few thoughts:
More pre-treatment measures should increase the reliability of your measurement of baseline differences. Increasing reliability of measuring baseline differences should increase your statistical power in detecti... | Taking advantage of many pre-treatment measurements
This is not a complete answer, but just a few thoughts:
More pre-treatment measures should increase the reliability of your measurement of baseline differences. Increasing reliability of measuring ba |
36,783 | Taking advantage of many pre-treatment measurements | Excuse my previous post. I now see that you are not referring to 9000 different covariates.
What I have written does not apply to your situation.
Sincerest apologies.
Paul
There is a lot of discussion about matching and dimensionality reduction on pre-treatment covariates that may be worthwhile examining - i.e. prope... | Taking advantage of many pre-treatment measurements | Excuse my previous post. I now see that you are not referring to 9000 different covariates.
What I have written does not apply to your situation.
Sincerest apologies.
Paul
There is a lot of discussi | Taking advantage of many pre-treatment measurements
Excuse my previous post. I now see that you are not referring to 9000 different covariates.
What I have written does not apply to your situation.
Sincerest apologies.
Paul
There is a lot of discussion about matching and dimensionality reduction on pre-treatment cova... | Taking advantage of many pre-treatment measurements
Excuse my previous post. I now see that you are not referring to 9000 different covariates.
What I have written does not apply to your situation.
Sincerest apologies.
Paul
There is a lot of discussi |
36,784 | How to choose df for comparisons between summary statistics (e.g. slope values)? | Here's how I have understood your question:
you have two groups of participants
Five observations per participant
Based on the five observations, you can extract a single summary statistic (e.g., if the five observations were performance over five time points, the summary statistic might be the slope of the regression... | How to choose df for comparisons between summary statistics (e.g. slope values)? | Here's how I have understood your question:
you have two groups of participants
Five observations per participant
Based on the five observations, you can extract a single summary statistic (e.g., if | How to choose df for comparisons between summary statistics (e.g. slope values)?
Here's how I have understood your question:
you have two groups of participants
Five observations per participant
Based on the five observations, you can extract a single summary statistic (e.g., if the five observations were performance ... | How to choose df for comparisons between summary statistics (e.g. slope values)?
Here's how I have understood your question:
you have two groups of participants
Five observations per participant
Based on the five observations, you can extract a single summary statistic (e.g., if |
36,785 | How to choose df for comparisons between summary statistics (e.g. slope values)? | This a very simple multi-level (a.k.a. hierarchical) model. Douglas Bate his currently working on a book on the subject (draft avalaible here: http://lme4.r-forge.r-project.org/book/). While there are many books on this subject, Doug's has the added benefit of being designed arround the 'lme' R package, a very handy pa... | How to choose df for comparisons between summary statistics (e.g. slope values)? | This a very simple multi-level (a.k.a. hierarchical) model. Douglas Bate his currently working on a book on the subject (draft avalaible here: http://lme4.r-forge.r-project.org/book/). While there are | How to choose df for comparisons between summary statistics (e.g. slope values)?
This a very simple multi-level (a.k.a. hierarchical) model. Douglas Bate his currently working on a book on the subject (draft avalaible here: http://lme4.r-forge.r-project.org/book/). While there are many books on this subject, Doug's has... | How to choose df for comparisons between summary statistics (e.g. slope values)?
This a very simple multi-level (a.k.a. hierarchical) model. Douglas Bate his currently working on a book on the subject (draft avalaible here: http://lme4.r-forge.r-project.org/book/). While there are |
36,786 | How to choose df for comparisons between summary statistics (e.g. slope values)? | Concerning your more specific question (i.e. how many degrees of freedom): the question is how many replicates do you have. Look at the early pages of chapter 19 of the R book for examples and guidelines for such accounting.
We could do the accounting here but i don't understand the design of your experiment (probably ... | How to choose df for comparisons between summary statistics (e.g. slope values)? | Concerning your more specific question (i.e. how many degrees of freedom): the question is how many replicates do you have. Look at the early pages of chapter 19 of the R book for examples and guideli | How to choose df for comparisons between summary statistics (e.g. slope values)?
Concerning your more specific question (i.e. how many degrees of freedom): the question is how many replicates do you have. Look at the early pages of chapter 19 of the R book for examples and guidelines for such accounting.
We could do th... | How to choose df for comparisons between summary statistics (e.g. slope values)?
Concerning your more specific question (i.e. how many degrees of freedom): the question is how many replicates do you have. Look at the early pages of chapter 19 of the R book for examples and guideli |
36,787 | Intraclass correlation and aggregation | I think (1) is not a statistical question but a subject-area one. E.g., in the described example it would be up to those who study group psychology to determine appropriate language for the strength of ICCs. This is analogous to a Pearson correlation -- what constitutes 'strong' differs depending on whether one is wor... | Intraclass correlation and aggregation | I think (1) is not a statistical question but a subject-area one. E.g., in the described example it would be up to those who study group psychology to determine appropriate language for the strength o | Intraclass correlation and aggregation
I think (1) is not a statistical question but a subject-area one. E.g., in the described example it would be up to those who study group psychology to determine appropriate language for the strength of ICCs. This is analogous to a Pearson correlation -- what constitutes 'strong' ... | Intraclass correlation and aggregation
I think (1) is not a statistical question but a subject-area one. E.g., in the described example it would be up to those who study group psychology to determine appropriate language for the strength o |
36,788 | Intraclass correlation and aggregation | 1) With correlations, you can never really give sensible cut-offs, but the general rules of the normal correlation apply I'd say.
2) Regarding the appropriateness of the ICC : depending on the data, the ICC is equivalent to an F-test (see eg Commenges & Jacqmin, 1994 and Kistner & Muller, 2004). So in essence, the mix... | Intraclass correlation and aggregation | 1) With correlations, you can never really give sensible cut-offs, but the general rules of the normal correlation apply I'd say.
2) Regarding the appropriateness of the ICC : depending on the data, | Intraclass correlation and aggregation
1) With correlations, you can never really give sensible cut-offs, but the general rules of the normal correlation apply I'd say.
2) Regarding the appropriateness of the ICC : depending on the data, the ICC is equivalent to an F-test (see eg Commenges & Jacqmin, 1994 and Kistner ... | Intraclass correlation and aggregation
1) With correlations, you can never really give sensible cut-offs, but the general rules of the normal correlation apply I'd say.
2) Regarding the appropriateness of the ICC : depending on the data, |
36,789 | Intraclass correlation and aggregation | Paul Bliese has an article discussing the intraclass correlation in teams research. He writes that
In [his extensive] experience with U.S. Army [teams] data ...he never encountered ICC(1) values greater than .30 [, and that he] typically [sees] values between .05 and .20.
He goes on to suggest that he would be
sur... | Intraclass correlation and aggregation | Paul Bliese has an article discussing the intraclass correlation in teams research. He writes that
In [his extensive] experience with U.S. Army [teams] data ...he never encountered ICC(1) values gre | Intraclass correlation and aggregation
Paul Bliese has an article discussing the intraclass correlation in teams research. He writes that
In [his extensive] experience with U.S. Army [teams] data ...he never encountered ICC(1) values greater than .30 [, and that he] typically [sees] values between .05 and .20.
He go... | Intraclass correlation and aggregation
Paul Bliese has an article discussing the intraclass correlation in teams research. He writes that
In [his extensive] experience with U.S. Army [teams] data ...he never encountered ICC(1) values gre |
36,790 | On the high dimensional bootstrap | TL;DR The article that you refer to makes things look more worse than they actually are. Their bootstrapping procedure is not a good way to apply bootstrapping. In the case of OLS there shouldn't be big problems with high dimensionality if the sample size is large. If you can not get correct results with OLS, where a c... | On the high dimensional bootstrap | TL;DR The article that you refer to makes things look more worse than they actually are. Their bootstrapping procedure is not a good way to apply bootstrapping. In the case of OLS there shouldn't be b | On the high dimensional bootstrap
TL;DR The article that you refer to makes things look more worse than they actually are. Their bootstrapping procedure is not a good way to apply bootstrapping. In the case of OLS there shouldn't be big problems with high dimensionality if the sample size is large. If you can not get c... | On the high dimensional bootstrap
TL;DR The article that you refer to makes things look more worse than they actually are. Their bootstrapping procedure is not a good way to apply bootstrapping. In the case of OLS there shouldn't be b |
36,791 | What is the roadmap to self-taught probability and statistics for artificial intelligence? | If you were an academic, one must assume you already have a good reference for multivariable calculus, linear algebra, and differential equations – these are not optional. I personally heard from Witten and Tibshirani that their texts have the greatest value in working out the problems at excruciating detail including ... | What is the roadmap to self-taught probability and statistics for artificial intelligence? | If you were an academic, one must assume you already have a good reference for multivariable calculus, linear algebra, and differential equations – these are not optional. I personally heard from Witt | What is the roadmap to self-taught probability and statistics for artificial intelligence?
If you were an academic, one must assume you already have a good reference for multivariable calculus, linear algebra, and differential equations – these are not optional. I personally heard from Witten and Tibshirani that their ... | What is the roadmap to self-taught probability and statistics for artificial intelligence?
If you were an academic, one must assume you already have a good reference for multivariable calculus, linear algebra, and differential equations – these are not optional. I personally heard from Witt |
36,792 | Does convergence in distribution with correlation tending to 1 implies convergence in probability? | Convergence in probability holds under additional (weak) conditions
It is possible to establish convergence in probability here if you can first establish the moment convergence $\mathbb{E}(X_n) \rightarrow \mathbb{E}(Z)$ and $\mathbb{V}(X_n) \rightarrow \mathbb{V}(Z)$. Additional conditions for the moment convergence... | Does convergence in distribution with correlation tending to 1 implies convergence in probability? | Convergence in probability holds under additional (weak) conditions
It is possible to establish convergence in probability here if you can first establish the moment convergence $\mathbb{E}(X_n) \righ | Does convergence in distribution with correlation tending to 1 implies convergence in probability?
Convergence in probability holds under additional (weak) conditions
It is possible to establish convergence in probability here if you can first establish the moment convergence $\mathbb{E}(X_n) \rightarrow \mathbb{E}(Z)$... | Does convergence in distribution with correlation tending to 1 implies convergence in probability?
Convergence in probability holds under additional (weak) conditions
It is possible to establish convergence in probability here if you can first establish the moment convergence $\mathbb{E}(X_n) \righ |
36,793 | Does convergence in distribution with correlation tending to 1 implies convergence in probability? | Two notes on the convergence in moments assumed for @Ben's answer
It's not easy.
Suppose we had instead that $X_n\stackrel{d}{\to} Z$, and $Z_n\stackrel{p}{\to}Z$ and $\mathbb{Corr}[X_n, Z_n]\to 1$. Convergence in probability of $X_n$ to $Z$ need not hold in this slightly modified problem.
Take
$U\sim U[0,1]$,
$V\sim ... | Does convergence in distribution with correlation tending to 1 implies convergence in probability? | Two notes on the convergence in moments assumed for @Ben's answer
It's not easy.
Suppose we had instead that $X_n\stackrel{d}{\to} Z$, and $Z_n\stackrel{p}{\to}Z$ and $\mathbb{Corr}[X_n, Z_n]\to 1$. C | Does convergence in distribution with correlation tending to 1 implies convergence in probability?
Two notes on the convergence in moments assumed for @Ben's answer
It's not easy.
Suppose we had instead that $X_n\stackrel{d}{\to} Z$, and $Z_n\stackrel{p}{\to}Z$ and $\mathbb{Corr}[X_n, Z_n]\to 1$. Convergence in probabi... | Does convergence in distribution with correlation tending to 1 implies convergence in probability?
Two notes on the convergence in moments assumed for @Ben's answer
It's not easy.
Suppose we had instead that $X_n\stackrel{d}{\to} Z$, and $Z_n\stackrel{p}{\to}Z$ and $\mathbb{Corr}[X_n, Z_n]\to 1$. C |
36,794 | Does convergence in distribution with correlation tending to 1 implies convergence in probability? | Isn't this a reminiscent of the CLT? If the distribution of $X_{n}$ converges to Z, this means that the probability converges to Z as well. After all, the probabilities are obtained from distributions. Pearson coefficient:
\begin{equation}
\rho_{X,Z}=\frac{cov(X,Z)}{\sigma_{X} \sigma_{Z}},
\end{equation}
but in the lim... | Does convergence in distribution with correlation tending to 1 implies convergence in probability? | Isn't this a reminiscent of the CLT? If the distribution of $X_{n}$ converges to Z, this means that the probability converges to Z as well. After all, the probabilities are obtained from distributions | Does convergence in distribution with correlation tending to 1 implies convergence in probability?
Isn't this a reminiscent of the CLT? If the distribution of $X_{n}$ converges to Z, this means that the probability converges to Z as well. After all, the probabilities are obtained from distributions. Pearson coefficient... | Does convergence in distribution with correlation tending to 1 implies convergence in probability?
Isn't this a reminiscent of the CLT? If the distribution of $X_{n}$ converges to Z, this means that the probability converges to Z as well. After all, the probabilities are obtained from distributions |
36,795 | How competitive is stepwise regression when it comes to pure prediction? | Stepwise regression is not generally bad at prediction, in the sense that it is not generally worse than, say, LASSO or best subset selection. Which is to say it may be quite good! Recent evidence on that can be found in Hastie et al. (2020). (I regard the authors as pretty much the ultimate experts in the field.) Noti... | How competitive is stepwise regression when it comes to pure prediction? | Stepwise regression is not generally bad at prediction, in the sense that it is not generally worse than, say, LASSO or best subset selection. Which is to say it may be quite good! Recent evidence on | How competitive is stepwise regression when it comes to pure prediction?
Stepwise regression is not generally bad at prediction, in the sense that it is not generally worse than, say, LASSO or best subset selection. Which is to say it may be quite good! Recent evidence on that can be found in Hastie et al. (2020). (I r... | How competitive is stepwise regression when it comes to pure prediction?
Stepwise regression is not generally bad at prediction, in the sense that it is not generally worse than, say, LASSO or best subset selection. Which is to say it may be quite good! Recent evidence on |
36,796 | Does $E\frac{1}{\|x\|^{4}} \rightarrow \frac{1}{E\|x\|^4}$ in high dimensions? | Reformulation in terms of linear combination of $\chi^2(1)$ variables
We can reformulate the problem.
Let's rewrite $$\Vert \mathbf{x} \Vert^4 =\left(\sum_{i=1}^n x_k^2\right)^2 = Y_n^2$$
Such that we can focus on the variable
$$Y_n = \sum_{k=1}^n x_k^2$$
and the problem statement in terms of $Y_n$ becomes
$$E[1/Y_n^2]... | Does $E\frac{1}{\|x\|^{4}} \rightarrow \frac{1}{E\|x\|^4}$ in high dimensions? | Reformulation in terms of linear combination of $\chi^2(1)$ variables
We can reformulate the problem.
Let's rewrite $$\Vert \mathbf{x} \Vert^4 =\left(\sum_{i=1}^n x_k^2\right)^2 = Y_n^2$$
Such that we | Does $E\frac{1}{\|x\|^{4}} \rightarrow \frac{1}{E\|x\|^4}$ in high dimensions?
Reformulation in terms of linear combination of $\chi^2(1)$ variables
We can reformulate the problem.
Let's rewrite $$\Vert \mathbf{x} \Vert^4 =\left(\sum_{i=1}^n x_k^2\right)^2 = Y_n^2$$
Such that we can focus on the variable
$$Y_n = \sum_{... | Does $E\frac{1}{\|x\|^{4}} \rightarrow \frac{1}{E\|x\|^4}$ in high dimensions?
Reformulation in terms of linear combination of $\chi^2(1)$ variables
We can reformulate the problem.
Let's rewrite $$\Vert \mathbf{x} \Vert^4 =\left(\sum_{i=1}^n x_k^2\right)^2 = Y_n^2$$
Such that we |
36,797 | Is there a Good Illustrative Example where the Hinge Loss (SVM) Gives a Higher Accuracy than the Logistic Loss | The example attributed to Olivier Bousquet doesn't work as clearly as depicted in the blog post mentioned in an answer to a related question, but I have been able to make it work to some extent in a more realistic setting, so I'll post it here in case it stimulates further (hopefully simpler or more informative) exampl... | Is there a Good Illustrative Example where the Hinge Loss (SVM) Gives a Higher Accuracy than the Log | The example attributed to Olivier Bousquet doesn't work as clearly as depicted in the blog post mentioned in an answer to a related question, but I have been able to make it work to some extent in a m | Is there a Good Illustrative Example where the Hinge Loss (SVM) Gives a Higher Accuracy than the Logistic Loss
The example attributed to Olivier Bousquet doesn't work as clearly as depicted in the blog post mentioned in an answer to a related question, but I have been able to make it work to some extent in a more reali... | Is there a Good Illustrative Example where the Hinge Loss (SVM) Gives a Higher Accuracy than the Log
The example attributed to Olivier Bousquet doesn't work as clearly as depicted in the blog post mentioned in an answer to a related question, but I have been able to make it work to some extent in a m |
36,798 | Is there a Good Illustrative Example where the Hinge Loss (SVM) Gives a Higher Accuracy than the Logistic Loss | The results you shared are fascinating. Here's some more exploration in a similar direction.
The idea behind the Bousquet example is to create a situation where optimizing the logistic loss prioritizes fitting the underlying probability distribution at the expense of accuracy. But, it's not clear to me that accuracy an... | Is there a Good Illustrative Example where the Hinge Loss (SVM) Gives a Higher Accuracy than the Log | The results you shared are fascinating. Here's some more exploration in a similar direction.
The idea behind the Bousquet example is to create a situation where optimizing the logistic loss prioritize | Is there a Good Illustrative Example where the Hinge Loss (SVM) Gives a Higher Accuracy than the Logistic Loss
The results you shared are fascinating. Here's some more exploration in a similar direction.
The idea behind the Bousquet example is to create a situation where optimizing the logistic loss prioritizes fitting... | Is there a Good Illustrative Example where the Hinge Loss (SVM) Gives a Higher Accuracy than the Log
The results you shared are fascinating. Here's some more exploration in a similar direction.
The idea behind the Bousquet example is to create a situation where optimizing the logistic loss prioritize |
36,799 | Permutation testing for machine learning: permute entire set or only training set? | There are few things to unpack here. The goal of permutation testing is to get a null distribution for your test statistic by permuting labels and repeating your procedure many times.
Your test statistic is e.g., average accuracy, and your procedure is CV. So you should permute the labels (all labels, because all label... | Permutation testing for machine learning: permute entire set or only training set? | There are few things to unpack here. The goal of permutation testing is to get a null distribution for your test statistic by permuting labels and repeating your procedure many times.
Your test statis | Permutation testing for machine learning: permute entire set or only training set?
There are few things to unpack here. The goal of permutation testing is to get a null distribution for your test statistic by permuting labels and repeating your procedure many times.
Your test statistic is e.g., average accuracy, and yo... | Permutation testing for machine learning: permute entire set or only training set?
There are few things to unpack here. The goal of permutation testing is to get a null distribution for your test statistic by permuting labels and repeating your procedure many times.
Your test statis |
36,800 | Permutation testing for machine learning: permute entire set or only training set? | At prediction time, you have the $(y_i, \hat y_i)$ pairs of the actual labels and the predictions. Notice that the result would be the same if you permuted the actual labels $y_i$'s and if you permuted the predictions $\hat y_i$'s, since permuting them breaks the pairing. So such a permutation test would create the nul... | Permutation testing for machine learning: permute entire set or only training set? | At prediction time, you have the $(y_i, \hat y_i)$ pairs of the actual labels and the predictions. Notice that the result would be the same if you permuted the actual labels $y_i$'s and if you permute | Permutation testing for machine learning: permute entire set or only training set?
At prediction time, you have the $(y_i, \hat y_i)$ pairs of the actual labels and the predictions. Notice that the result would be the same if you permuted the actual labels $y_i$'s and if you permuted the predictions $\hat y_i$'s, since... | Permutation testing for machine learning: permute entire set or only training set?
At prediction time, you have the $(y_i, \hat y_i)$ pairs of the actual labels and the predictions. Notice that the result would be the same if you permuted the actual labels $y_i$'s and if you permute |
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