## Solved – “mixture” in a gaussian mixture model

We often study Gaussian Mixture model as a useful model in machine learning and its applications. What is the physical significance of this "Mixture"? Is it used because a Gaussian Mixture Model models the probability of a number of random variables each with its own value of mean? If not, then what is the correct … Read more

## Solved – Good resources (online or book) on the mathematical foundations of statistics

Before I ask my question, let me give you a bit of background about what I know about statistics so that you have a better sense of the types of resources that I'm looking for. I'm a graduate student in psychology, and as such, I use statistics almost every day. By now I'm familiar with … Read more

## Solved – invariance of correlation to linear transformation: \$text{corr}(aX+b, cY+d) = text{corr}(X,Y)\$

This is actually one of the problems in Gujarati's Basic Econometrics 4th edition (Q3.11) and says that the correlation coefficient is invariant with respect to the change of origin and scale, that is \$\$text{corr}(aX+b, cY+d) = text{corr}(X,Y)\$\$ where \$a\$,\$b\$,\$c\$,\$d\$ are arbitrary constants. But my main question is the following: Let \$X\$ and \$Y\$ be paired … Read more

## Solved – invariance of correlation to linear transformation: \$text{corr}(aX+b, cY+d) = text{corr}(X,Y)\$

This is actually one of the problems in Gujarati's Basic Econometrics 4th edition (Q3.11) and says that the correlation coefficient is invariant with respect to the change of origin and scale, that is \$\$text{corr}(aX+b, cY+d) = text{corr}(X,Y)\$\$ where \$a\$,\$b\$,\$c\$,\$d\$ are arbitrary constants. But my main question is the following: Let \$X\$ and \$Y\$ be paired … Read more

## Solved – Distribution of the quotient of two gamma random variables with different rate parameters

I have a question about how to derive the distribution of the quotient of two random gamma variables drawn from two different Gamma distributions with the same shape, but different rates. For example, given \$\$ theta sim frac{1}{Gamma(a, c_1)} \ tau sim frac{1}{Gamma(b, c_2)} \$\$ How do I find the distribution of the following? \$\$ … Read more

## Solved – Who uses R with multicore, SNOW or CUDA package for resource intense computing

Who of you in this forum uses ">R with the multicore, snow packages, or CUDA, so for advanced calculations that need more power than a workstation CPU? On which hardware do you compute these scripts? At home/work or do you have data center access somewhere? The background of these questions is the following: I am … Read more

## Solved – Who uses R with multicore, SNOW or CUDA package for resource intense computing

Who of you in this forum uses ">R with the multicore, snow packages, or CUDA, so for advanced calculations that need more power than a workstation CPU? On which hardware do you compute these scripts? At home/work or do you have data center access somewhere? The background of these questions is the following: I am … Read more

## Solved – Matrix multiplication to find correlation matrix

In this book on matrix factorizations, the author states the following, which I don't find to be true empirically. Is it true and under what conditions? ADD: Trying to recreate the answer in R, what is the issue? > D<-matrix(c(7,1,4,5,2,2,4,5,5,2,5,1,7,8,0,7),nrow=4,ncol=2,byrow=TRUE) > D [,1] [,2] [1,] 7 1 [2,] 4 5 [3,] 2 2 [4,] 4 … Read more

## Solved – Matrix multiplication to find correlation matrix

In this book on matrix factorizations, the author states the following, which I don't find to be true empirically. Is it true and under what conditions? ADD: Trying to recreate the answer in R, what is the issue? > D<-matrix(c(7,1,4,5,2,2,4,5,5,2,5,1,7,8,0,7),nrow=4,ncol=2,byrow=TRUE) > D [,1] [,2] [1,] 7 1 [2,] 4 5 [3,] 2 2 [4,] 4 … Read more

## Solved – What exactly are moments? How are they derived

We are typically introduced to method of moments estimators by "equating population moments to their sample counterpart" until we have estimated all of the population's parameters; so that, in the case of a normal distribution, we would only need the first and second moments because they fully describe this distribution. \$E(X) = mu implies sum_{i=1}^n … Read more