# make.gaussian: Gaussian distribution objects In SamplerCompare: A Framework for Comparing the Performance of MCMC Samplers

## Description

Gaussian distribution objects

## Usage

 ```1 2 3 4``` ```make.gaussian(mean, sigma=NULL, rho=NULL) N2weakcor.dist N4poscor.dist N4negcor.dist ```

## Arguments

 `mean` The mean of the distribution as a numeric vector; implicitly specifies the dimension. `sigma` The covariance of the distribution. `rho` The marginal correlations between parameters.

## Details

`make.gaussian` returns a distribution object representing a multivariate normal distribution. If `sigma` is specified, that is taken to be its covariance. Otherwise, if `rho` is specified, the covariance is taken to be a matrix with ones on the diagonal and `rho` on the off-diagonal elements. To preserve positive definiteness, `rho` must be between `-1/(length(mean)-1)` and 1.

`N2weakcor.dist`, `N4poscor.dist`, and `N4negcor.dist` are predefined distributions generated with `make.gaussian`. They are intended to be used as test cases with `compare.samplers`. The examples below show how they are defined. `N2weakcor.dist` is a weakly positively correlated two-dimensional Gaussian. `N4poscor.dist` is a highly positively correlated four-dimensional Gaussian. `N4negcor.dist` is a highly negatively correlated four-dimensional Gaussian. `N4poscor.dist` and `N4negcor.dist` are similarly conditioned, but `N4poscor.dist` has one large eigenvalue and three small ones, while `N4negcor.dist` has one small eigenvalue and three large ones.

`compare.samplers`, `make.dist`
 ```1 2 3``` ``` N2weakcor.dist <- make.gaussian(c(0,0), rho=0.8) N4poscor.dist <- make.gaussian(c(1,2,3,4), rho=0.999) N4negcor.dist <- make.gaussian(c(1,2,3,4), rho=-0.3329) ```