dWishart: Density function of Wishart distribution

In bbricks: Bayesian Methods and Graphical Model Structures for Statistical Modeling

Description

For a random matrix x, the density function of Wishart distribution is defined as:

(2^{(df p)/2} Gamma_p(df/2) |rate|^{-df/2})^{-1} |x|^{(df-p-1)/2} exp(-1/2 tr(x rate))

Where x is a pxp symmetric positive definite matrix, Gamma_p() is the multivariate Gamma function of dimension p.

Usage

dWishart(x, df, rate, LOG = TRUE)

Arguments

x	matrix, a symmetric positive-definite matrix.
df	numeric, the degree of freedom.
rate	matrix, a symmetric positive-definite matrix, the 'rate', or 'inverse-scale' parameter. The 'rate' parameter in Wishart is the 'scale' parameter in InvWishart
LOG	logical, return log density of LOG=TRUE, default TRUE.

Value

A numeric vector, the density values.

References

Wishart, John. "The generalized product moment distribution in samples from a normal multivariate population." Biometrika (1928): 32-52.

MARolA, K. V., JT KBNT, and J. M. Bibly. Multivariate analysis. AcadeInic Press, Londres, 1979.

Examples

##generate a symmetric positive-definite matrix
x <- crossprod(matrix(rnorm(15),5,3))
rate <- crossprod(matrix(rnorm(15),5,3)) #the prior inverse-scale of x
dWishart(x,df = 5,rate = rate,LOG = TRUE)
dWishart(x,df = 5,rate = rate,LOG = FALSE)

bbricks documentation built on July 8, 2020, 7:29 p.m.