dpostNIW {mombf}

Posterior Normal-IWishart density

Description

dpostNIW evalutes the posterior Normal-IWishart density at (mu,Sigma). rpostNIW draws independent samples. This posterior corresponds to a Normal model for the data

x[i,] ~ N(mu,Sigma) iid i=1,...,n

under conjugate priors

mu | Sigma ~ N(mu0, g Sigma) Sigma ~ IW(nu0, S0)

Usage

dpostNIW(mu, Sigma, x, g=1, mu0=rep(0,length(mu)), nu0=nrow(Sigma)+1, S0,
  logscale=FALSE)

rpostNIW(n, x, g=1, mu0=0, nu0, S0, precision=FALSE)

Arguments

mu

Vector of length p

Sigma

p x p positive-definite covariance matrix

x

n x p data matrix (individuals in rows, variables in columns)

g

Prior dispersion parameter for mu

mu0

Prior mean for mu

nu0

Prior degrees of freedom for Sigma

S0

Prior scale matrix for Sigma, by default set to I/nu0

logscale

set to TRUE to get the log-posterior density

n

Number of samples to draw

precision

If set to TRUE, samples from the precision matrix (inverse of Sigma) are returned instead

Value

dpostNIW returns the Normal-IW posterior density evaluated at (mu,Sigma).

rpostNIW returns a list with two elements. The first element are posterior draws for the mean. The second element are posterior draws for the covariance (or its inverse if precision==TRUE). Only lower-diagonal elements are returned (Sigma[lower.tri(Sigma,diag=TRUE)]).

Author(s)

David Rossell

See Also

diwish for the inverse Wishart prior density, marginalNIW for the integrated likelihood under a Normal-IW prior

Examples

#Simulate data
x= matrix(rnorm(100),ncol=2)
#Evaluate posterior at data-generating truth
mu= c(0,0)
Sigma= diag(2)
dpostNIW(mu,Sigma,x=x,g=1,nu0=4,log=FALSE)