dist.Normal.Inverse.Wishart: Normal-Inverse-Wishart Distribution

In LaplacesDemon: Complete Environment for Bayesian Inference

Description

These functions provide the density and random number generation for the normal-inverse-Wishart distribution.

Usage

dnorminvwishart(mu, mu0, lambda, Sigma, S, nu, log=FALSE) 
rnorminvwishart(n=1, mu0, lambda, S, nu)

Arguments

mu	This is data or parameters in the form of a vector of length k or a matrix with k columns.
mu0	This is mean vector mu[0] with length k or matrix with k columns.
lambda	This is a positive-only scalar.
n	This is the number of random draws.
nu	This is the scalar degrees of freedom nu.
Sigma	This is a k x k covariance matrix Sigma.
S	This is the symmetric, positive-semidefinite, k x k scale matrix S.
log	Logical. If log=TRUE, then the logarithm of the density is returned.

Details

• Application: Continuous Multivariate

• Density: p(mu, Sigma) = N(mu | mu[0], (1/lambda) Sigma) W^(-1)(Sigma | nu, S)

• Inventors: Unknown

• Notation 1: (mu, Sigmaa) ~ NIW(mu[0], lambda, S, nu)

• Notation 2: p(mu, Sigma) = NIW(mu, Sigma | mu[0], lambda, S, nu)

• Parameter 1: location vector mu[0]

• Parameter 2: lambda > 0

• Parameter 3: symmetric, positive-semidefinite k x k scale matrix S

• Parameter 4: degrees of freedom nu >= k

• Mean: Unknown

• Variance: Unknown

• Mode: Unknown

The normal-inverse-Wishart distribution, or Gaussian-inverse-Wishart distribution, is a multivariate four-parameter continuous probability distribution. It is the conjugate prior of a multivariate normal distribution with unknown mean and covariance matrix.

Value

dnorminvwishart gives the density and rnorminvwishart generates random deviates and returns a list with two components.

Author(s)

Statisticat, LLC. [e-mail]

See Also

dmvn and dinvwishart.

Examples

library(LaplacesDemon)
K <- 3
mu <- rnorm(K)
mu0 <- rnorm(K)
nu <- K + 1
S <- diag(K)
lambda <- runif(1) #Real scalar
Sigma <- as.positive.definite(matrix(rnorm(K^2),K,K))
x <- dnorminvwishart(mu, mu0, lambda, Sigma, S, nu, log=TRUE)
out <- rnorminvwishart(n=10, mu0, lambda, S, nu)
joint.density.plot(out$mu[,1], out$mu[,2], color=TRUE)

Example output

LaplacesDemon documentation built on July 9, 2021, 5:07 p.m.