Normal-Wishart Distribution
These functions provide the density and random number generation for the normal-Wishart distribution.
dnormwishart(mu, mu0, lambda, Omega, S, nu, log=FALSE) rnormwishart(n=1, mu0, lambda, S, nu)
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. |
Omega |
This is a k x k precision matrix Omega. |
S |
This is the symmetric, positive-semidefinite, k x k scale matrix S. |
log |
Logical. If |
Application: Continuous Multivariate
Density: p(mu, Omega) = N(mu | mu[0], (lambda Omega)^(-1)) W(Omega | nu, S)
Inventors: Unknown
Notation 1: (mu, Omega) ~ NW(mu[0], lambda, S, nu)
Notation 2: p(mu, Omega) = NW(mu, Omega | 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-Wishart distribution, or Gaussian-Wishart distribution, is a multivariate four-parameter continuous probability distribution. It is the conjugate prior of a multivariate normal distribution with unknown mean and precision matrix.
dnormwishart gives the density and
rnormwishart generates random deviates and returns a list with
two components.
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library(LaplacesDemon) K <- 3 mu <- rnorm(K) mu0 <- rnorm(K) nu <- K + 1 S <- diag(K) lambda <- runif(1) #Real scalar Omega <- as.positive.definite(matrix(rnorm(K^2),K,K)) x <- dnormwishart(mu, mu0, lambda, Omega, S, nu, log=TRUE) out <- rnormwishart(n=10, mu0, lambda, S, nu) joint.density.plot(out$mu[,1], out$mu[,2], color=TRUE)
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