dist.Normal.Wishart | R Documentation |
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
|
mu0 |
This is mean vector |
lambda |
This is a positive-only scalar. |
n |
This is the number of random draws. |
nu |
This is the scalar degrees of freedom |
Omega |
This is a |
S |
This is the symmetric, positive-semidefinite, |
log |
Logical. If |
Application: Continuous Multivariate
Density: p(\mu, \Omega) = \mathcal{N}(\mu | \mu_0,
(\lambda\Omega)^{-1}) \mathcal{W}(\Omega | \nu, \textbf{S})
Inventors: Unknown
Notation 1: (\mu, \Omega) \sim \mathcal{NW}(\mu_0, \lambda,
\textbf{S}, \nu)
Notation 2: p(\mu, \Omega) = \mathcal{NW}(\mu, \Omega |
\mu_0, \lambda, \textbf{S}, \nu)
Parameter 1: location vector \mu_0
Parameter 2: \lambda > 0
Parameter 3: symmetric, positive-semidefinite
k \times k
scale matrix \textbf{S}
Parameter 4: degrees of freedom \nu \ge 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.
Statisticat, LLC. software@bayesian-inference.com
dmvnp
and
dwishart
.
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)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.