rniw: Random draws from a Normal-Inverse-Wishart distribution.

In nicheROVER: Niche Region and Niche Overlap Metrics for Multidimensional Ecological Niches

Random draws from a Normal-Inverse-Wishart distribution.

Description

Generates random draws from a Normal-Inverse-Wishart (NIW) distribution. Can be used to compare prior to posterior parameter distributions.

Usage

rniw(n, lambda, kappa, Psi, nu)

Arguments

n	Number of samples to draw.
lambda	Location parameter. See 'Details'.
kappa	Scale parameter. See 'Details'.
Psi	Scale matrix. See 'Details'.
nu	Degrees of freedom. See 'Details'.

Details

The NIW distribution p(\mu, \Sigma | \lambda, \kappa, \Psi, \nu) is defined as

\Sigma \sim W^{-1}(\Psi, \nu), \quad \mu | \Sigma \sim N(\lambda, \Sigma/\kappa).

Value

Returns a list with elements mu and Sigma of sizes c(n,length(lambda)) and c(nrow(Psi),ncol(Psi),n).

See Also

rwish(), niw.mom(), niw.coeffs().

Examples

d <- 4 # number of dimensions
nu <- 7 # degrees of freedom
Psi <- crossprod(matrix(rnorm(d^2), d, d)) # scale
lambda <- rnorm(d)
kappa <- 2
n <- 1e4

niw.sim <- rniw(n, lambda, kappa, Psi, nu)

# diagonal elements of Sigma^{-1} are const * chi^2
S <- apply(niw.sim$Sigma, 3, function(M) diag(solve(M)))

ii <- 2
const <- solve(Psi)[ii,ii]
hist(S[ii,], breaks = 100, freq = FALSE,
     main = parse(text = paste0("\"Histogram of \"*(Sigma^{-1})[", ii,ii,"]")),
     xlab = parse(text = paste0("(Sigma^{-1})[", ii,ii,"]")))
curve(dchisq(x/const, df = nu)/const,
      from = min(S[ii,]), to = max(S[ii,]), col = "red", add = TRUE)

# elements of mu have a t-distribution
mu <- niw.sim$mu

ii <- 4
const <- sqrt(Psi[ii,ii]/(kappa*(nu-d+1)))
hist(mu[,ii], breaks = 100, freq = FALSE,
     main = parse(text = paste0("\"Histogram of \"*mu[", ii, "]")),
     xlab = parse(text = paste0("mu[", ii, "]")))
curve(dt((x-lambda[ii])/const, df = nu-d+1)/const, add = TRUE, col = "red")

nicheROVER documentation built on Oct. 13, 2023, 5:10 p.m.