# niw.mom: Mean and variance of the Normal-Inverse-Wishart distribution. In nicheROVER: Niche Region and Niche Overlap Metrics for Multidimensional Ecological Niches

## Description

This function computes the mean and variance of the Normal-Inverse-Wishart (NIW) distribution. Can be used to very quickly compute Bayesian point estimates for the conjugate NIW prior.

## Usage

 1 niw.mom(lambda, kappa, Psi, nu) 

## Arguments

 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(μ, Σ | λ, κ, Ψ, ν) is defined as

Σ \sim W^{-1}(Ψ, ν), \quad μ | Σ \sim N(λ, Σ/κ).

Note that cov(μ, Σ) = 0.

Returns a list with elements mu and Sigma, each containing lists with elements mean and var. For mu these elements are of size length(lambda) and c(length(lambda),length(lambda)). For Sigma they are of size dim(Psi) and c(dim(Psi), dim(Psi)), such that cov(Σ_{ij}, Σ_{kl})=Sigma$var[i,j,k,l]. ## See Also rniw(), niw.coeffs(), niw.post(). ## Examples   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 # NIW parameters d <- 3 # number of dimensions lambda <- rnorm(d) kappa <- 2 Psi <- crossprod(matrix(rnorm(d^2), d, d)) nu <- 10 # simulate data niw.sim <- rniw(n = 1e4, lambda, kappa, Psi, nu) # check moments niw.mV <- niw.mom(lambda, kappa, Psi, nu) # mean of mu ii <- 1 c(true = niw.mV$mu$mean[ii], sim = mean(niw.sim$mu[,ii])) # variance of Sigma II <- c(1,2) JJ <- c(2,3) c(true = niw.mV$var[II[1],II[2],JJ[1],JJ[2]], sim = cov(niw.sim$Sigma[II[1],II[2],], niw.sim\$Sigma[JJ[1],JJ[2],])) 

### Example output

Loading required package: mvtnorm
true         sim
-0.04494216 -0.04225873
sim
-0.02887313


nicheROVER documentation built on June 4, 2021, 1:09 a.m.