mrbsizeR (version 1.3)

rmvtDCT: Sampling from marginal posterior multivariate t-distribution.

Description

Samples from a marginal posterior multivariate t-distribution with normal-inverse-chi-squared-prior are generated.

Usage

rmvtDCT(object, lambda, sigma, nu0, ns)

Value

A list containing the following elements:

sample Samples of the marginal posterior of the input.

mu Mean of the marginal posterior of the input.

Arguments

object

Observed object, as matrix.

lambda

Scaling parameter (\(\lambda\)) of the normal-inverse-chi-squared-prior.

sigma

Square root of the \(\sigma_{0}^{2}\) parameter of the normal-inverse-chi-squared-prior.

nu0

Degrees of freedom (\(\nu_{0}\)) of the normal-inverse-chi-square-prior.

ns

Number of samples that should be generated.

Details

An eigenvalue decomposition is used for sampling. To speed up computations, a 2D discrete cosine transform (DCT) has been implemented, see dctMatrix. The output is a list containing

1. Samples of the marginal posterior of the input as column vectors.

2. The mean of the marginal posterior of the input as a vector.

Examples

# Artificial sample data
set.seed(987)
sampleData <- matrix(stats::rnorm(100), nrow = 10)
sampleData[4:6, 6:8] <- sampleData[4:6, 6:8] + 5

# Sampling from a multivariate t-distribution
t_dist_samp <- rmvtDCT(object = sampleData, lambda = 1, sigma = 10,
                       nu0 = 50, ns = 1000)