Sampling from marginal posterior multivariate t-distribution.

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

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

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.

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.

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)