sample_post_nor_ref_marg_mu {BayesMultMeta}

Metropolis-Hastings algorithm for the normal distribution and the Berger and Bernardo reference prior, where \mathbf{\mu} is generated from the marginal posterior.

Description

This function implements Metropolis-Hastings algorithm for drawing samples from the posterior distribution of \mathbf{\mu} and \mathbf{\Psi} under the assumption of the normal distribution when the Berger and Bernardo reference prior is employed. At each step, the algorithm starts with generating a draw from the marginal distribution of \mathbf{\mu}.

Usage

sample_post_nor_ref_marg_mu(X, U, Np)

Arguments

X

A p \times n matrix which contains n observation vectors of dimension p.

U

A p n \times p n block-diagonal matrix which contains the covariance matrices of observation vectors.

Np

Length of the generated Markov chain.

Value

List with the generated samples from the joint posterior distribution of \mathbf{\mu} and \mathbf{\Psi}, where the values of \mathbf{\Psi} are presented by using the vec operator.