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Generate Inverse-Wishart Random Matrix

Source: R/RcppExports.R
sim_iw.Rd

This function samples one matrix IW matrix.

Usage

sim_iw(mat_scale, shape)

Arguments

mat_scale

Scale matrix

shape

Shape

Value

One k x k matrix following IW distribution

Details

Consider \(\Sigma \sim IW(\Psi, \nu)\).

  1. Upper triangular Bartlett decomposition: k x k matrix \(Q = [q_{ij}]\) upper triangular with

    1. \(q_{ii}^2 \chi_{\nu - i + 1}^2\)

    2. \(q_{ij} \sim N(0, 1)\) with i < j (upper triangular)

  2. Lower triangular Cholesky decomposition: \(\Psi = L L^T\)

  3. \(A = L (Q^{-1})^T\)

  4. \(\Sigma = A A^T \sim IW(\Psi, \nu)\)