scaled.matrix.normal.prior: Scaled Matrix-Normal Prior
In Boom: Bayesian Object Oriented Modeling

scaled.matrix.normal.prior

R Documentation

Scaled Matrix-Normal Prior

Description

A matrix-normal prior distribution, intended as the conjugate prior for the regression coefficients in a multivariate linear regression.

Usage

ScaledMatrixNormalPrior(mean, nu)

Arguments

`mean`	A matrix giving the mean of the distributions
`nu`	A scale factor affecting the variance.

Details

The matrix normal distribution is a 3-parameter distribution MN(mu, Omega, V), where mu is the mean. A deviate from the distribution is a matrix B, where Cov(B[i, j], B[k, m]) = Omega[i, k] * Sigma[j, m]. If b = Vec(B) is the vector obtained by stacking columns of B, then b is multivariate normal with mean Vec(mu) and covariance matrix

\Sigma \otimes Omega

(the kronecker product).

This prior distribution assumes the underlying C++ code knows where to find the predictor (X) matrix in the regression, and the residual variance matrix Sigma. The assumed prior distribution is B ~ MN(mu, X'X / nu, Sigma).

Like most other priors in Boom, this function merely encodes information expected by the underlying C++ code, ensuring correct names and formatting.