| scaled.matrix.normal.prior {Boom} | 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.
Author(s)
Steven L. Scott steve.the.bayesian@gmail.com