equi_mcmc.Samples from the square root of an inverse-gamma.
sample_sig(X, phi_inv)A numeric. The update for the total variation parameter in the MCMC
implemented in equi_bayes.
An array. The tensor data.
A list of the current values of inverse of the lower-triangular Cholesky square root of the the component covariance matrices. This is equivalent to the transpose of the upper-triangular Cholesky square root of the inverse component covariance matrices.
phi_inv[[i]] is a lower triangluar matrix where
solve(phi_inv[[i]]) %*% t(solve(phi_inv[[i]])) is the current
estimate of the \(i\)th component covariance matrix.
David Gerard.
This function provides a Gibbs update for the total variation parameter from
the MCMC implemented in equi_mcmc. This corresponds to the square root
of an inverse-gamma distributed random variable whose parameters depend on
the data and the component covariance matrices. Roughly, this is the update
for the standard deviation, not the variance.
Gerard, D., & Hoff, P. (2015). Equivariant minimax dominators of the MLE in the array normal model. Journal of Multivariate Analysis, 137, 32-49. tools:::Rd_expr_doi("10.1016/j.jmva.2015.01.020")
equi_mcmc for a Gibbs sampler where this function is
used.