Variance estimation from integrated likelihoods (VEIL)

Abstract

A method of variance component estimation is univariate mixed linear models based on the exact or approximate posterior distributions of the variance components is presented. From these distributions, posterior means, modes and variances can be calculated exactly, via numerical methods, or approximately, using inverted-chi-2 distributions. Although particular attention is given to a Bayesian analysis with flat priors informative prior distributions can be used without great additional difficulty. Implementation of the exact analysis can be taxing from a numerical point of view, but the computational requirements of the approximate method are not greater than those of REML.