BAYESIAN-INFERENCE ABOUT DISPERSION PARAMETERS OF UNIVARIATE MIXED MODELS WITH MATERNAL EFFECTS - THEORETICAL CONSIDERATIONS

Mixed linear models for maternal effects include fixed and random elements, and dispersion parameters (variances and covariances). In this paper a Bayesian model for inferences about such parameters is presented. The model includes a normal likelihood for the data, a "flat" prior for the fixed effects and a multivariate normal prior for the direct and maternal breeding values. The prior distribution for the genetic variance-covariance components is in the inverted Wishart form and the environmental components follow inverted chi-2 prior distributions. The kernel of the joint posterior density of the dispersion parameters is derived in closed form. Additional numerical and analytical methods of interest that are suggested to complete a Bayesian analysis include Monte-Carlo Integration, maximum entropy fit, asymptotic approximations, and the Tierney-Kadane approach to marginalization.