Empirical Bayesian Approach for Variance Component Model in Genetic Analysis of Psychological Disorder

Variance component model can be effectively used in quantitative genetic analysis of psychological disorder and various estimation methods have been presented in literatures. It´s obvious that the current development of MCMC and Gibbs sampling has virtually brought in a popular application of Bayesian method, since the complex integration of posterior distribution has been solved effectively. However, many simulation studies have pointed out that the choice of priors could have considerable influence on the final results. Consequently, additional simulation studies are necessarily carried out to determine the proper priors. This paper proposes the empirical Bayesian approach for variance component model when the prior distribution is unknown or is difficult to determine. We first transform the conditional distribution of parameters in variance component model into the multi-parameter exponential form, and then construct its empirical Bayesian estimator based on the kernel estimation of density with the historical samples. At last, we prove the convergence of empirical Bayesian estimator with the relevant results about multi-parameter exponential family. The convergence guarantees the reasonability and feasibility of empirical Bayesian approach for variance component model.