Comparison of sampling based approaches for Bayesian computations

From the computational point of view, Bayesian statistical inference requires high dimensional numerical integration to calculate the characteristics of the posterior distribution. The Gibbs Sampler, an iterative Markov chain simulation technique, is a widely used sampling based approach for Bayesian computation. To study the numerical integration problem from a more general point of view, five specialized random sampling algorithms are implemented to perform the Gibbs sampler when nonconjugate specification is presented, and a overall performance comparison is proceeded.; The factors which affect the convergence of the Gibbs sampler, correlation structure and dimensionality, will be discussed in an easily understood manner. A technique which is useful for monitoring the Gibbs sampler will be introduced from the numerical and computational point of view. Two types of acceleration to the Gibbs sampler algorithm are proposed which shortcuts the convergence and saves computing time.; Several applications and examples are illustrated including the analysis of incomplete data and constrained parameters.