Mixture Normal Distribution for Gibbs Sampler and its Application in the Surface of Single Crystal

Abstract

Gibbs sampler is widely used in Bayesian analysis. But it is often difficult to sample from the full conditional distribution, and this hardly weakens the efficiency of Gibbs sampler. In this paper, we propose to use mixture normal distribution for Gibbs sampler. The mixture normal distribution can approximate the target distribution. So carrying more information from target distribution, the mixture normal distribution tremendously improves the efficiency of Gibbs sampler. Further more, combining with mixture normal method, Hit-and-Run algorithm can also get more efficient sampling results. Simulation results show that Gibbs sampler with mixture normal distribution outperforms other sampling algorithms. The Gibbs sampler with mixture normal distribution can also be applied to explorer the surface of single crystal.