On Simulation Methods for Two Component Normal Mixture Models under Bayesian Approach
Liwen Liang · KTH Publication Database DiVA (KTH Royal Institute of Technology) · 2009
EM-Algorithm and Gibbs sampler are two useful Bayesian simulation methods for parameter estimation of finite normal mixture model. The EM-Algorithm is an iterative estimate of maximum likelihood for incomplete data problem. Gibbs sampler is an approach of generating random sample from a multivariate distribution. We introduce and derive Dempster EM-Algorithm for the two-component normal mixture models to get the iterative computation estimates, also use data augmentation and general Gibbs sampler to get the sample from posterior distribution under conjugate prior. The estimate results from both simulation methods under two-component normal mixture model with unknown mean parameters are compared and the connections and differences between both methods are represented. Data set from astronomy is used for comparison. Acknowledgement I would like to thank my supervisor Silvelyn Zwanzig for the patience, guidance and encouragement that she always gave to me, not only in the thesis, but also in the whole procedure of my statistics studying. I would also like to thank my friend Han Jun for the the assistances of LATEX, thank Alena for the data source, and thank my parents for the spiritual and substantial support and wholesouled love they gave me all my life. At last I would like to thank the department of mathematics of Uppsala University for giving me the opportunity to study.