The Markov Chain Monte-Carlo (MCMC) born in early 1950s has recently aroused great interest
among statisticians, particularly researchers working in image analysis, discrete optimization, neural
networks, genetic sequencing and other related Eelds. Recent theoretical achievements in resampling
procedures provide a new perspective for handling errors in Bayesian inference, which treats all unknowns
as random variables. The unknowns include uncertainties in the model such as fixed effects, random
effects, unobserved indicator variables and missing data. Only in few cases, the posterior distribution is in
standard analytic form. In most other models like generalized linear models, mixture models,
epidemiological models and survival analysis, the exact analytic Bayesian inference is impossible. This
paper surveys some of the recent advances in this area that allows exact Bayesian computation using
simulations and discusses some applications to biomedical data
