Post-Processing for MCMC

Markov Chain Monte Carlo methods (MCMC) can sample from a target distribution and approximate this distribution. MCMC methods employ the apriori known unnormalized target distribution to decide on the acceptance of new states, but not to approximate the final distribution. This paper investigates how the unnormalized target distribution can be used for approximation purposes. It is shown that this function can be used to obtain an unbiased estimate of the target distribution. Under certain circumstances, this approach can greatly reduce the variance of the resulting estimate. A useful side-effect of our estimation method is that the sampling method no longer has to follow the target distribution. Based on this observation, a sampling method with a variable degree of exploration is described that still converges to the target function. Thus, exploration can be performed, thereby improving mixing, without discarding sample points. Both methods are demonstrated in experiments.