Research Interest

Markov chain Monte Carlo (MCMC) becomes indispensable methodology when it is intractable to sample directly from a distribution of interest. In MCMC one designs a Markov kernel whose stationary distribution is the distribution of interest, and runs the Markov chain for a long time. The analysis of rate of convergence to stationarity can provide information necessary to decide the running time; however, such analysis is very difficult or even found impossible in practice. The emergence of perfect sampling techniques, if applicable, not only eliminates the necessity of such analysis but also provides an algorithm to simulate exactly from the stationary distribution. There are two main ideas for perfect sampling--coupling from the past (CFTP) by Propp and Wilson (1996) and the perfect rejection sampling method by Fill (1998). My research is motivated by the development of the perfect rejection sampling algorithm--a currently less-used alternative.