Executive Summary

We present a new approach to the estimation of likelihood surfaces from a single run of a Markov chain in some Markov Chain Monte Carlo (MCMC) methods. It alleviates the need to multiple chains applied in some previous applications of MCMC in population genetics. We also present a new MCMC method applicable to DNA sequence data, based on data augmentation. In this method, mutations in the geneology are treated as missing data. this method facilitates inferences regarding the age and identity of specific mutations while taking the full complexities of the mutational process in DNA sequences into account. ~1 ~