Methods of Markov chain Monte Carlo are attracting great interest in many areas of Statistics. They provide realizations from probability distributions known only up to a normalizing constant, and thus from intractable probability distributions of latent variables conditional upon observed data. These realizations can be used to obtain Monte Carlo approximants too therwise intractable likelihood functions and posterior probability distributions. The methods permit exploration of large and complex hypothesis spaces of models and parameters. Estimation of genealogical structure from genetic data is a long-standing problem, recently attracting renewed interest with the advent of new types of data that are potentially much more informative. The availability and quantity of such data are increasing rapidly. The estimation of genealogies becomes of increasing practical importance with the increasing necessity to evaluate detailed population structure in the severely numerically restricted populations of highly endangered species. The major problem in a coherent statistical analysis of genealogical structure lies in the plethora of alternative genealogical hypotheses that could relate a set of individuals. The development of the use of Markov chain Monte Carlo methods towards the inference of genealogies and the estimation of population structure offers a solution of this complex problem. The current award will support research that is both methodological and computational. Markov chain Monte CarloMethods are very flexible; developing an effective method for a particular class of problems is not routine. Methods will be developed and evaluated. Software to implement the methods will be developed, and will be applied in the context of some available data sets. This award is being supported by four programs: Statistics and Probability, Computational Mathematics, Systematics and Population Biology, and Computational Biology.
