Abstract
Samples of ancient DNA can be used to estimate the frequencies of a given allele at a range of times in the past. One would like to use these frequencies to make inferences about historic population sizes, selection strengths, etc. The likelihood of the frequency data involves the transition densities of a diffusion process for which there are no closed form expressions, and computing these transition densities numerically requires, in principle, solving a partial differential equation for every choice of the underlying parameters. I will describe recent work with Josh Schraiber (UC Berkeley Integrative Biology) in which we "interpolate" the paths of the allele frequency diffusion process and use rejection sampling ideas process as part of a Bayesian procedure for inferring demographic and genetic parameters from allele frequency time series.