Paul Jenkins (University of Warwick)

Sequential importance sampling and resampling in population genetic inference

Since 2008, the reduction in DNA sequencing costs has far outpaced Moore's law, giving rise to a wealth of data on sequence variation in contemporary populations. The patterns of variation we see are shaped both by biological processes such as mutation, recombination, and natural selection, and by demographic processes such as population expansion, contraction, and migration. In principle the nature of these processes can be inferred from the data, and one powerful approach is to use a stochastic model like Kingman's coalescent for the random genealogical relationships relating the sampled sequences. The problem then is to compute the likelihood under this model, which can be computationally very challenging. In this talk I will describe how we can make progress on this problem by using the Monte Carlo-based approaches of sequential importance sampling and resampling. I will discuss our approach to questions including the design of a suitable proposal distribution, and when and how to resample the particle-based approximation to the posterior distribution of genealogies.