Stopping-time resampling for sequential Monte Carlo methods

Motivated by the statistical inference problem in population genetics, we present a new sequential importance sampling with resampling strategy. The idea of resampling is key to the recent surge of popularity of sequential Monte Carlo methods in the statistics and engineering communities, but existing resampling techniques do not work well for coalescent-based inference problems in population genetics. We develop a new method called ‘stopping-time resampling’, which allows us to compare partially simulated samples at different stages to terminate unpromising partial samples and to multiply promising samples early on.To illustrate the idea, we first apply the new method to approximate the solution of a Dirichlet problem and the likelihood function of a non-Markovian process. Then we focus on its application in population genetics. All our examples show that the new resampling method can significantly improve the computational efficiency of existing sequential importance sampling methods.