Demographic inference using a particle filter for continuous Markov Jump processes

Demographic events shape a populations genetic diversity, a process described by the coalescent-with-recombination (CwR) model that relates demography and genetics by an unobserved sequence of genealogies. The space of genealogies over genomes is large and complex, making inference under this model challenging. We approximate the CwR with a continuous-time and -space Markov jump process. We develop a particle filter for such processes, using way-points to reduce the problem to the discrete-time case, and generalising the Auxiliary Particle Filter for discrete-time models. We use Variational Bayes for parameter inference to model the uncertainty in parameter estimates for rare events, avoiding biases seen with Expectation Maximization. Using real and simulated genomes, we show that past population sizes can be accurately inferred over a larger range of epochs than was previously possible, opening the possibility of jointly analyzing multiple genomes under complex demographic models. Code is available at https://github.com/luntergroup/smcsmc MSC 2010 subject classificationsPrimary 60G55, 62M05, 62M20, 62F15; secondary 92D25.