Alive SMC2: Bayesian model selection for low-count time series models with intractable likelihoods

In this article we present a new method for performing Bayesian parameter inference and model choice for low- count time series models with intractable likelihoods. The method involves incorporating an alive particle filter within a sequential Monte Carlo (SMC) algorithm to create a novel exact-approximate algorithm, which we refer to as alive SMC2. The advantages of this approach over competing methods are that it is naturally adaptive, it does not involve between-model proposals required in reversible jump Markov chain Monte Carlo, and does not rely on potentially rough approximations. The algorithm is demonstrated on Markov process and integer autoregressive moving average models applied to real biological datasets of hospital-acquired pathogen incidence, animal health time series, and the cumulative number of prion disease cases in mule deer.