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Abstract:
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Statistical inference for high-dimensional partially observed, nonlinear, stochastic processes is a methodological challenge with applications including spatiotemporal analysis of epidemiological and ecological systems. Standard particle filter algorithms, which provide an effective approach for general low-dimensional partially observed Markov processes, suffer from a curse of dimensionality (COD). We show that many independent Monte Carlo calculations, each of which does not attempt to solve the filtering problem, can be combined to give a global filtering solution that theoretically beats COD under weak coupling conditions. The independent Monte Carlo calculations are called islands, and the operation carried out on each island is called adapted simulation, so the complete algorithm is called an adapted simulation island filter (ASIF). Adapted simulation can be implemented using a Monte Carlo technique called intermediate resampling to give improved theoretical and empirical scaling. Our focus is on evaluation of the likelihood function. We demonstrate our methodology and software package on coupled population dynamics in the context of infectious disease epidemiology.
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