Abstract: We consider inference for a collection of partially observed stochastic interacting nonlinear dynamic processes. Each process is identified with a label, called its unit. Here, our primary motivation arises in biological metapopulation systems, in which a unit corresponds to a spatially distinct sub-population. Metapopulation systems are characterized by strong dependence over time within a single unit, and relatively weak interactions between units. These properties make block particle filters effective for simulation-based likelihood evaluation. Iterated filtering algorithms can facilitate likelihood maximization for simulation-based filters. Here, we introduce an iterated block particle filter that can be applied when parameters are unit-specific or shared between units. We demonstrate the proposed algorithm by performing inference on a coupled epidemiological model describing spatiotemporal measles case report data for 20 towns.

Key words and phrases: Data assimilation, inverse problem, state space model, stochastic gradient Markov chain Monte Carlo, uncertainty quantification.