  Parameter learning for high-dimensional, partially observed, and nonlinear
stochastic processes is a methodological challenge. Spatiotemporal disease
transmission systems provide examples of such processes giving rise to open
inference problems. We propose the iterated block particle filter (IBPF)
algorithm for learning high-dimensional parameters over graphical state space
models with general state spaces, measures, transition densities and graph
structure. Theoretical performance guarantees are obtained on beating the curse
of dimensionality (COD), algorithm convergence, and likelihood maximization.
Experiments on a highly nonlinear and non-Gaussian spatiotemporal model for
measles transmission reveal that the iterated ensemble Kalman filter algorithm
(Li et al. (2020)) is ineffective and the iterated filtering algorithm (Ionides
et al. (2015)) suffers from the COD, while our IBPF algorithm beats COD
consistently across various experiments with different metrics.
