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Abstract:
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We propose a new class of dynamic multiscale models for Poisson spatiotemporal processes. Specifically, we use a multiscale spatial Poisson factorization to decompose the Poisson process at each time point into spatiotemporal multiscale coefficients. We then connect these spatiotemporal multiscale coefficients through time with a novel Dirichlet evolution. Further, we develop filtering equations for updating of information forward in time and smoothing equations for integration of information backward in time, and use these equations to develop a forward filter backward sampler for the spatiotemporal multiscale coefficients. Our full Bayesian posterior analysis is scalable, computationally efficient, and highly parallelizable. We present novel results on the spatial and spatiotemporal dependence structure. Two applications to mortality ratios and tornado reports illustrate the usefulness of our multiscale spatiotemporal Poisson methodology.
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