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Abstract:
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We will present Bayesian nonparametric modeling approaches for spatial point processes recorded over irregular domains. The key building block is a prior model for spatial intensities, developed from structured weighted combinations of beta densities. The model can be used directly for the Poisson process intensity or for the background intensity in space-time Hawkes processes, as well as in spatial Hawkes processes. Combined with the Hawkes process branching structure, the prior models allow for full inference for point process functionals, avoiding the need for approximations to the point process likelihood or to the posterior distribution. The methods will be explored for modeling of crime, including illustrations with crime data from the city of Boston.
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