UCSC-SOE-20-08: Nonparametric Bayesian Modeling and Inference for Hawkes Processes

Hyotae Kim and Athanasios Kottas
09/01/2020 02:03 PM
We propose a Bayesian nonparametric modeling and inference framework for Hawkes processes. The objective is to increase the inferential scope for this practically important class of point processes by exploring flexible models for its conditional intensity function. In particular, we develop different types of nonparametric prior models for the immigrant intensity and for the offspring density, the two functions that define the Hawkes process conditional intensity. The prior models are carefully constructed such that, along with the Hawkes process branching structure, they enable efficient handling of the complex likelihood normalizing terms in implementation of inference. We discuss prior specification for model hyperparameters, and design posterior simulation algorithms to obtain inference for different point process functionals. The modeling approach is studied empirically using several synthetic data examples, and is further illustrated through reexamination of a data set from the literature involving earthquake occurrences.

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