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Activity Number:
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333
- Advances in Bayesian Modeling
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Type:
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Contributed
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Date/Time:
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Tuesday, August 9, 2022 : 2:00 PM to 3:50 PM
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Sponsor:
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International Society for Bayesian Analysis (ISBA)
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Abstract #323088
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Title:
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Bayesian Nonparametric Modeling for Spatial Hawkes Processes
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Author(s):
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Chunyi Zhao* and Athanasios Kottas
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Companies:
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University of California, Santa Cruz and University of California, Santa Cruz
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Keywords:
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Bayesian nonparametrics;
Hawkes Process;
Markov chain Monte Carlo
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Abstract:
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We develop a semi-parametric Bayesian modeling approach for spatial Hawkes processes focusing on application in crime modeling. The spatial Hawkes process can be represented as a superposition of generations of cluster Poisson processes given the branching structure, which naturally motivates a Bayesian hierarchical modeling approach. The fundamental building block is a nonparametric prior model for the Hawkes process immigrant intensity, based on weighted combinations of beta densities, which allows for flexible and computationally efficient inference over irregular domains. Combined with parametric models for the Hawkes process offspring intensity, the methods provide full inference for point process functionals and attributes through posterior simulation and posterior predictive simulation. We apply our model to crime point patterns with additional assumptions on the point process and provide illustrations with crime data from the city of Boston.
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Authors who are presenting talks have a * after their name.
