B0743
Title: Bayesian nonparametric marked Hawkes processes for earthquake modeling
Authors: Athanasios Kottas - University of California Santa Cruz (United States) [presenting]
Hyotae Kim - Duke University (United States)
Abstract: The Hawkes process is a versatile stochastic model for point processes that exhibit self-excitation, that is, the property that the occurrence of an event increases the rate of occurrence for some period of time in the future. Including extensions to incorporate marks, Hawkes processes have been successfully applied in several scientific areas. We will present a nonparametric Bayesian modeling approach for marked Hawkes processes. The prior models for the functions that define the point process conditional intensity are constructed to achieve flexible, computationally efficient inference, utilizing the Hawkes process branching structure. The motivating application involves earthquake data modeling, where the mark is given by the earthquake magnitude. The methodology builds from a prior for the Hawkes process excitation function that allows flexible shapes for mark-dependent offspring densities. In the context of the application, the modeling approach enables the estimation of aftershock densities that vary with the magnitude of the main shock, thus significantly expanding the inferential scope of existing self-exciting point process models for earthquake occurrences. The methodology will be studied empirically with data on earthquake occurrences from Japan.
