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Activity Number: 625 - Environmental Epidemiology and Spatial Statistics
Type: Contributed
Date/Time: Thursday, August 3, 2017 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistics in Epidemiology
Abstract #324556
Title: Dynamic Spatial-Temporal Point Process Models via Conditioning
Author(s): Athanasios Micheas* and Justin Okenye and Christopher Wikle
Companies: Univ of Missouri- Columbia and University of Missouri and University of Missouri
Keywords: Data Augmentation ; Marked Hawkes Process ; Finite Mixture Models ; Marked Non-Homogeneous Poisson Point Process

We propose a Dynamic Spatial-Temporal Poisson Point Process (DSTPPP) model that accounts for the temporal and spatial clustering as a Marked Non Homogeneous Poisson Point Process (MNHPPP) via conditioning. We propose models for the intensity function of a (DSTPPP) using a Marked Non-Homogeneous Poisson Point Process (MNHPPP) via conditioning arguments that allow for additional interpretations. More precisely, the DSTPPP intensity function is modeled as a product of two functions; the first one representing the intensity of the temporal (time) component and the second a function of the intensity of the spatial (location) process, which is defined conditionally upon the temporal component of the event. In particular, the temporal component is modeled by a Hawkes Process and the spatial (location) process is modeled via a mixture of bivariate normal components. We propose a flexible hierarchical Bayesian framework for estimation of the parameters of the intensity function using a Markov chain Monte Carlo (MCMC) algorithm. The methodology is illustrated using simulated data and an application involving modeling and inference for earthquake data.

Authors who are presenting talks have a * after their name.

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