A class of spatially correlated self-exciting statistical models
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Authors
Clark, Nicholas J.
Dixon, Philip M.
Issue Date
2021
Type
journal-article
Language
Keywords
Crime , Bayesian , Spatio-temporal
Alternative Title
Abstract
The statistical modeling of multivariate count data observed on a space–time lattice has generally focused on using a hierarchical modeling approach where space–time correlation structure is placed on a continuous, latent, process. The count distribution is then assumed to be conditionally independent given the latent process. However, in many real-world applications, especially in the modeling of criminal or terrorism data, the conditional independence between the count distributions is inappropriate. In this manuscript we propose a class of models that capture spatial variation and also account for the possibility of data model dependence. The resulting model allows both data model dependence, or self-excitation, as well as spatial dependence in a latent structure. We demonstrate how second-order properties can be used to characterize the spatio-temporal process and how misspecification of error may inflate self-excitation in a model. Finally, we give an algorithm for efficient Bayesian inference for the model demonstrating its use in capturing the spatio-temporal structure of burglaries in Chicago from 2010–2015.
Description
Citation
Clark and Dixon, “A Class of Spatially Correlated Self-Exciting Statistical Models.”
Publisher
Spatial Statistics
License
Journal
Volume
Issue
PubMed ID
ISSN
2211-6753