Campus Units

Statistics

Document Type

Article

Publication Version

Published Version

Publication Date

2018

Journal or Book Title

The Annals of Applied Statistics

Volume

12

Issue

1

First Page

633

Last Page

653

DOI

10.1214/17-AOAS1112

Abstract

Spatio-temporal hierarchical modeling is an extremely attractive way to model the spread of crime or terrorism data over a given region, especially when the observations are counts and must be modeled discretely. The spatio-temporal diffusion is placed, as a matter of convenience, in the process model allowing for straightforward estimation of the diffusion parameters through Bayesian techniques. However, this method of modeling does not allow for the existence of self-excitation, or a temporal data model dependency, that has been shown to exist in criminal and terrorism data. In this manuscript we will use existing theories on how violence spreads to create models that allow for both spatio-temporal diffusion in the process model as well as temporal diffusion, or self-excitation, in the data model. We will further demonstrate how Laplace approximations similar to their use in Integrated Nested Laplace Approximation can be used to quickly and accurately conduct inference of self-exciting spatio-temporal models allowing practitioners a new way of fitting and comparing multiple process models. We will illustrate this approach by fitting a self-exciting spatio-temporal model to terrorism data in Iraq and demonstrate how choice of process model leads to differing conclusions on the existence of self-excitation in the data and differing conclusions on how violence spread spatially-temporally in that country from 2003–2010.

Comments

This article is published as Clark, Nicholas J., and Philip M. Dixon. "Modeling and estimation for self-exciting spatio-temporal models of terrorist activity." The Annals of Applied Statistics 12, no. 1 (2018): 633-653. doi: 10.1214/17-AOAS1112. Posted with permission.

Copyright Owner

Institute of Mathematical Statistics

Language

en

File Format

application/pdf

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