A Class of Spatially Correlated Self-Exciting Models

TL;DR

This paper introduces a new class of spatially correlated self-exciting models for multivariate count data on space-time lattices, addressing limitations of traditional hierarchical models by capturing both data dependence and spatial variation.

Contribution

The paper proposes a novel modeling framework that incorporates both self-excitation and spatial dependence, improving analysis of complex spatio-temporal count data.

Findings

Model effectively captures burglary patterns in Chicago (2010-2015).

Second-order properties help characterize the spatio-temporal process.

Misspecification of error can inflate self-excitation estimates.

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 misspecificaiton 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.