Bayesian Sparse Covariance Structure Analysis for Correlated Count Data

TL;DR

This paper introduces a Bayesian Graphical LASSO model tailored for correlated count data, specifically applied to spatial crime data, to estimate sparse inverse covariance and partial correlations of latent variables.

Contribution

It presents a novel Bayesian approach for sparse covariance estimation in count data, integrating Gaussian graphical models for latent variables, with application to spatial crime analysis.

Findings

Effective estimation of sparse inverse covariance matrices.

Identification of significant partial correlations in crime data.

Demonstrated model's utility on real spatial crime datasets.

Abstract

In this paper, we propose a Bayesian Graphical LASSO for correlated countable data and apply it to spatial crime data. In the proposed model, we assume a Gaussian Graphical Model for the latent variables which dominate the potential risks of crimes. To evaluate the proposed model, we determine optimal hyperparameters which represent samples better. We apply the proposed model for estimation of the sparse inverse covariance of the latent variable and evaluate the partial correlation coefficients. Finally, we illustrate the results on crime spots data and consider the estimated latent variables and the partial correlation coefficients of the sparse inverse covariance.