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Journal of Probability and Statistics
Volume 2012 (2012), Article ID 194018, 12 pages
http://dx.doi.org/10.1155/2012/194018
Research Article

Monitoring Murder Crime in Namibia Using Bayesian Space-Time Models

1Department of Statistics, University of Namibia, P.O. Box 13301, Windhoek, Namibia
2School of Mathematics and Southampton Statistical Sciences Research Institute, University of Southampton, Southampton SO17 1BJ, UK

Received 4 January 2012; Revised 25 April 2012; Accepted 9 May 2012

Academic Editor: Shein-chung Chow

Copyright © 2012 Isak Neema and Dankmar Böhning. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper focuses on the analysis of murder in Namibia using Bayesian spatial smoothing approach with temporal trends. The analysis was based on the reported cases from 13 regions of Namibia for the period 2002–2006 complemented with regional population sizes. The evaluated random effects include space-time structured heterogeneity measuring the effect of regional clustering, unstructured heterogeneity, time, space and time interaction and population density. The model consists of carefully chosen prior and hyper-prior distributions for parameters and hyper-parameters, with inference conducted using Gibbs sampling algorithm and sensitivity test for model validation. The posterior mean estimate of the parameters from the model using DIC as model selection criteria show that most of the variation in the relative risk of murder is due to regional clustering, while the effect of population density and time was insignificant. The sensitivity analysis indicates that both intrinsic and Laplace CAR prior can be adopted as prior distribution for the space-time heterogeneity. In addition, the relative risk map show risk structure of increasing north-south gradient, pointing to low risk in northern regions of Namibia, while Karas and Khomas region experience long-term increase in murder risk.