Bayesian variable window scan statistics

In this article two-stage hierarchical Bayesian models are used for the observed occurrences of events in a rectangular region. Two Bayesian variable window scan statistics are introduced to test the null hypothesis that the observed events follow a specified two-stage hierarchical model vs an alternative that indicates a local increase in the average number of observed events in a subregion (clustering). Both procedures are based on a sequence of Bayes factors and their p-values that have been generated via simulation of posterior samples of the parameters, under the null and alternative hypotheses. The posterior samples of the parameters have been generated by employing Gibbs sampling via introduction of auxiliary variables. Numerical results are presented to evaluate the performance of these variable window scan statistics.