Bayesian Scan Statistics

In this chapter we describe Bayesian scan statistics, a class of methods which build both on the prior literature on scan statistics and on Bayesian approaches to cluster detection and modeling. We first compare and contrast the Bayesian scan to the traditional, frequentist hypothesis testing approach to scan statistics and summarize the advantages and disadvantages of each approach. We then focus on three different Bayesian scan statistic approaches: the Bayesian variable window scan statistic, the multivariate Bayesian scan statistic and extensions, and scan statistic approaches based on Bayesian networks. We describe each of these approaches in detail and compare these to related Bayesian scan methods and to the wider literature on Bayesian cluster detection and modeling. Finally, we discuss several promising areas for future work in Bayesian scan statistics, including multiple cluster detection, nonparametric Bayesian approaches, extension of Bayesian spatial scan to nonspatial datasets, and computationally efficient methods for model learning and detection.