A Bayesian approach to the Bernoulli spatial scan statistic

This document describes a novel approach to finding localised clusters in spatially distributed, binary labelled point data. The frequentist spatial scan statistic, introduced by Martin Kulldorff in 1995, was developed into a Bayesian spatial scan statistic for areal data by Daniel Neill, circa 2006, where computationally expensive Monte Carlo testing is replaced by the use of historical data and expert judgement. Following Neill's approach, I present here my derivation of a Bayesian spatial scan statistic for binary labelled point data. I have also developed a method for replacing historic data with expert judgement, by using a prior probability distribution of relative risk. Please note this document describes work in progress, and content may be subject to revision.