Bayes factors for grouped data

Abstract

In this paper we apply Bayes factors to grouped data. Group testing is where units are pooled together and tested as a group rather than individually. The Bayes factor is the ratio of the posterior probabilities of the null and the alternative hypotheses divided by the ratio of the prior probabilities for the null and the alternative hypotheses. A beta prior will be used, also known as a conjugate prior for the binomial distribution. An application to mosquito data will be considered, where a comparison is made between West Nile virus (WNV) infection prevalences in field collected Culex nigripalpus mosquitoes trapped at different heights.