Hidden Markov model in multiple testing on dependent count data

Multiple testing on dependent count data faces two basic modelling elements: the choice of distributions under the null and the non-null states and the modelling of the dependence structure across observations. A Bayesian hidden Markov model is constructed for Poisson count data to handle these two issues. The proposed Bayesian method is based on the posterior probability of the null state and exhibits the property of an optimal test procedure, which has the lowest false-negative rate with the false discovery rate under control. Furthermore, the model has either single or mixture of Poisson distributions used under the non-null state. Model selection methods are employed here to decide the number of components in the mixture. Different approaches of calculating marginal likelihood are discussed. Extensive simulation studies and a case study are employed to examine and compare a collection of commonly used testing procedures and model selection criteria.