Multiple hypotheses testing on dependent count data with covariate effects

Dynamics in the sequence of count data is usually not only affected by the underlying hidden states to be detected, but also quite likely associated with other static or dynamically changing covariates. The multiple hypotheses testing procedure developed here takes these covariates into consideration by the Poisson regression model. Also, a hidden Markov process is applied to model the switches between the null and non-null states as well as the dependence across counts. All model parameters are estimated through Bayesian computation. While a simple distribution is assumed on the null state, the observation distribution under the non-null state usually requires more flexibility. Here a mixture of parametric distributions is assumed. The number of mixture components is decided by model selection criteria, including the Bayesian Information Criterion as well as marginal likelihood methods. Simulation studies are carried out to evaluate the performance of the proposed model and that of the model selection methods. The real data example shows the application of the proposed model and its inference goal differs from the previous testing procedures with no covariate effects considered.

Keywords

Bayesian hierarchical model, Markov switch regression model, multiple hypotheses testing, Poisson regression, sampling-based marginal likelihood

2010 Mathematics Subject Classification

Primary 62F03, 62M05. Secondary 62J12.

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Dr. Xia Wang’s work was supported in part by NIH/NIMH Grant R01MH119814.

Received 25 December 2020

Accepted 6 February 2022

Published 14 April 2023