Effects of statistical dependence on multiple testing under a hidden Markov model

TL;DR

This paper investigates how the dependence structure in a hidden Markov model influences the likelihood ratios used in optimal multiple hypothesis testing, providing convergence results and explicit parameter effects.

Contribution

It offers new theoretical insights into the impact of HMM dependence on likelihood ratios, including convergence properties and parameter influence analysis.

Findings

Convergence results for likelihood ratios as observations increase

Explicit effects of HMM parameters on likelihood ratios

Analytic expansions for binary state HMMs

Abstract

The performance of multiple hypothesis testing is known to be affected by the statistical dependence among random variables involved. The mechanisms responsible for this, however, are not well understood. We study the effects of the dependence structure of a finite state hidden Markov model (HMM) on the likelihood ratios critical for optimal multiple testing on the hidden states. Various convergence results are obtained for the likelihood ratios as the observations of the HMM form an increasing long chain. Analytic expansions of the first and second order derivatives are obtained for the case of binary states, explicitly showing the effects of the parameters of the HMM on the likelihood ratios.