  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.
