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Title: Semi-parametric hidden Markov model and large scale multiple testing under dependency Authors:  Joungyoun Kim - Chungbuk National University (Korea, South) [presenting]
Jong Soo Lee - University of Massachusetts Lowell (United States)
Johan Lim - Seoul National University (Korea, South)
Abstract: The optimal procedure for testing many hypotheses under dependence is known theoretically to depend on the local index of significance, called LIS, of each site, the conditional probability that the hypothesis of the site is non-true given the entire observed data. To evaluate the LIS, an assumption should be made for the dependence among observations and the finite state hidden Markov model (HMM) is popularly assumed. We study a two state HMM, denoted by semi-HMM, whose observational distribution for the null state is parametric but that for the non-null state is non-parametric. The main focus of the semi-HMM is on non-null distribution, the observational distribution of the non-null state. The observations from the non-null state are heterogeneous for many unknown reasons and no assumptions are made for the non-null distribution in the proposed semi-HMM. We show that the semi-HMM is not identifiable despite its model flexibility for non-null observations. To estimate the model, we adopt the recent results on the estimation of the semi-parametric mixture model and propose an EM type algorithm. The model and estimation procedure are numerically investigated and compared with existing parametric HMM in the context of multiple testing. Finally, it is applied to two real examples in the literature.