Multiple Testing in Nonparametric Hidden Markov Models: An Empirical\n Bayes Approach

2021/01/11 by Kweku Abraham, Abraham, Kweku, Ismaël Castillo +3 · 2 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Statistical Methods and Inference #Statistical Methods and Bayesian Inference

paper · pdf · doi:10.48550/arxiv.2101.03838

Abstract

Given a nonparametric Hidden Markov Model (HMM) with two states, the question\nof constructing efficient multiple testing procedures is considered, treating\none of the states as an unknown null hypothesis. A procedure is introduced,\nbased on nonparametric empirical Bayes ideas, that controls the False Discovery\nRate (FDR) at a user--specified level. Guarantees on power are also provided,\nin the form of a control of the true positive rate. One of the key steps in the\nconstruction requires supremum--norm convergence of preliminary estimators of\nthe emission densities of the HMM. We provide the existence of such estimators,\nwith convergence at the optimal minimax rate, for the case of a HMM with J\≥\n2 states, which is of independent interest.\n

Citations

• Statistical Inference for Probabilistic Functions of Finite State Markov Chains
• A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains

Cited by

• Empirical Bayes cumulative ℓ-value multiple testing procedure for sparse sequences
• Post hoc false discovery proportion inference under a Hidden Markov Model

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