Selective inference for false discovery proportion in a hidden Markov model

Marie Perrot-Dockès (), Gilles Blanchard (), Pierre Neuvial () and Etienne Roquain ()
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Marie Perrot-Dockès: Université de Paris
Gilles Blanchard: Université Paris-Saclay
Pierre Neuvial: Université de Toulouse
Etienne Roquain: Sorbonne Université, Université de Paris

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2023, vol. 32, issue 4, No 13, 1365-1391

Abstract: Abstract We address the multiple testing problem under the assumption that the true/false hypotheses are driven by a hidden Markov model (HMM), which is recognized as a fundamental setting to model multiple testing under dependence since the seminal work of Sun and Cai (J R Stat Soc Ser B (Stat Methodol) 71:393–424, 2009). While previous work has concentrated on deriving specific procedures with a controlled false discovery rate under this model, following a recent trend in selective inference, we consider the problem of establishing confidence bounds on the false discovery proportion, for a user-selected set of hypotheses that can depend on the observed data in an arbitrary way. We develop a methodology to construct such confidence bounds first when the HMM model is known, then when its parameters are unknown and estimated, including the data distribution under the null and the alternative, using a nonparametric approach. In the latter case, we propose a bootstrap-based methodology to take into account the effect of parameter estimation error. We show that taking advantage of the assumed HMM structure allows for a substantial improvement of confidence bound sharpness over existing agnostic (structure-free) methods, as witnessed both via numerical experiments and real data examples.

Keywords: Post hoc bounds; Hidden Markov model; False discovery proportion; Posterior distribution; Bootstrap; 62J15 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11749-023-00886-7

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