Selective inference for false discovery proportion in a hidden Markov model
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 (2009). While previous work has concentrated on deriving specific procedures with a controlled False Discovery Rate (FDR) under this model, following a recent trend in selective inference, we consider the problem of establishing confidence bounds on the false discovery proportion (FDP), 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.
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BibTeX
@article{perrotdockes2026selective,
title = {{Selective inference for false discovery proportion in a hidden Markov model}},
author = {Marie Perrot-Dockès and Gilles Blanchard and Pierre Neuvial and Etienne Roquain},
journal = {Test},
year = {2026},
month = sep,
doi = {10.1007/s11749-023-00886-7},
eprint = {2105.00288},
archivePrefix = {arXiv},
url = {https://hal.science/hal-03214472v2},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Selective inference for false discovery proportion in a hidden Markov model
AU - Marie Perrot-Dockès
AU - Gilles Blanchard
AU - Pierre Neuvial
AU - Etienne Roquain
PY - 2026
DA - 2026/09/03
JO - Test
DO - 10.1007/s11749-023-00886-7
UR - https://hal.science/hal-03214472v2
AB - 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 (2009). While previous work has concentrated on deriving specific procedures with a controlled False Discovery Rate (FDR) under this model, following a recent trend in selective inference, we consider the problem of establishing confidence bounds on the false discovery proportion (FDP), 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.
SN - 1133-0686
SN - 1863-8260
ER -