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Modern scientific studies often require the identification of a subset ofrelevant explanatory variables, in the attempt to understand an interestingphenomenon. Several statistical methods have been developed to automate thistask, but only recently has the framework of model-free knockoffs proposed ageneral solution that can perform variable selection under rigorous type-Ierror control, without relying on strong modeling assumptions. In this paper,we extend the methodology of model-free knockoffs to a rich family of problemswhere the distribution of the covariates can be described by a hidden Markovmodel (HMM). We develop an exact and efficient algorithm to sample knockoffcopies of an HMM. We then argue that combined with the knockoffs selectiveframework, they provide a natural and powerful tool for performing principledinference in genome-wide association studies with guaranteed FDR control.Finally, we apply our methodology to several datasets aimed at studying theCrohn's disease and several continuous phenotypes, e.g. levels of cholesterol.

Gene Hunting with Knockoffs for Hidden Markov Models