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Motivated by a real-world application in cardiology, we develop an algorithmto perform Bayesian bi-level variable selection in a generalized linear model,for datasets that may be large both in terms of the number of individuals andthe number of predictors. Our algorithm relies on the waste-free SMC SequentialMonte Carlo methodology of Dau and Chopin (2022), a new proposal mechanism todeal with the constraints specific to bi-level selection (which forbid toselect an individual predictor if its group is not selected), and the ALA(approximate Laplace approximation) approach of Rossell et al. (2021). We showin our numerical study that the algorithm may offer reliable performance onlarge datasets within a few minutes, on both simulated data and real datarelated to the aforementioned cardiology application.

Scalable Bayesian bi-level variable selection in generalized linear models