A Semiparametric Bayesian Method for Sufficient Dimension Reduction

SLADS Section C Paper7 Authors

Abstract: This work proposes a novel semiparametric Bayesian approach for statistical inference of the central subspace in the problem of sufficient dimension reduction. Unlike conventional Bayesian approaches for sufficient dimension reduction that model the conditional distributions of the response variable given the projected predictive variables, the new approach chooses to model their joint distribution instead via a Dirichlet process Gaussian mixture model, leading to both conceptual simplicity and computational convenience. Posterior consistency of the proposed approach is established under the framework of Schwartz’s theorem. A Monte Carlo strategy based on the Gibbs sampler and geodesic Monte Carlo is developed for efficient posterior sampling. Both simulation studies and real data applications confirm the advantages of the proposed approach over existing Bayesian and frequentist methods.

Submission Type: Special issue on Statistics and AI

Submission Number: 7