Laplace Approximation in High-Dimensional Bayesian Regression

摘要: We consider Bayesian variable selection in sparse high-dimensional regression, where the number of covariates p may be large relative to sample size n, but at most a moderate q are active. Specifically, we treat generalized linear models. For single fixed model with well-behaved prior distribution, classical theory proves that Laplace approximation marginal likelihood is accurate for sufficiently n. extend this by giving results on uniform accuracy across all models scenario which and q, thus also considered models, increase Moreover, show how connection between can used obtain consistency approaches regression.