Rossell Ribera, DavidAbril Pla, OriolBhattacharya, Anirban2022-05-242022-05-242021Rosell D, Abril O, Bhattacharya A. Approximate Laplace approximations for scalable model selection. J R Stat Soc Series B. 2021 Sep;83(4):853-79. DOI: 10.1111/rssb.124661369-7412http://hdl.handle.net/10230/53231Includes supplementary materials for the online appendix.We propose the approximate Laplace approximation (ALA) to evaluate integrated likelihoods, a bottleneck in Bayesian model selection. The Laplace approximation (LA) is a popular tool that speeds up such computation and equips strong model selection properties. However, when the sample size is large or one considers many models the cost of the required optimizations becomes impractical. ALA reduces the cost to that of solving a least-squares problem for each model. Further, it enables efficient computation across models such as sharing pre-computed sufficient statistics and certain operations in matrix decompositions. We prove that in generalized (possibly non-linear) models ALA achieves a strong form of model selection consistency for a suitably-defined optimal model, at the same functional rates as exact computation. We consider fixed- and high-dimensional problems, group and hierarchical constraints, and the possibility that all models are misspecified. We also obtain ALA rates for Gaussian regression under non-local priors, an important example where the LA can be costly and does not consistently estimate the integrated likelihood. Our examples include non-linear regression, logistic, Poisson and survival models. We implement the methodology in the R package mombf.application/pdfeng© 2021 The Authors. Journal of the Royal Statistical Society: Series B (Statistical Methodology) published by John Wiley & Sons Ltd on behalf of Royal Statistical Society. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.info:eu-repo/semantics/articlehttp://dx.doi.org/10.1111/rssb.12466Approximate inferenceHierarchical constraintsGroup constraintsModel misspecificationModel selectionNon- local priorsNon- parametric regressioninfo:eu-repo/semantics/openAccess