Approximate Laplace Approximations for Scalable Model Selection

Abstract We propose the approximate Laplace approximation (ALA) to evaluate integrated likelihoods, a bottleneck in Bayesian model selection. The (LA) is popular tool that speeds up such computation and equips strong selection properties. However, when sample size large or one considers many models cost of required optimizations becomes impractical. ALA reduces solving least-squares problem for each model. Further, it enables efficient across as sharing pre-computed sufficient statistics certain operations matrix decompositions. prove generalized (possibly non-linear) achieves form consistency suitably-defined optimal model, at same functional rates exact computation. consider fixed- high-dimensional problems, group hierarchical constraints, possibility all are misspecified. also obtain Gaussian regression under non-local priors, an important example where LA can be costly does not consistently estimate likelihood. Our examples include non-linear regression, logistic, Poisson survival models. implement methodology R package mombf.