A subsampling approach for Bayesian model selection

It is common practice to use Laplace approximations decrease the computational burden when computing marginal likelihoods in Bayesian versions of generalised linear models (GLM). Marginal combined with model priors are then used different search algorithms compute posterior probabilities and individual covariates. This allows performing selection averaging. For large sample sizes, even approximation becomes computationally challenging because optimisation routine involved needs evaluate likelihood on full dataset multiple iterations. As a consequence, algorithm not scalable for datasets. To address this problem, we suggest using stochastic approaches, which only subsample data each iteration. We combine Markov chain Monte Carlo (MCMC) based methods provide some theoretical results convergence estimates resulting time-inhomogeneous MCMC. Finally, report from experiments illustrating performance proposed algorithm.