Nonasymptotic Laplace approximation under model misspecification

Abstract

We present non-asymptotic two-sided bounds to the log-marginal likelihood in Bayesian inference. The classical Laplace approximation is recovered as the leading term. Our derivation permits model misspecification and allows the parameter dimension to grow with the sample size. We do not make any assumptions about the asymptotic shape of the posterior, and instead require certain regularity conditions on the likelihood ratio and that the posterior to be sufficiently concentrated.

23 pages. Fixed minor technical glitches in the proof of Theorem 2 in the updated version

References in corpus (2)

• Needles and Straw in a Haystack: Posterior concentration for possibly sparse sequences
• Misspecification in infinite-dimensional Bayesian statistics