Nonasymptotic Laplace approximation under model misspecification
Statistics Theory
2020-06-23 v2 Statistics Theory
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.
Cite
@article{arxiv.2005.07844,
title = {Nonasymptotic Laplace approximation under model misspecification},
author = {Anirban Bhattacharya and Debdeep Pati},
journal= {arXiv preprint arXiv:2005.07844},
year = {2020}
}
Comments
23 pages. Fixed minor technical glitches in the proof of Theorem 2 in the updated version