Nonasymptotic Laplace approximation under model misspecification

2020/05/16 by Anirban Bhattacharya, Bhattacharya, Anirban, Debdeep Pati +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.2005.07844

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

openalex publication_date 2020/05/16 · arxiv created 2020/06/20 · arxiv updated 2020/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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