Nonasymptotic Laplace approximation under model misspecification
Abstract: In this note, 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 is sufficiently concentrated. We envision the derived bounds to be widely applicable in establishing model selection consistency of Bayesian procedures in non-conjugate settings, especially when the true model potentially lies outside the class of candidate models considered.
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Pierre_Alquier1
Submission Number: 2473
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