模型误设定下的非渐近Laplace逼近
Nonasymptotic Laplace approximation under model misspecification
摘要：
本文给出了贝叶斯推断中对数边际似然的非渐近双边界。经典的拉普拉斯近似恢复为首项。我们的推导允许模型误指定，并允许参数尺寸的增长与样本量。我们不对后验的渐近形状做任何假设，而是要求似然比满足一定的正则性条件，并且后验要足够集中。
英文摘要：
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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