Improving power posterior estimation of statistical evidence
Nial Friel, Merrilee Hurn, Jason Wyse
备注：
Revised version (to appear in Statistics and Computing). This version corrects the typo in Equation (17), with thanks to Sabine Hug for pointing this out
The statistical evidence (or marginal likelihood) is a key quantity in Bayesian statistics, allowing one to assess the probability of the data given the model under investigation. This paper focuses on refining the power posterior approach to improve estimation of the evidence. The power posterior method involves transitioning from the prior to the posterior by powering the likelihood by an inverse temperature. In common with other tempering algorithms, the power posterior involves some degree of tuning. The main contributions of this article are twofold -- we present a result from the numerical analysis literature which can reduce the bias in the estimate of the evidence by addressing the error arising from numerically integrating across the inverse temperatures. We also tackle the selection of the inverse temperature ladder, applying this approach additionally to the Stepping Stone sampler estimation of evidence.
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Mila – Québec Artificial Intelligence Institute（米拉-魁北克人工智能研究所）；Université de Montréal（蒙特利尔大学）；Ciela Institute（谢拉研究所）；CCA – Flatiron Institute（计算天体物理学中心-弗拉蒂伦研究所）；Cavendish Laboratory（卡文迪什实验室）；Kavli Institute for Cosmology（卡夫利宇宙学研究所）；Gonville and Caius College, University of Cambridge（剑桥大学冈维尔与凯斯学院）；Canadian Institute for Advanced Research (CIFAR)（加拿大高等研究院）
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ZJU-UIUC Institute（ZJU-UIUC联合学院）；Zhejiang University（浙江大学）；School of Information Science and Technology（信息科学与技术学院）；Tsinghua University（清华大学）；Institute for Physics of Intelligence（智能物理研究所）；The University of Tokyo（东京大学）
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University of Tübingen（图宾根大学）；MPI for Intelligent Systems（马克斯·普朗克智能系统研究所）
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Machine Learning Group - Computer Science Department（计算机科学系机器学习小组）；Escuela Politécnica Superior（理工大学）；Department of Computer Science（计算机科学系）；University of Granada Spain（西班牙格拉纳达大学）；Information and Communication Technologies Research Centre (CITIC)（信息与通信技术研究中心（CITIC））；Centro de Investigación Avanzada en Física Fundamental（先进物理基础研究中心）
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Harvard University（哈佛大学）；University of Washington（华盛顿大学）；Google Brain（谷歌大脑）
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