Improving power posterior estimation of statistical evidence
Improving power posterior estimation of statistical evidence
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DOI：
10.1007/s11222-013-9397-1
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发表时间：
2014-09-01
影响因子：
2.2
通讯作者：
Wyse, Jason
中科院分区：
文献类型：
--
作者：
Friel, Nial;Hurn, Merrilee;Wyse, Jason
统计证据(或边际似然)是贝叶斯统计中的一个关键量，使人们能够评估给定调查模型的数据的概率。本文的重点是提炼后验功率方法，以提高证据的估计能力。功率后验方法包括通过逆温度使可能性变强来从前向后过渡。与其他回火算法一样，功率后验算法涉及到一定程度的调整。这篇文章的主要贡献有两个--我们提出了一个来自数值分析文献的结果，它可以通过解决跨逆温度的数值积分所产生的误差来减少证据估计中的偏差。我们还解决了逆温度阶梯的选择问题，并将这种方法额外应用于证据的Steps Stone采样器估计。一个关键的实际问题是，这两项创新几乎都不会产生额外的成本。
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. A key practical point is that both of these innovations incur virtually no extra cost.