Computing Bayes factors by combining simulation and asymptotic approximations
Computing Bayes factors by combining simulation and asymptotic approximations
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DOI：
10.2307/2965554
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发表时间：
1997-09-01
影响因子：
3.7
通讯作者：
Wasserman, L
中科院分区：
文献类型：
--
作者：
DiCiccio, TJ;Kass, RE;Wasserman, L
贝叶斯因子是两个后验归一化常数的比率。这可能很难计算。我们比较了几种估计贝叶斯因子的方法，当可以从后验分布模拟观测时，通过马尔科夫链蒙特卡罗或其他技术。我们研究的方法都很容易应用，而不需要考虑问题的特殊特征，只要每个后验分布在具有单一主导模式的意义上表现良好。我们考虑拉普拉斯方法的模拟版本、巴特利特校正的模拟版本、重要性抽样和互惠重要性抽样技术。我们还为其中的每一个引入了本地音量校正。此外，我们还采用了孟和黄的桥抽样方法。我们发现，拉普拉斯方法的模拟版本，加上局部体积校正，提供了一个精确的近似，当似然函数评估成本很高时，这一点特别有用。一种简单的电桥采样技术与拉普拉斯方法相结合，通常可以在精度上实现数量级的提高。
The Bayes factor is a ratio of two posterior normalizing constants. which may be difficult to compute. We compare several methods of estimating Bayes factors when it is possible to simulate observations from the posterior distributions, via Markov chain Monte Carlo or other techniques. The methods that we study are all easily applied without consideration of special features of the problem, provided that each posterior distribution is well behaved in the sense of having a single dominant mode. We consider a simulated version of Laplace's method, a simulated version of Bartlett correction, importance sampling, and a reciprocal importance sampling technique. We also introduce local volume corrections for each of these. In addition, we apply the bridge sampling method of Meng and Wong. We find that a simulated version of Laplace's method, with local volume correction, furnishes an accurate approximation that is especially useful when likelihood function evaluations are costly. A simple bridge sampling technique in conjunction with Laplace's method often achieves an order of magnitude improvement in accuracy.