Using Stacking to Average Bayesian Predictive Distributions (with Discussion)
Using Stacking to Average Bayesian Predictive Distributions (with Discussion)
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DOI：
10.1214/17-ba1091
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发表时间：
2018-09-01
影响因子：
4.4
通讯作者：
Tonellato, Stefano
中科院分区：
文献类型：
--
作者：
Yao, Yuling;Vehtari, Aki;Tonellato, Stefano
贝叶斯模型平均在 M-open 设置中存在缺陷，其中真实的数据生成过程不是适合的候选模型之一。我们从点估计文献中汲取堆叠的想法，并将其推广到预测分布的组合。我们将效用函数扩展到任何适当的评分规则，并使用帕累托平滑重要性采样来有效计算所需的留一后验分布。我们将预测分布的堆叠与几种替代方案进行比较：均值堆叠、贝叶斯模型平均 (BMA)、伪 BMA 以及使用贝叶斯引导程序稳定的伪 BMA 变体。基于模拟和真实数据应用，我们建议堆叠预测分布，当计算成本成为问题时，使用自举伪 BMA 作为近似替代方案。
Bayesian model averaging is flawed in the M-open setting in which the true data-generating process is not one of the candidate models being fit. We take the idea of stacking from the point estimation literature and generalize to the combination of predictive distributions. We extend the utility function to any proper scoring rule and use Pareto smoothed importance sampling to efficiently compute the required leave-one-out posterior distributions. We compare stacking of predictive distributions to several alternatives: stacking of means, Bayesian model averaging (BMA), Pseudo-BMA, and a variant of Pseudo-BMA that is stabilized using the Bayesian bootstrap. Based on simulations and real-data applications, we recommend stacking of predictive distributions, with bootstrapped-Pseudo-BMA as an approximate alternative when computation cost is an issue.