模型空间先验对模型不确定性统计推断的影响

Anupreet Porwal, A. Raftery
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引用次数: 1

摘要

贝叶斯模型平均(BMA)为统计推理任务中的模型不确定性提供了一种连贯的方法。BMA要求规范模型空间先验和参数空间先验。在本文中,我们重点比较了模型不确定性存在下不同的模型空间先验。我们考虑了文献中使用的8个参考模型空间先验和Porwal和Raftery推荐的3个自适应参数先验。我们评估了线性回归模型中变量选择的这些先验规范组合的性能,用于参数估计、区间估计、推理、点和区间预测等统计任务。我们基于14个真实数据集进行了广泛的模拟研究,这些数据集代表了实践中遇到的一系列情况。我们发现,根据模型大小的先验概率指定的β -二项模型空间先验在各种统计任务和数据集中平均表现最好,优于在模型中均匀的先验。最近提出的复杂性先验表现相对较差。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Effect of Model Space Priors on Statistical Inference with Model Uncertainty
Bayesian model averaging (BMA) provides a coherent way to account for model uncertainty in statistical inference tasks. BMA requires specification of model space priors and parameter space priors. In this article we focus on comparing different model space priors in the presence of model uncertainty. We consider eight reference model space priors used in the literature and three adaptive parameter priors recommended by Porwal and Raftery [37]. We assess the performance of these combinations of prior specifications for variable selection in linear regression models for the statistical tasks of parameter estimation, interval estimation, inference, point and interval prediction. We carry out an extensive simulation study based on 14 real datasets representing a range of situations encountered in practice. We found that beta-binomial model space priors specified in terms of the prior probability of model size performed best on average across various statistical tasks and datasets, outperforming priors that were uniform across models. Recently proposed complexity priors performed relatively poorly.
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