The Posterior Predictive Null
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后验预测零假设检验
- 研究问题
- 当研究者反复构建多个贝叶斯模型时，如何在逐个检查拟合之外，比较模型之间的关系及它们对数据提供的不同解释？
- 方法与思路
- 作者提出 PPN，检验某模型预测分布生成的数据能否通过另一模型的预测检验，并将多个此类比较组成模型关系研究。
- 材料陈述的贡献
- 摘要称该方法补充传统预测检验，可辅助理解模型相似性，并在混合模型成分选择及线性、神经网络因子模型比较中展示。
- 阅读关注点
- 应核对预测检验量、模型间比较方向和判定规则，辨明文中模型等价的具体含义，并审查简约选择的依据与复现实现。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收未核实；通过特定预测检验不等于模型全面等价，摘要未说明误差控制条件。
原文摘要
Bayesian model criticism is an important part of the practice of Bayesian statistics. Traditionally, model criticism methods have been based on the predictive check, an adaptation of goodness-of-fit testing to Bayesian modeling and an effective method to understand how well a model captures the distribution of the data. In modern practice, however, researchers iteratively build and develop many models, exploring a space of models to help solve the problem at hand. While classical predictive checks can help assess each one, they cannot help the researcher understand how the models relate to each other. This paper introduces the posterior predictive null check (PPN), a method for Bayesian model criticism that helps characterize the relationships between models. The idea behind the PPN is to check whether data from one model's predictive distribution can pass a predictive check designed for another model. This form of criticism complements the classical predictive check by providing a comparative tool. A collection of PPNs, which we call a PPN study, can help us understand which models are equivalent and which models provide different perspectives on the data. With mixture models, we demonstrate how a PPN study, along with traditional predictive checks, can help select the number of components by the principle of parsimony. With probabilistic factor models, we demonstrate how a PPN study can help understand relationships between different classes of models, such as linear models and models based on neural networks. Finally, we analyze data from the literature on predictive checks to show how a PPN study can improve the practice of Bayesian model criticism. Code to replicate the results in this paper is available at \url{https://github.com/gemoran/ppn-code}.