Informally, ‘information inconsistency’ is the property that has been observed in some Bayesian hypothesis testing and model selection scenarios whereby the Bayesian conclusion does not become definitive when the data seem to become definitive. An example is that, when performing a t test using standard conjugate priors, the Bayes factor of the alternative hypothesis to the null hypothesis remains bounded as the t statistic grows to infinity. The goal of this paper is to thoroughly investigate information inconsistency in various Bayesian testing problems. We consider precise hypothesis tests, one-sided hypothesis tests, and multiple hypothesis tests under normal linear models with dependent observations. Standard priors are considered, such as conjugate and semi-conjugate priors, as well as variations of Zellner’s g prior (e.g., fixed g priors, mixtures of g priors, and adaptive (data-based) g priors). It is shown that information inconsistency is a widespread problem using standard priors while certain theoretically recommended priors, including scale mixtures of conjugate priors and adaptive priors, are information consistent.

非正式地，“信息不一致”是在某些贝叶斯假设检验和模型选择场景中观察到的属性，当数据似乎变得确定时，贝叶斯结论不会变得确定。一个例子是，当使用标准共轭先验进行t检验时，对原假设的替代假设的贝叶斯因子仍然限制为t统计量增长到无穷大。本文的目的是彻底调查各种贝叶斯测试问题中的信息不一致。我们考虑具有相关观测值的正常线性模型下的精确假设检验，单面假设检验和多重假设检验。标准先验被认为是，如共轭和半共轭先验，以及的Zellner的的变化克之前（例如，固定克先验的混合物，克基于先验数据，和自适应（）克先验）。结果表明，使用标准先验信息不一致是一个普遍的问题，而某些理论上推荐的先验信息（包括共轭先验和自适应先验的比例混合）则是信息一致的。