ABSTRACT Although there is a significant literature on the asymptotic theory of Bayes factor, the set-ups considered are usually specialized and often involves independent and identically distributed data. Even in such specialized cases, mostly weak consistency results are available. In this article, for the first time ever, we derive the almost sure convergence theory of Bayes factor in the general set-up that includes even dependent data and misspecified models. Somewhat surprisingly, the key to the proof of such a general theory is a simple application of a result of Shalizi to a well-known identity satisfied by the Bayes factor. Supplementary materials for this article are available online.

中文翻译：

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关于一般设置中贝叶斯因子几乎肯定收敛的简短说明

摘要 尽管关于贝叶斯因子的渐近理论有大量文献，但所考虑的设置通常是专门的，并且通常涉及独立且同分布的数据。即使在这种特殊情况下，大多数弱一致性结果也是可用的。在本文中，我们有史以来第一次在一般设置中推导出几乎可以肯定的贝叶斯因子收敛理论，该设置甚至包括相关数据和错误指定的模型。有点令人惊讶的是，证明这种一般理论的关键是将 Shalizi 的结果简单应用于满足贝叶斯因子的众所周知的恒等式。本文的补充材料可在线获取。