# A Short Note on Almost Sure Convergence of Bayes Factors in the General Set-Up

arXiv: https://arxiv.org/abs/1703.04956 · HTML: https://mlsanity.com/paper/1703.04956/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2017.

## Built on by (most cited first, 1 of 1)

- [Differentially private Bayesian tests](https://mlsanity.com/paper/2401.15502/) (2024)

## Abstract (arXiv)

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 (2009) to a well-known identity satisfied by the Bayes factor.