Title: A Short Note on Almost Sure Convergence of Bayes Factors in the General Set-Up,
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 (2009) to a well-known identity
satisfied by the Bayes factor.