In a comment on my entry on why I don’t like so-called Bayesian hypothesis testing, Stephen Senn writes:

Bayesian hypothesis tests are the work of Harold Jeffreys who realised that you could not proceed using vague priors for parameters unless you have a means of choosing between simpler and more complex models. Also he was keen to find ways of proving that scientific laws are true. If you think you can do this and want to do it you need Bayesian hypothesis tests.

I, personally, don’t like Jeffreys’s approach. However, I think that it is a tribute to his genius that he realised that such a system had to be part and parcel of any attempt to be semi-objective in the use of Bayes. Unfortunately we now have many so-called Bayesians who think they can use uninformative priors without a system of deciding between simpler and more complex hypotheses. This is not possible.

My reply: When deciding between simpler and more complex hypotheses, I generally prefer the more complex hypothesis. When I choose the simpler hypothesis, I view this as a combination of labor-saving device and approximate Bayes, pooling a parameter estimate all the way to zero instead of merely pooling it most of the way. I certainly don’t see Bayes factors having any relevance, given the oft-noted problem that Bayes factors can depend decisively on aspects of the prior distribution that have no influence on the posterior distribution under each of the individual models.