[gaur]

> I'm also not sure why the OP thinks that calculating the normalizing constant is a huge issue. Most of the time you rarely need it since you're likely going to end up doing an MCMC or some other sampling method for the posterior, in which case you only need proportionality.

Right, and when doing Bayesian model selection the evidence drops out of the problem completely. All you need are the priors and the likelihoods.

The claim that ~H is "not itself a valid hypothesis" is dubious. If H is the hypothesis that a certain continuous parameter has a value in the range [a, b], then it's perfectly obvious what ~H means.

Of course it's possible to choose a vague, overly broad hypothesis, but a frequentist analysis of such a hypothesis is going to be just as bad as a Bayesian analysis. "Garbage in, garbage out" is true no matter what tool you use.