[ced]

Are there any situations where you want to use a frequentist procedure?

I've concluded that given a perfect, infinite-power MCMC simulator, I would always do a Gelman-style Bayesian analysis (with model falsification and improvement), but in practice, frequentist methods are computationally convenient.

Inference can be framed either way but means different things.

A Bayesian posterior P(H|D,M) is the probability that hypothesis H is true given data D and modelling assumptions M.

What does a frequentist p-value mean?

[keithwinstein]

Sure, see my link above (http://stats.stackexchange.com/a/2287/1122). If you want to put an upper bound on the worst-case probability of making a mistake, you use a p-value. If you want to express the conditional probability of a particular hypothesis given the observation (and given a prior belief), you use a posterior probability. The Bayesians also can do silly things (see the cookie example with the inept Bayesian robots). In the end there is no free lunch.

[arrrg]

The frequentist p-value is about H0, not (directly) the hypothesis you are testing. More specifically, it denotes the probability of rejecting H0, even though it's true.