Bayesian alternative or complement to the Student t-test

I was just recently using the Student t-Test to check whether values from two samples could have an identical mean or not. I was wondering whether there is a complementary technique in bayesian statistics that does a similar thing.

Especially I am wondering about the $P$ values that I obtain as a result (http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_ind.html). With a sample size of 2 in my two samples, I figure that the resulting p value would probably fluctuate quite a bit if I added some more measurements or take some away.

• A typical very simple Bayesian approach would be to form an interval for the difference in means, based off the posterior for it. One might make all the same kinds of assumptions as in the t-test or one might make a variety of changes toward more robustness/wider applicability (e.g. considering possible contamination of the data or heavier tailed distributions, putting hyperiors in and so on). Of course there's also a more formal Bayesian decision-theoretic approach and a variety of more nearly hypothesis-testing style things one might do. – Glen_b -Reinstate Monica Jun 27 '14 at 0:18