Bayesian Logical Data Analysis in the Physical Sciences

This is my new favorite book about Bayesian stat that I learned about from the Penn. State Astrostat summer school.

Note that it's written by an astronomer and provides Mathematica code (can't get more astro/ physics than that!!! i think only physicists / astrophysicists have such a love for Mathematica which is very expensive in my opinion ... )

Today I have been reading about sample comparison: Given two samples, determine if they come from the same distribution.

For such a problem, frequentists assume a null hypothesis that the samples are different then do some tests to reject the null hypothesis. Bayesians evaluate the probability of different cases when....

• means being the same, variances being the same
• means being the same, variances being different
• means being different, variances being the same
• mean being different and variances being different

For details, read Appendix C of the book. Is this what I want for answering the scientific question that I have in mind? I am not sure. I have to think harder / talk to some Bayesians.