I am attempting to use Bayesian analysis to compare distributions to help with decision analysis - when to treat a patient based on a blood measurement X.
Here you can see 1000 samples from two posterior distributions (student t) that I am trying to compare. I have computed the difference between means, and p(mu_delta > 0 | data) = 0.335 --> not entirely convincing.
That said, the blue distribution has a much longer tail on the right (higher level of X) than the red distribution. The blue distribution is patients who shouldn't be treated. The aim is to reduce the number of patients who receive treatment who shouldn't. Is there a way I can select a threshold to say any marker > VALUE(X) should not receive treatment since there is a higher probability they will not respond? Or is it only fair to compare means?
I understand that this is a sample distribution which may not behave in the same way with real data but that is of course something I can test.
If it makes a difference - this work was done using SciPy (python) and I have other measurements I wold also like to include (multivariate) using Stan.
EDIT:I have since realised that I am also sampling values below 0 which cannot actually happen. Is there a way to correct for this or should I use rejection/ MCMC sampling to reject all points below?