Say we have event A (saving a life) and event B (person living after initially getting saved). A and B are dependent events as p(A|B) = 1. I want to model the probability of a person living which is p(A)p(B). However, since B is dependent on A = 1 the data is limited and noisy. I was wondering if I could use STAN or any other modelling technique to fit a distribution on this to calculate p(A) and p(B) separately (or in a single model) and get a single distriution of p(A)p(B). Is this possible?
Edit: Let's say we have patients [x1,x2,...] and surgeries [s1,s2] then I want to model probability of life saved for each treatment: p((A=1 and B=1) | s1) and p((A=1 and B=1) | s2). My train of thought is that Is should break these down. So, given s = s1 then p((A=1 and B=1) | s1) becomes p(A=1)*p(A=1 and B=1). If I could model these two multiples separately