Hmmm. Is this a fundamental math problem, or just a limitation of pymc3?
So suppose I have many samples of some substance which changes state spontaneously. Like time bombs. All my samples have different ages. I want to estimate the half-life of my samples. So I have a series [a, s] where age is a continuous variable, and s is either “live” or “exploded”. How should I set up the calibration of the half-life, in pymc3?
One thought is to define a new quantity c(A) = count(s = 1 & a < A)/count(a < A), and fit that directly. ?
I also know that logistic regression is often used for modeling probabilities, but it’s not clear to me that it would be a natural model for a half-life (or, what I’m after next, a linear combination of half-lives).