… where \(X, P\) are random variables. Then:
The distribution of \(X\) is only dependant on the expectation of \(P\).
Another way to see this:
So, random probabilities, random hazard rates or ‘random effects’ across groups which have just one observation are probably meaningless to talk about.
First of my experiments on audio modelling using gaussian processes. Here, I construct a GP that, when sampled, plays middle c the way a grand piano would.
… using Stan & HMC
A Minimal Working Example