Consider:

… 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.

## 2019

### Gaussian Process Middle C

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.

Consider: