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.

### An Ising-Like Model

## … using Stan & HMC

### Sparse Gaussian Process Examples

## A Minimal Working Example

### Random Stuff

## Random Stuff

### Stochastic Bernoulli Probabilities

Consider: