8.8 Cox processes
Now we are going to model count data. We will see two examples; one with a time-varying rate and one with a 2D spatially varying rate. To do this, we will use a Poisson likelihood and the rate will be modeled using a Gaussian process. Because the rate of the Poisson distribution is limited to positive values, we will use an exponential as the inverse link function, as we did for the NegativeBinomial regression from Chapter 4.
We can think of a Poisson process as a distribution over collections of points in a given space where every finite collection of those random variables has a Poisson distribution. When the rate of the Poisson process is itself a stochastic process, such as, for example, a Gaussian process, then we have a Cox process.
8.8.1 Coal mining disasters
The first example is known as the coal mining disasters. This example consists of a record of coal-mining disasters in the UK from 1851 to 1962. The number of disasters is thought to have been affected...
