Gaussian processes
We’re going to look in detail at a specific non-parametric Bayesian method that makes use of GPs. As the name suggests, GPs involve a Gaussian distribution. In fact, the Gaussian distribution is the prior that we put on our function, 
. This makes GPs widely used in non-parametric Bayesian methods. We can use them for constructing both regression models and classification models. To keep this chapter short, we’ll only illustrate GPR, but many of the concepts and ideas are the same for both GPR and GP classification. Personally, I also find GPR the easiest non-parametric Bayesian method to understand, so it is a good place to start.
To start we need to set up our model. We’ll model our observations, 
, as follows:
Eq. 2
For a fixed choice of , Eq. 2 says that our observation, , is a Gaussian noise corrupted version of 
. We will also assume that the noise values, 
, from different observations are independent of each other.
Eq. 2...
