What are non-parametric Bayesian methods?
As the name suggests, non-parametric Bayesian methods are Bayesian, so it may be a good time to review the section in Chapter 5 on Bayesian probabilistic modeling. Because we are using Bayesian methods, we will be using priors. As usual with Bayesian methods, there is a subjective element to setting the prior. The prior is something we choose. Choose a slightly different prior and we will get slightly different inferences. However, it is what we use the prior for that is the interesting aspect of non-parametric Bayesian methods.
In Chapter 5, when we were using Bayesian methods to build probabilistic models, we had the data points, 
. We modeled the target variable values, 
, as random variables whose probability density function was given by some function, 
, with 
being the model parameters. We’d write this in statistical modeling notation as follows:
Eq. 1
What Eq. 1 says is that the observations of the target (response...
