9.3 Distributional BART models

As we saw in Chapter 6, for generalized linear models, we are not restricted to creating linear models for the mean or location parameter; we can also model other parameters, for example, the standard deviation of a Gaussian or even both the mean and standard deviation. The same applies to BART models.

To exemplify this, let’s model the bike dataset. We will use rented as the response variable and hour, temperature, humidity, and workday as predictor variables. As we did previously, we are going to use a NegativeBinomial distribution as likelihood. This distribution has two parameters μ and alpha. We are going to use a sum of trees for both parameters. The following code block shows the model:

Code 9.5

with pm.Model() as model_bb: 
    μ = pmb.BART("μ", X, np.log(Y), shape=(2, 348), separate_trees=True) 
    pm.NegativeBinomial('yl', np.exp(μ...