6.5 Distributional models

We saw earlier that we can use linear models for parameters other than the mean (or location parameter). For example, we can use a linear model for the mean and a linear model for the standard deviation of a Gaussian distribution. These models are usually called distributional models. The syntax for distributional models is very similar; we just need to add a line for the auxiliary parameters we want to model. For instance, σ for a Gaussian, or α for a NegativeBinomial.

Let’s now reproduce an example from Chapter 4, the babies example:

Code 6.16

formula = bmb.Formula( 
    "length ∼ np.sqrt(month)", 
    "sigma ∼ month" 
) 
model_dis = bmb.Model(formula, babies) 
idata_dis = model_dis.fit()

Figure 6.9 shows the posterior distribution values of sigma for model_dis (varying sigma) and for a model with constant sigma. We can see...