7.8 Continuous mixtures

The focus of this chapter was on discrete mixture models, but we can also have continuous mixture models. And indeed we already know some of them. For instance, hierarchical models can also be interpreted as continuous mixture models where the parameters in each group come from a continuous distribution in the upper level. To make it more concrete, think about performing linear regression for several groups. We can assume that each group has its own slope or that all the groups share the same slope. Alternatively, instead of framing our problem as two extreme discrete options, a hierarchical model allows us to effectively model a continuous mixture of these two options.

7.8.1 Some common distributions are mixtures

The BetaBinomial is a discrete distribution generally used to describe the number of successes y for n Bernoulli trials when the probability of success p at each trial is unknown and assumed to follow a beta distribution with parameters α and...