Continuous mixtures

This chapter was focused on discrete mixture models but we can also have continuous mixture models. And indeed we already know some of them. One example of a continuous mixture model is the robust logistic regression model that we saw earlier. This is a mixture of two components: a logistic on one hand and a random guessing on the other. Note that the parameter is not an on/off switch, but instead is more like a mix-knob controlling how much random guessing and how much logistic regression we have in the mix. Only for extreme values of do we have a pure random-guessing or pure logistic regression.

Hierarchical models can be 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 it own slope or that all the groups share the same slope. Alternatively, instead of framing...