Chapter 4. Bayesian Modeling – Basic Models

After learning how to represent graphical models, how to compute posterior distributions, how to use parameters with maximum likelihood estimation, and even how to learn the same models when data is missing and variables are hidden, we are going to delve into the problem of modeling using the Bayesian paradigm. In this chapter, we will see that some simple problems are not easy to model and compute and will necessitate specific solutions. First of all, inference is a difficult problem and the junction tree algorithm only solves specific problems. Second, the representation of the models has so far been based on discrete variables.

In this chapter we will introduce simple, yet powerful, Bayesian models, and show how to represent them as probabilistic graphical models. We will see how their parameters can be learned efficiently, by using different techniques, and also how to perform inference on those models in the most efficient...