Chapter 9. The three rules of probabilistic inference
This chapter covers
- Three important rules for working with probabilistic models:
- The chain rule, which lets you build complex models out of simple components
- The total probability rule, which lets you simplify a complex probabilistic model to answer simple queries
- Bayes’ rule, with which you can draw conclusions about causes from observations of their effects
- The basics of Bayesian modeling, including how to estimate model parameters from data and use them to predict future cases
In part 2 of this book, you learned all about writing probabilistic programs for a variety of applications. You know that probabilistic programming systems use inference algorithms operating on these programs to answer queries, given evidence. How do they do that? That’s what this part of the book is all about. It’s important that you know about this, so you can design models and choose algorithms that support fast and accurate inference.
This chapter begins with the basics of inference: the three rules of probabilistic inference. The inputs and output of each of the three rules is summarized in figure 9.1: