In the previous two chapters, we learned the core ideas of the Bayesian approach and how to use PyMC3 to do Bayesian inference. If we want to build models of arbitrary complexity (and we certainly do), we must learn how to build multi-parametric models. Almost all interesting problems out there need to be modeled using more than one parameter. Moreover, in many real-world problems, some parameters depend on the values of other parameters; such relationships can be elegantly modeled using Bayesian hierarchical models. We will learn how to build these models and the advantages of using them. These are such important concepts that we will keep revisiting them over and over again throughout the rest of the book.
In this chapter, we will cover the following topics:
Nuisance parameters and marginalized distributions
The Gaussian model
Robust estimation in the presence of outliers
Comparing groups and measuring the effect size
Hierarchical...