ABSTRACT
In the previous chapter, we saw how explicitly adding noise to our model allowed us to obtain more than just point predictions. In particular, we were able to quantify the uncertainty present in our parameter estimates and our subsequent predictions. Once content with the idea that there will be uncertainty in our parameter estimates, it is a small step towards considering our parameters themselves as random variables. Bayesian methods are becoming increasingly important within Machine Learning and we will devote the next two chapters to providing an introduction to an area that many people find challenging. In this chapter, we will cover some of the fundamental ideas of Bayesian statistics through two examples. Unfortunately, the calculations required to perform Bayesian inference are often not analytically tractable. In Chapter 4 we will introduce three approximation methods that are popular in the Machine Learning community.
