Bayesian inference is a different paradigm for statistics; it is not a method or algorithm such as cluster finding or linear regression. It stands next to classical statistical analysis. Everything that we have done so far in this book, and everything that you can do in classical (or frequentist) statistical analysis, you can do in Bayesian statistics. The main difference between frequentist (classical) and Bayesian statistics is that while frequentist assumes that the model parameters are fixed, Bayesian assumes that they have a range, a distribution. Thus, from the frequentist approach, it is easy to create point estimates—mean, variance, or fixed model parameters—directly from the data. The point estimates are unique to the data; each new dataset needs new point estimates.
In this chapter, we will cover the following topics:
Examples of Bayesian analysis: one where we try to identify a switch point in a time series and another with linear regression, where we...