ABSTRACT
This chapter describes principles of Bayesian approaches to inference, with a focus on the mechanics of Bayesian inference. To develop the mechanics of Bayesian inference, it reviews frequentist approaches to inference, in particular maximum likelihood (ML) approaches, which then serves as a launching point for the description of Bayesian inference. The likelihood function plays a key role in Bayesian inference just as in ML estimation. In a Bayesian analysis, the authors combine the information in the data, expressed in the likelihood, with the prior information about the parameter. Bayesian models may be advantageously represented as a particular type of graphical model. The correspondence between the mathematical model and the directed acyclic graphs is a general point of Bayesian modeling, which simplifies model construction and calculations of posterior distributions. Finally, the chapter discusses the mechanics of Bayesian inference in part by contrasting it with frequentist inference, as developed by the authors.
