Introduction, Rates I

In this chapter we start by introducing the Bayesian approach to statistical inference. Given a statistical model and a prior distribution on the model parameters, one forms the posterior distribution, a data-dependent conditional distribution which is the main object of interest for inference. The terminology and framework necessary to study convergence rates of Bayesian posterior distributions in a frequentist sense, as the number of data goes to infinity, are reviewed. We state and prove a general result that yields a convergence rate, provided a number of generic conditions are satisfied, following seminal work by Ghosal, Ghosh and van der Vaart. Specific examples of the use of this approach are given in the following chapters.