In this chapter we provide a brief overview of hierarchical Bayesian modeling and computing for readers not already familiar with these topics. Of course, in one chapter we can only scratch the surface of this rapidly expanding field, and readers may well wish to consult one of the many recent textbooks on the subject, either as preliminary work or on an as-needed basis. By contrast, readers already familiar with the basics of Bayesian methods and computing may wish to skip ahead to Section 2.5, where we outline the principles of Bayesian clinical trial design and analysis. It should come as little surprise that the Bayesian book we most highly

recommend is the one by Carlin and Louis (2009); the Bayesian methodology and computing material below roughly follows Chapters 2 and 3, respectively, in that text. However, a great many other good Bayesian books are available, and we list a few of them and their characteristics. First we must mention texts stressing Bayesian theory, including DeGroot (1970), Berger (1985), Bernardo and Smith (1994), and Robert (2001). These books tend to focus on foundations and decision theory, rather than computation or data analysis. On the more methodological side, a nice introductory book is that of Lee (1997), with O’Hagan and Forster (2004) and Gelman, Carlin, Stern, and Rubin (2004) offering more general Bayesian modeling treatments.