Applied Bayesian Modelling, 2nd Edition

Chapter 1Bayesian methods and Bayesian estimation

1.1 Introduction

Bayesian analysis of data in the health, social and physical sciences has been greatly facilitated in the last two decades by improved scope for estimation via iterative sampling methods. Recent overviews are provided by Brooks et al. (2011), Hamelryck et al. (2012), and Damien et al. (2013). Since the first edition of this book in 2003, the major changes in Bayesian technology relevant to practical data analysis have arguably been in distinct new approaches to estimation, such as the INLA method, and in a much extended range of computer packages, especially in R, for applying Bayesian techniques (e.g. Martin and Quinn, 2006; Albert, 2007; Statisticat LLC, 2013).

Among the benefits of the Bayesian approach and of sampling methods of Bayesian estimation (Gelfand and Smith, 1990; Geyer, 2011) are a more natural interpretation of parameter uncertainty (e.g. through credible intervals) (Lu et al., 2012), and the ease with which the full parameter density (possibly skew or multi-modal) may be estimated. By contrast, frequentist estimates may rely on normality approximations based on large sample asymptotics (Bayarri and Berger, 2004). Unlike classical techniques, the Bayesian method allows model comparison across non-nested alternatives, and recent sampling estimation developments have facilitated new methods of model choice (e.g. Barbieri and Berger, 2004; Chib and Jeliazkov, 2005). The flexibility of Bayesian sampling ...