Applied Bayesian Modelling - Free

PrefaceThis book follows Bayesian Statistical Modelling (Wiley, 2001) in seeking to make theBayesian approach to data analysis and modelling accessible to a wide range ofresearchers, students and others involved in applied statistical analysis. Bayesian statisticalanalysis as implemented by sampling based estimation methods has facilitated theanalysis of complex multi-faceted problems which are often difficult to tackle using`classical' likelihood based methods.The preferred tool in this book, as in Bayesian Statistical Modelling, is the packageWINBUGS; this package enables a simplified and flexible approach to modelling inwhich specification of the full conditional densities is not necessary and so small changesin program code can achieve a wide variation in modelling options (so, inter alia,facilitating sensitivity analysis to likelihood and prior assumptions). As Meyer and Yuin the Econometrics Journal (2000, pp. 198±215) state, ``any modifications of a modelincluding changes of priors and sampling error distributions are readily realised withonly minor changes of the code.'' Other sophisticated Bayesian software for MCMCmodelling has been developed in packages such as S-Plus, Minitab and Matlab, but islikely to require major reprogramming to reflect changes in model assumptions; so myown preference remains WINBUGS, despite its possible slower performance and convergencethan tailored made programs.There is greater emphasis in the current book on detailed modelling questions such asmodel checking and model choice, and the specification of the defining components (interms of priors and likelihoods) of model variants. While much analytical thought hasbeen put into how to choose between two models, say M 1 and M 2 , the processunderlying the specification of the components of each model is subject, especially inmore complex problems, to a range of choices. Despite an intention to highlight thesequestions of model specification and discrimination, there remains considerable scopefor the reader to assess sensitivity to alternative priors, and other model components.My intention is not to provide fully self-contained analyses with no issues still to resolve.The reader will notice many of the usual `specimen' data sets (the Scottish lip cancerand the ship damage data come to mind), as well as some more unfamiliar and largerdata sets. Despite recent advantages in computing power and speed which allowestimation via repeated sampling to become a serious option, a full MCMC analysisof a large data set, with parallel chains to ensure sample space coverage and enableconvergence to be monitored, is still a time-consuming affair.Some fairly standard divisions between topics (e.g. time series vs panel data analysis)have been followed, but there is also an interdisciplinary emphasis which means thatstructural equation techniques (traditionally the domain of psychometrics and educationalstatistics) receive a chapter, as do the techniques of epidemiology. I seek to reviewthe main modelling questions and cover recent developments without necessarily goinginto the full range of questions in specifying conditional densities or MCMC sampling