Some Recent Developments in Bayesian Analysis, with Astronomical Illustrations

James O. Berger

New developments in default Bayesian hypothesis testing and model selection are reviewed. As motivation, the surprising differences between Bayesian and classical answers in hypothesis testing are discussed, using a simple example. Next, an example of model selection is considered, and used to illustrate a new default Bayesian technique called the ``intrinsic Bayes factor''. The example involves selection of the order of an autoregressive time series model of sunspot data. Classification and clustering is next considered, with the default Bayesian approach being illustrated on two astronomical data sets. In part, Bayesian analysis is experiencing major growth because of the development of powerful new computational tools, typically called Markov Chain Monte Carlo methods. A brief review of these developments is given. Finally, some philosophical comments about reconciliation of Bayesian and classical schools of statistics are presented. Postscript File (483kB) Postscript File (figures 3 and 4: 1981kB)