#### 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)