Pacific Institute for the Mathematical Sciences - PIMS

Statistical theory is often categorized as either "Bayesian" or
"frequentist", and statisticians often self-identify in the same
categories. During the development of theoretical statistics as a
separate field in the twentieth century this categorisation led to a
great deal of discussion, some of which was surprisingly bitter and
antagonistic. With the development of several key results in the
asymptotic theory of inference based on the likelihood function, it is
becoming clear that the mathematical differences between Bayesian and
frequentist methods are rather less important than the philosophical
ones. Some of this work is based on efforts to construct priors which
minimize the difference between the two approaches and some is based on
an ongoing effort to develop so-called 'reference', or 'objective' or
;default' priors. Perhaps not surprisingly, even the correct
terminology to be used in this setting has been the subject of debate!

I will give an overview of some of the asymptotic theory behind the
development of approaches to constructing priors that minimize the
differences between Bayesian and frequentist inference, with special
attention to 'strong matching' priors that have been developed recently
in joint work with Don Fraser and colleagues. The construction of these
priors provides some insight into the exact points of departure between
Bayesian and frequentist methods, at least from the mathematical point
of view. The philosophical debate may well continue for some time.

10th Anniversary Speaker Series 2007