## The interface between Bayesian and frequentist statistics

- Date: 03/26/2007

Nancy Reid (University of Toronto)

University of British Columbia

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