Bayesian Statistics Seminar
North Carolina State University
presents
Dr. Bertrand Clarke
Duke University/University of British Columbia
"Sample Size and Effective Samples"
ABSTRACT
We distinguish between two classes of sample size problems.
The first is the actual sample size needed to achieve a specific
inference goal. The second is an effective sample where we try to interpret one sample under one model as another sample under a different model. An effective sample leads to an
effective sample size which may be more important that the
sample itself.
For the actual case, we give asymptotic expressions for the expected value, under a fixed parameter, for certain types of functionals of the posterior density in a Bayesian analysis. The generality of our approach permits us to choose functionals that
encapsulate different inference criteria. The dependence of our expressions
on the sample size means that we can pre-experimentally obtain adequate sample sizes to get inferences with a pre-specified level of accuracy.
For the effective sample case, we find a `virtual' sample under one model that gives the same inferences as an actual sample under
another model. We use the same prior for both models, but this is
not necessary. We show these effective samples exist and give some
examples to show that their behavior is consistent with statistical
intuition and the procedure can be extended to give a notion of effective number of parameters as well.
Tuesday, September, 28, 2004
4:00 - 5:00 pm
208 Patterson Hall
Refreshments will be served on the second floor of Patterson Hall (outside Room 208) at 3:45 pm.