Deterministic simulation models are used in many areas, including demographic population projections, the investigation of social scientific theories, the making of environmental and other policy decisions, atmospheric science, engineering, and pharmaceutical research. They tend to be complex, and to require the specification of many inputs. This is often done in an ad-hoc manner, and little attention has been given to taking proper account of uncertainty and evidence about the inputs and outputs to the model. Statisticians have only fairly recently started to be involved in the analysis of such models, although their skills have the potential to contribute a great deal.
I got involved in this problem through my work for the International
Whaling Comission on determining if bowhead whales could safely be subjected
to aboriginal subsistence hunting by the Inuit people of Alaska, and on
setting the quota. This has traditionally been done using deterministic
population dynamics models, similar to those that are used by demographers
for population projections. Our first effort to take proper account of
the uncertainties involved was the Bayesian synthesis method of Raftery,
Givens and Zeh (1995, JASA). However, this suffers from the Borel
paradox, according to which the results may not be invariant to reparameterizations
of the model. I will describe the Bayesian melding method, which overcomes
this difficulty by bringing together ideas from modeling, measure theory
and the pooling of expert opinions. It provides a formal framework for
estimating and taking account of
uncertainties and evidence about model inputs and outputs, model comparison,
model validation, and accounting for model uncertainty via Bayesian model
averaging.
I will also briefly describe a new project that is just starting on assessing and visualizing uncertainty in mesoscale numerical weather prediction. This is a very high-dimensional problem and poses significant research challenges to the Bayesian melding approach. It is an interdisciplinary project involving atmospheric scientists and psychologists, as well as statisticians.
A light lunch will be available at 11:45 am, Seminar will begin at 12:00 noon.