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Statistical Inference for Deterministic Simulation Models: The Bayesian Melding Approach

Deterministic simulation models are used in many areas, including demographic population projections, the investigation of social scientific theories, environmental science, engineering, and atmospheric science. 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.

I first 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. I will describe our Bayesian melding method, which 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 big research challenges to the Bayesian melding approach. It is an interdisciplinary project involving atmospheric scientists and psychologists, as well as statisticians.