Sponsoring Section/Society: ASA-SBSS
Session Slot: 10:30-12:20 Tuesday
Estimated Audience Size: 80-120
AudioVisual Request: Overhead Projector, Slide Projector
Session Title: Inference for Deterministic Models in Environmental Policy
Theme Session: Yes
Applied Session: No
Session Organizer: Raftery, Adrian E. University of Washington
Address: Adrian Raftery Department of Statistics University of Washington Box 354322 Seattle, WA 98195-4322
Phone: 206-543-4505
Fax: 206-685-7419
Email: raftery@stat.washington.edu
Session Timing: 110 minutes total (Sorry about format):
Opening Remarks by Chair - 5 First Speaker - 30 minutes Second Speaker - 30 minutes Third Speaker - 30 minutes Discussant - 0 minutes Floor Discusion - 15 minutes
Session Chair: Raftery, Adrian E. University of Washington
Address: Adrian Raftery Department of Statistics University of Washington Box 354322 Seattle, WA 98195-4322
Phone: 206-543-4505
Fax: 206-685-7419
Email: raftery@stat.washington.edu
1. Assessing Uncertainty in Projections of Forest Growth Under Varying Climate Scenario
Green, Edwin J., Rutgers University
Address: Prof. Edwin J. Green Dept of Ecology, Evolution & Natural Resources Cook College - Rutgers University New Brunswick, NJ 08903-0231
Phone: 732-932-9152
Fax: 732-932-8746
Email: green@crssa.rutgers.edu
Valentine, Harry T., USDA Forest Service
Abstract: Valentine et al. have developed a mechanistic forest growth model, called PIPESTEM. The model has been calibrated for loblolly pine. When used in conjunction with the determinsitc carbon flux model MAESTRO, PIPESTEM can deliver predictions regarding the growth of loblolly pine under various scenarios regarding climate change and atmospheric carbon dioxide concentrations. Unfortunately, the projections suffer from the fact that they are not accompanied by any statement of uncertainty. We present our work on determining uncertainty estimates for loblolly pine growth projections under specified climatic scenarios, using the Bayesian Synthesis method to incorporate incorporate expert knowledge and auuxilliary data.
2. Supra-Bayesian Pooling for Simulation Models
Roback, Paul, Colorado State University
Address: Paul Roback Department of Statistics Colorado State University Fort Collins, CO 80523
Phone: 970-491-3824
Fax: 970-491-7895
Email: proback@stat.colostate.edu
Givens, Geoff, Colorado State University
Abstract: We consider a deterministic simulation model, such as phi=M(theta). For instance, theta could be whale mortality and productivity, while phi could be whale population and age distribution; the mapping M could be invertible, or it could be non-invertible and highly complex. Our goal is to make Bayesian inference about either the inputs (theta) or the outputs (phi) when prior distributions (representing expert opinion) and likelihoods (based on data which has been collected) are available for both inputs and outputs. At the heart of this problem, expert opinions which have been rendered in different probability spaces must be combined into one probability space. One method for combining these opinions is the supra-Bayesian approach, in which the experts' prior opinions are considered data for a meta-decision maker, who uses Bayes' Theorem to update his/her beliefs. Advocates of this method tout its ability to account for miscalibration, dishonesty, and nonindependence of the experts, as well as its adherence to several desirable philosophical principles. We describe the supra-Bayesian approach and its motivations, and we apply it in several examples.
3. Bayesian Synthesis Inference for Noninvertible Deterministic Simulation Models via Geometric Pooling
Poole, David, University of Washington
Address: David Poole Department of Statistics University of Washington Box 354322 Seattle, WA 98195-4322
Phone: 206-543-8484
Fax: 206-685-7419
Email: poole@stat.washington.edu
Raftery, Adrian E., University of Washington
Abstract: Two key issues with the Bayesian synthesis assessment method are considered. The first is the Borel paradox, according to which different parameterizations of model inputs and outputs lead to different results. A modification of the Bayesian synthesis method called geometric pooling, proposed last year by Raftery, Poole and Givens (1996), is extended so as to apply to inputs in noninvertible models. It is applied to a simplified population dynamics model (PDM) for bowhead whales. This turns the Bayesian synthesis method into a fully Bayesian method and so avoids the Borel paradox.The second issue is that of relabelling inputs as outputs or vice versa. For example, in the "forwards" variant, initial population size is considered as an input and current population size as an output, while in the "backwards" variant it is the other way round. The two variants yield different results. Recognizing that the deterministic PDM is used only as an approximation to a more realistic stochastic PDM, we extend the Bayesian synthesis method to stochastic mechanistic models. We find that the forwards variant gives results that are close to those from a stochastic PDM, while the backwards variant gives results that are quite different. We also provide a mathematical explanation of the difference between the forwards and backwards variants, and propose a further modification, the ``full pooling'' method, that resolves it.
List of speakers who are nonmembers: None