Decisions concerning public health and public expenditures must often be based on highly uncertain data; for example, consider the uneven quality of measurements of individual economic decisions and effects of public programs and policies. In the field of environmental policy, data such as pollutant measurements that are required for informed decisions are usually sparse, spatially dispersed, and subject to substantial measurement error. One response by regulators and other policy makers to the large uncertainties typical of environmental and other public decision problems has been the use of `conservative` (often inflated) estimates of exposure, risk, etc. However, the recognition that policy should be based on assessment of both likely costs and benefits has led to increased use of benefit-cost analysis in recent years. A key step forward that needs to be made, especially for spatially-varying environmental hazards, is to calibrate risk estimates: this means recommending different courses of actions and also different data-gathering strategies in different areas. In order to do this effectively, it is useful to spatially model the relevant exposures and risks. The goal of this project is to develop more reliable methods of models and model-checking for spatially-varying hazards, in settings with uncertainty (due to incomplete information) and also true underlying variability. In recent years, much progress has been made in the field of statistics in modeling complex data structures using Bayesian methods. Areas in which more progress needs to be made and on which the investigators plan to work include model fitting, computation, model checking, and display of inferences using graphs or maps. The investigators plan to particularly focus on the use of model-checking and graphical methods to build confidence in the results of the modeling fitting, so that individuals and policy-makers will have trustworthy tools to allow them to take better account of uncertainty and variability when making decisions. As an important example, the investigators propose to develop their model in the context of remediation of risks from home radon, based on a combined analysis of home radon data from many sources.
