Spatial Modeling in the Validation of Complex Computer Models

• Activity Number: 115
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2003 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Stat. Sciences
• Author(s): M. J. Bayarri*+ and James O. Berger and Jerome Sacks
• Companies: Universitat de València and Duke University and Duke University
• Keywords: Bayesian methods ; fast simulators ; Gaussian processes ; Kronecker product

Abstract

Use of spatial models in the validation of complex computer models is explored. Computer implementation of math-based models (simulators) is increasingly used in many areas; an important question that arises is whether the model adequately represents reality. We propose a six-step framework for model validation. Bayesian methods are particularly suited to treating the major issues associated with the validation process: quantifying multiple sources of error and uncertainty in computer models; combining multiple sources of information; and updating validation assessments as new information is acquired. Moreover, hierarchical Bayesian techniques allow inferential statements to be made about predictive error associated with model predictions in untested situations. However, Bayesian analyses for complex models are usually implemented via Monte Carlo (MC) or Markov chain Monte Carlo (MCMC) methods, requiring thousands of computer model runs, making it infeasible for slow simulators. We propose use of spatial models to approximate the outputs of computer models, thus allowing MC and MCMC (and Bayesian) analyses.