Mixtures of Experts for Prediction and Understanding Model Discrepancy in Dynamic Computer Models
David Nott¹, Lucy Marshall², Mark Fielding³, Shie-Yui Liong⁴
¹Department of Statistics and Applied Probability, National University of Singapore, Singapore; ²Department of Land Resources and Environmental Sciences, Montana State University, Bozeman, MT, United States; ³School of Mathematics and Applied Statistics, University of Wollongong, NSW, Australia; ⁴Tropical Marine Science Institute, National University of Singapore, Singapore

There are many areas of science and engineering where research and decision making are done using computer models. These computer models are usually deterministic and may take minutes, hours or days to produce an output for a single value of the model inputs. Here we consider fitting mixtures of experts of computer models where the expert components use different values of the computer model parameters. We discuss the efficient calibration of such models using emulators, which are fast statistical surrogates for the computer model, and argue that mixtures of experts are often insightful for describing model discrepancy and ways in which the computer model can be improved. This is not a strength of standard approaches to the statistical analysis of computer models where a certain “best input” assumption is usually made and model discrepancy is often described through a stationary Gaussian process prior on the discrepancy function. Application of our framework is presented for a dynamic hydrological rainfall runoff model in which the mixture approach is helpful for highlighting model deficiencies.

Biography: David Nott is Associate Professor in the Department of Statistics and Applied Probability at the National University of Singapore. Prior to his current appointment he was Senior Lecturer in the Department of Statistics at University of New South Wales, Sydney. His research interests are in Bayesian inference and computation and environmental statistics.