Bayesian Emulators for Multivariate Computer Models with Categorical Inputs

• Activity Number: 238
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): David Woods*+ and Antony Overstall
• Companies: Southampton Statistical Sciences Research Institute and Southampton Statistical Sciences Research Institute
• Keywords: Computer experiment ; Gaussian Process ; Bayesian statistics ; Markov Chain Monte Carlo Model Composition ; Sensitivity analysis ; Dispersion modelling

Abstract

Computer models, or simulators, are mathematical representations of physical systems. They are used for real-world problems where it would be expensive, impossible or unethical to use a physical experiment. Many simulators are computationally expensive and hence an emulator, a statistical meta-model, is used to predict the simulator output at any particular set of inputs. Emulators make practicable tasks such as sensitivity analysis, uncertainty analysis and model calibration.

We consider simulators for real problems from emergency planning that have several defining features: the output is multivariate, potentially dynamic and may be zero-inflated; the input may include both continuous and categorical input variables. Challenges for such models include the definition and incorporation of appropriate distance metrics for the categorical variables and implementing efficient methods for approximating the multivariate posterior predictive distribution.

We explore a variety of Bayesian methods for constructing emulators, including Gaussian Process regression and the use of "lightweight" emulators, and address issues including predictive accuracy and model selection.