Exchangeable Computer Models

House, L.; Goldstein, M.; Vernon, I.R.

Abstract

Analysts often use deterministic computer models to predict the behavior of com- plex physical systems when observational data are limited. However, inferences based partially or entirely on simulated data require adequate assessments of model uncer- tainty that can be hard to quantify. The deterministic nature of computer models limits the information we can extract from simulations to separate model signal from model error. In this paper we present a new approach to assess the uncertainty of computer models to which we refer as multi-deterministic. Evaluations from a multi- deterministic computer model can be considered to be a collection of deterministic simulators which share the same input and output space, do not present obvious the- oretical or computational advantages, and generate disparate predictions. To quantify the uncertainty of predictions from multi-deterministic models we use the construct of a latent model about which we learn from observed evaluations. We assume that outcomes from multi-deterministic models are sequences of second-order exchangeable functions (SOEF) and use Bayes linear methods to assess the latent model a posteriori. We demonstrate our methods using multi-deterministic results from a galaxy forma- tion model called Galform for which the system condition is the specification of dark matter over time and space.

Citation

House, L., Goldstein, M., & Vernon, I. (2009). Exchangeable Computer Models. MUCM

• Report Type: Project Report
• Online Publication Date: Dec 1, 2009
• Publication Date: Dec 1, 2009
• Deposit Date: Mar 21, 2011
• Publicly Available Date: Oct 20, 2017
• Series Title: MUCM Technical Reports
• Keywords: Computer Models, Multiple Models, Exchangeable Beliefs, System Condition, Bounding or Forcing conditions, Model Variance, Galaxy Formation, Bayes linear Methods, Prior Specification
• Publisher URL: http://www.mucm.ac.uk/Pages/Dissemination/TechnicalReports.html
• Additional Information: Additional Information: This is a Technical Report in the Managing Uncertainty for Complex Models (MUCM: funded by a Basic Technology Grant) Technical Report Series. The paper has also been submitted to RSS B.; University Name: Sheffield University; Publisher: MUCM; Type: monograph; Subtype: project_report