Imprecision arises naturally in the context of computer models and their relation to reality. An imprecise treatment of general computer models is presented, illustrated with an analysis of a complex galaxy formation simulation known as Galform. The analysis involves several different types of uncertainty, one of which (the Model Discrepancy) comes directly from expert elicitation regarding the deficiencies of the model. The Model Discrepancy is therefore treated within an Imprecise framework to reflect more accurately the beliefs of the expert concerning the discrepancy between the model and reality. Due to the conceptual complexity and computationally intensive nature of such a Bayesian imprecise uncertainty analysis, Bayes Linear Methodology is employed which requires consideration of only expectations and variances of all uncertain quantities. Therefore incorporating an Imprecise treatment within a Bayes Linear analysis is shown to be relatively straightforward. The impact of an imprecise assessment on the input space of the model is determined through the use of an Implausibility measure.
Keywords. Bayesian Inference, Computer models, Calibration, Imprecise model discrepancy, Implausibility, Galaxy Formation, Graphical Representation of Model Imprecision.
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Authors addresses:
Ian Vernon
Department of Mathematical Sciences
Durham University
Science Laboratories
South Road
DURHAM
DH1 3LE
Michael Goldstein
Dept Mathematical Sciences
Durham University
Science Site
Durham
E-mail addresses:
| Ian Vernon | i.r.vernon@durham.ac.uk |
| Michael Goldstein | Michael.Goldstein@durham.ac.uk |