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Optimal Design under Heteroscedasticity for Gaussian Process Emulators with replicated observations

Presented by: 
A Boukouvalas [Aston]
Date: 
Friday 2nd September 2011 - 12:00 to 12:30
Venue: 
INI Seminar Room 1
Session Title: 
Advances in Computational Design and Computer Experiments
Session Chair: 
Hugo Maruri-Aguilar
Abstract: 
Computer models, or simulators, are widely used in a range of scientific fields to aid understanding of the processes involved and make predictions. Such simulators are often computationally demanding and are thus not amenable to statistical analysis. Emulators provide a statistical approximation, or surrogate, for the simulators accounting for the additional approximation uncertainty.

For random output, or stochastic, simulators the output dispersion, and thus variance, is typically a function of the inputs. This work extends the emulator framework to account for such heteroscedasticity by constructing two new heteroscedastic Gaussian process representations and proposes an experimental design technique to optimally learn the model parameters. The design criterion is an extension of Fisher information to heteroscedastic variance models. Replicated observations are efficiently handled in both the design and model inference stages. We examine the effect of such optimal designs on both model parameter uncertainty and predictive variance through a series of simulation experiments on both synthetic and real world simulators.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons