Hierarchical Emulation: A Method for Modeling and Comparing Nested Simulators

Abstract

Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract.Computer simulators often contain options to include extensions, leading to different versions of a particular simulator with slightly different input spaces. We develop hierarchical emulation, a method for emulating such simulators and for learning about the differences between versions of a simulator. In an example using data from an ocean carbon cycle model, hierarchical emulators outperformed standard emulators both in their predictive accuracy and their coherence with the emulation model. The hierarchical emulator performed particularly well when a comparatively small amount of training data came from the extended simulator. This benefit of hierarchical emulation is advantageous when the extended simulator is costly to run compared to the simpler version.

Comparison of Surrogate-Based Uncertainty Quantification Methods for Computationally Expensive Simulators

“…Emulators have also been applied to address various objectives, including uncertainty analysis (Oakley and O'Hagan, 2002), sensitivity analysis (Oakley and O'Hagan, 2004), calibration (Kennedy and O'Hagan, 2001;Higdon et al, 2004) and history matching (Williamson et al, 2013). Similar to polynomial chaos, more advanced formulations of Gaussian process emulation have been developed including: multi-fidelity (Kennedy and O'Hagan, 2000;Forrester et al, 2007;Le Gratiet, 2013), nested and hierarchical (Oughton and Craig, 2016), sequential and adaptive (Busby, 2009;Loeppky et al, 2010), gradient-enhanced (Dwight and Han, 2009) and dynamical or multivariate (Conti and OHagan, 2010;Fricker et al, 2013;Picheny and Ginsbourger, 2013).…”

Diagnostics-Driven Nonstationary Emulators Using Kernel Mixtures

“…When the nonstationarity is not adequately captured in this way, prediction intervals produced by the emulators can be too narrow in the region of high residual variability of f (the emulator is over-confident). On the contrary, the emulator is under-confident in the input space where f is 'well-behaved' [9,35,40].…”