Uncertainty quantication and propagation through complex chains of computational models

Abstract

There are many fields in which it is of interest to make predictions from a chain of computational models or simulators, in which the output of one simulator in the chain forms one of the inputs to the next simulator. In order to make reliable predictions from the chain, it is necessary to understand how uncertainty in the individual models will propagate through the chain. Each simulator will often be computationally intensive, and for computational feasibility must be approximated; we use a Gaussian process emulator to do this. This thesis focuses on a “linked” emulator, in which each model is emulated separately, and the emulators are linked to make predictions from the chain as a whole. We present two methods to make predictions from a chain of linked emulators. Both have precedent in previous research but are fully formalised and extended in our work. One method uses simulation and Monte Carlo integration to make empirical predictions from the chain; this is extremely flexible and can be applied to a wide class of emulators but can be computationally intensive and is open to Monte Carlo error. The second method uses theoretical results for the mean and variance of the linked emulator under certain restrictive conditions on the emulators of the individual models in the chain; this is fast and provides exact or near-exact results, but is possible only for a very limited set of emulators. Related problems include experimental design and sensitivity analysis for chains of models. We present an algorithm for single-stage design, and discuss approaches to sequential design strategies. We also propose methods for sensitivity analysis on the final model of a chain and develop techniques towards sensitivity analysis for the chain as a whole. The above methodology is demonstrated on a chain to assess the impact of a chemical, biological or radiological release which combines a model for atmospheric dispersion with a model for the probability of casualty.

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ORCID for David Woods: orcid.org/0000-0001-7648-429X

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