Bayesian Uncertainty Analysis and Decision Support for Complex Models of Physical Systems with Application to Production Optimisation of Subsurface Energy Resources
Important decision making problems are increasingly addressed using computer models for complex real world systems. However, there are major limitations to their direct use including: their complex structure; large numbers of inputs and outputs; the presence of many sources of uncertainty; which is further compounded by their long evaluation times. Bayesian methodology for the analysis of computer models has been extensively developed to perform inference for the physical systems. In this thesis, the Bayesian uncertainty analysis methodology is extended to provide robust decision support under uncertainty.
Bayesian emulators are employed as a fast and efficient statistical approximation for computer models. We establish a hierarchical Bayesian emulation framework that exploits known constrained simulator behaviour in constituents of the decision support utility function. In addition, novel Bayesian emulation methodology is developed for computer models with structured partial discontinuities. We advance the crucial uncertainty quantification methodology to perform a robust decision analysis developing a technique to assess and remove linear transformations of the utility function induced by sources of uncertainty to which conclusions are invariant, as well as incorporating structural model discrepancy and decision implementation error. These are encompassed within a novel iterative decision support procedure which acknowledges utility function uncertainty resulting from the separation of the analysts and final decision makers to deliver a robust class of decisions, along with any additional information, for further consideration. The complete toolkit is successfully demonstrated via an application to the problem of optimal petroleum field development, including an international and commercially important benchmark challenge
