Bayesian Information-Gap Decision Analysis Applied to a CO2 Leakage Problem

Abstract:

We describe a decision analysis in the presence of uncertainty that combines a non-probabilistic approach (information-gap decision theory) with a probabilistic approach (Bayes’ theorem). Bayes’ theorem is one of the most popular techniques for probabilistic uncertainty quantification (UQ). It is effective in many situations, because it updates our understanding of the uncertainties by conditioning on real data using a mathematically rigorous technique. However, the application of Bayes’ theorem in science and engineering is not always rigorous. There are two reasons for this: (1) We can enumerate the possible outcomes of dice-rolling, but not the possible outcomes of real-world contamination remediation; (2) We can precisely determine conditional probabilities for coin-tossing, but substantial uncertainty surrounds the conditional probabilities for real-world contamination remediation. Of course, Bayes’ theorem is rigorously applicable beyond dice-rolling and coin-tossing, but even in cases that are constructed to be simple with ostensibly good probabilistic models, applying Bayes’ theorem to the real world may not work as well as one might expect. Bayes’ theorem is rigorously applicable only if all possible events can be described, and their conditional probabilities can be derived rigorously. Outside of this domain, it may still be useful, but its use lacks at least some rigor. The information-gap approach allows us to circumvent some of the highlighted shortcomings of Bayes’ theorem. In particular, it provides a way to account for possibilities beyond those described by our models, and a way to deal with uncertainty in the conditional distribution that forms the core of Bayesian analysis. We have developed a three-tiered technique enables one to make scientifically defensible decisions in the face of severe uncertainty such as is found in many geologic problems. To demonstrate the applicability, we apply the technique to a CO2 leakage problem. The goal is to identify a safe injection rate that will not cause unacceptable environmental problems. The analyses take into account existing uncertainties in the form variables with known and unknown probabilistic distributions.