Probability Bounds Analysis as a General Approach to Sensitivity Analysis in Decision Making Under Uncertainty

Abstract

Engineers often perform sensitivity analyses to explore how changes in the inputs of a physical process or a model affect the outputs. This type of exploration is also important for the decision-making process. Specifically, engineers may want to explore whether the available information is sufficient to make a robust decision, or whether there exists sufficient uncertainty-i.e., lack of information-that the optimal solution to the decision problem is unclear, in which case it can be said to be sensitive to information state. In this paper, it is shown that an existing method for modeling and propagating uncertainty, called Probability Bounds Analysis (PBA), actually provides a general approach for exploring the global sensitivity of a decision problem that involves both probabilistic and imprecise information. Specifically, it is shown that PBA conceptually generalizes an approach to sensitivity analysis suggested in the area of decision analysis. The global nature of the analysis theoretically guarantees that the decision maker will identify any sensitivity in the formulated problem and information state. However, a tradeoff is made in the numerical implementation of PBA; a particular existing implementation that preserves the guarantee of identifying existing sensitivity is overly conservative and can result in “false alarms.” The use of interval arithmetic in sensitivity analysis is discussed, and additional advantages and limitations of PBA as a sensitivity analysis tool are identified.

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