Handbook of Uncertainty Quantification pp 1361-1399 | Cite as

# Decision Analytic and Bayesian Uncertainty Quantification for Decision Support

## Abstract

This essay introduces probability in support of decision-making, as a state of mind and not of things. Probability provides a framework for reasoning coherently about uncertainty. According to Cox’s theorem, it is the *only* way to reason coherently about uncertainty. Probability summarizes states of information. A basic desideratum is that states of information judged equivalent should lead to the same probability distributions. Some widely used probabilistic models have both sufficient statistics and maximum entropy characterizations. In practice, outside of certain physics and engineering applications, human judgment is usually needed to quantify uncertainty as probabilities. Reality is highly complex, but one can test judgments against what is known, drawing upon many specialized areas of human knowledge. Sensitivity analysis can evaluate the importance of multiple uncertainties in a decision context. When the choice between alternatives is close, what is the value of further information (VOI)? Important concepts discussed in this chapter are the expected value of perfect information and the expected value of further experimental testing.

Practical application is illustrated in two case studies. The first involves assessing the probability for replication of a terrestrial microbe on Mars, in the decision context of a constraint on planetary exploration. The second involves weather modification of hurricanes/typhoons: whether to deploy this technology to reduce damage from hurricanes impacting US coastal areas and valuing experimental testing offshore. The decision context is that of a natural disaster turned political by deployment of new technology where such deployment might be followed by a reduction, or by an increase, in adverse impacts, compared to not deploying the technology.

Decision support should be viewed as an iterative process of working with those with decision responsibility and with experts who are the best available sources of information. The decision support process includes characterizing uncertainties and values for outcomes in the context of a choice among decision alternatives. Sensitivity analysis and VOI can give insight on whether to act now or to seek more information and more refined analysis. In a public policy decision context, the process can facilitate stakeholders sharing and critiquing information as the basis for characterizing uncertainties and learning which uncertainties and value judgments are most important for decisions.

## Keywords

Bayes’ theorem Decision analysis Value of information## Notes

### Acknowledgements

This chapter draws from presentations on the two case studies at the November 2014 meeting of INFORMS (Institute for Operations Research and the Management Sciences) in San Francisco, on the occasion of the 50th Anniversary of Decision Analysis honoring its founders, Stanford University Professor Ronald Howard and Harvard University Professor Howard Raiffa. The author wishes to acknowledge the collaboration with colleagues in the two case studies, and appreciation to Tony Cox for detailed comments on the initial draft of this chapter. The author expresses gratitude to these and other colleagues over 50 years in decision and risk analysis for the many insights learned about assessing uncertainties and values in a decision support context.

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