Bayesian methods in risk assessment

Empirical data are almost always lacking in real-world risk analyses. In fact, some risk analysis problems try to forecast what risks may be associated with situations that are, at the time of the assessment, only hypothetical. It may therefore be impractical, unethical, or even impossible to collect relevant empirical data. To make matters worse for the analyst, the situations of concern in risk analyses are often novel and have never been studied before. This means that scientific understanding of the underlying processes may itself be in doubt. Because of these facts, computational problems in risk analysis are often characterized by three issues: (i) there may be little or even no empirical data available for some variables, (ii) it may be necessary to employ subjective information from the analyst's judgment or expert opinion, and (iii) uncertainty about the mathematical model used in the assessment may be substantial. These issues complicate and impede the assessment, and they can call into question any conclusions or inferences drawn from the assessment. A Bayesian approach might be useful in addressing these issues. By design, Bayesian methods natively consider the uncertainty associated with the parameters of a probability model (even if those uncertain parameters are believed to be fixed numbers). Bayesian methods are often recommended as the proper way to make formal use of subjective information such as expert opinion and personal judgments or beliefs of an analyst. An important advantage of Bayesian methods, unlike frequentist methods with which they are often contrasted, is that they can always yield a precise answer, even when no data at all are available. Finally, recent Bayesian literature has focused on the potential significance of model uncertainty and how it can be incorporated into quantitative analyses. This report reviews the technical and interpretational limitations of using Bayesian methods in risk and uncertainty analyses. It argues that the methods produce sometimes extreme overconfidence and arbitrariness in the computed answers. These deficiencies are illustrated using various computational problems including projecting uncertainty through predictive expressions, analyzing sample data, updating estimates based on new information, and accounting for model uncertainty. There are three main causes of this overconfidence and arbitrariness: (1) misuse of equiprobability as a model for incertitude, (2) overuse of averaging to aggregate information, which tends to erase variation rather than propagate it, and (3) reliance on precise values and particular distributions when available information does not justify such specificity. Frequentists use …