Constrained noninformative priors, a type of maximum entropy prior, have recently become popular in the risk assessment community for representing uncertainty in a parameter value. In this approach, a best-estimate value is specified, which is taken to be a mean value. A distribution is then found which satisfies this mean constraint, but which is as close as possible otherwise (in the sense of Kullback-Leibler information) to the corresponding Jeffreys noninformative prior. This approach leads to a diffuse prior, which when combined with data in a process of Bayesian updating, produces a posterior that is influenced only weakly by the prior. Some applications (e.g., the SPAR-H method of human reliability analysis) do not use this distribution for updating data; rather, it is used to represent uncertainty in a human error probability. This type of application does not include analyst-to-analyst variability in deriving the mean constraint, and this variability can be substantial, thus producing a distribution that represents only a portion of the total uncertainty in the parameter of interest. The approach taken to this problem here is to model uncertainty hierarchically: Analyst-to-analyst variability in the mean constraint is modeled with a lognormal distribution, and Monte Carlo sampling is used to simulate the resulting posterior distribution, which provides a more complete representation of overall uncertainty, as variability in the mean constraint is included in the resulting distribution.
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