We introduce a new rule for Bayesian updating of imprecise priors that are equivalent to classes of precise priors. The rule combines (a modified version of) Walley's generalized Bayes rule with a filter based on prior quantiles of the observational evidence. We introduce this new "quantile-filtered Bayesian update rule" because in many situations, Walley's generalized Bayes rule reveals counter-intuitively noninformative, dilation-type results while an alternative rule, the maximum likelihood update rule after Gilboa and Schmeidler, is not robust against imprecise priors that are contaminated with spurious information. Our new quantile-based update rule addresses the former issue and fully resolves the latter. We demonstrate the capabilities of the new rule by updating a variant of an imprecise prior that was recently further motivated by expert interviews with climate, ecosystem and economic modelers: Tchen's "correlation class" of precise priors with arbitrary correlation structure, however, prescribed precise marginals. Finally for a stylized insurance situation we demonstrate that according to our new update rule a subset of clients would be insured that is disregarded under standard generalized Bayesian updating.ized Bayesian updating.
Keywords. Bayesian updating, Generalized Bayes
Paper Download
The paper is availabe in the following formats:
Authors addresses:
PO Box 60 12 03
D-14412 Potsdam
E-mail addresses:
Hermann Held | held@pik-potsdam.de |