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
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