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Logic Tree Branch Weights And Probabilities: Summing Up To One Is Not Enough

Frank Scherbaum, Nicolas M. Kuehn

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Logic trees have become the most popular tool for the quantification of epistemic uncertainties in probabilistic seismic hazard assessment (PSHA). In a logic-tree framework, epistemic uncertainty is expressed in a set of branch weights, by which an expert or an expert group assigns degree-of-belief values to the applicability of the corresponding branch models. Despite the popularity of logic-trees, however, one finds surprisingly few clear commitments to what logic-tree branch weights are assumed to be (even by hazard analysts designing logic trees). In the present paper we argue that it is important for hazard analysts to accept the probabilistic framework from the beginning for assigning logic-tree branch weights. In other words, to accept that logic-tree branch weights are probabilities in the axiomatic sense, independent of one's preference for the philosophical interpretation of probabilities. We demonstrate that interpreting logic-tree branch weights merely as a numerical measure of “model quality,” which are then subsequently normalized to sum up to unity, will with increasing number of models inevitably lead to an apparent insensitivity of hazard curves on the logic-tree branch weights, which may even be mistaken for robustness of the results. Finally, we argue that assigning logic-tree branch weights in a sequential fashion may improve their logical consistency.