Second-Order Probabilities and Strictly Proper Scoring Rules

Allan H. Murphy Dept. of Meteorology and Oceanography, University of Michigan, Ann Arbor

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Carl-Axel S. Staël von Holstein Dept. of Engineering-Economic Systems, Stanford University, Stanford, Calif.

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Abstract

Some forecasters apparently subscribe to a model of the subjective probability forecasting process in which their judgments are expressed in terms of “second-order” probabilities. First, we briefly consider the nature of these second-order probabilities and describe the second-order model, and then we demonstrate that strictly proper scoring rules encourage forecasters who subscribe to the second-order model to make their forecasts correspond to their expected judgments.

Abstract

Some forecasters apparently subscribe to a model of the subjective probability forecasting process in which their judgments are expressed in terms of “second-order” probabilities. First, we briefly consider the nature of these second-order probabilities and describe the second-order model, and then we demonstrate that strictly proper scoring rules encourage forecasters who subscribe to the second-order model to make their forecasts correspond to their expected judgments.

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