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The consideration of a maxim and a statement, both of which are concerned with “hedging” on the part of meteorologists who prepare probability forecasts, leads to the identification of a property which all proper scoring systems for such forecasts should possess. A scoring system, to be proper, should encourage the meteorologist to make his probabilities correspond to his true beliefs. The conditions which a proper scoring system must satisfy are formulated in mathematical terms. Several existing scoring systems are examined to ascertain whether or not the systems are proper.
Murphy et al. (Fri,) studied this question.