On Testing the Validity of Sequential Probability Forecasts
On Testing the Validity of Sequential Probability Forecasts
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检验序贯概率预测的有效性
DOI：
10.1080/01621459.1993.10594328
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发表时间：
1993
影响因子：
3.7
通讯作者：
A. Dawid
中科院分区：
文献类型：
--
作者：
F. Seillier;A. Dawid
按顺序观察事件，并在每个阶段评估下一个事件的概率。我们考虑概率预测序列和结果序列之间的关系。我们认为，预测可能会被认为是“经验有效的”，当这两个序列是一致的共同的联合分布的事件。为了帮助评估有效性，我们引入了各种测试统计量，以自然的方式，根据所获得的结果来衡量概率预测的经验表现。结果表明，在预测有效性的零假设下，这样的统计量，经过适当的归一化，有一个标准的正常（或卡方）分布，几乎不管共同的联合分布应该是两个序列的基础。
Events are observed sequentially, and at each stage a probability for the next event is assessed. We consider the relationship between the sequence of probability forecasts and the sequence of outcomes. We argue that the forecasts may be considered “empirically valid” when both these sequences are consistent with a common joint distribution for the events. To aid in assessing validity, we introduce various test statistics that measure, in a natural way, the empirical performance of the probability forecasts in the light of the outcomes obtained. It is shown that under the null hypothesis of forecast validity, such statistics will, after suitable normalization, have a Standard normal (or chi-squared) distribution, virtually irrespective of the common joint distribution supposed to underlie both sequences.