Median Aggregation of Distribution Functions
Median Aggregation of Distribution Functions
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DOI：
10.1287/deca.2013.0282
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发表时间：
2013-12-01
影响因子：
1.9
通讯作者：
Susel, Irving
中科院分区：
文献类型：
--
作者：
Hora, Stephen C.;Fransen, Benjamin R.;Susel, Irving
当从主题专家那里获得多个冗余的概率判断时，通常的做法是将他们不同的观点汇总到一个概率或分布中。虽然提出了许多数学聚合的方法，但没有一种方法得到普遍接受。最广泛使用的方法是简单的算术平均，它既有可取的性质也有不可取的性质。在这里，我们提出了一种基于变量固定值的中位数累积概率的聚合分布函数的替代方法。结果表明，在一定条件下，按中位数聚合累积概率等同于按分位数聚合累积概率。此外，当专家独立且校准良好时，中位数集合比平均概率集合具有更好的校准效果，并且当他们报告共同的位置尺度分布时，校准良好且独立的专家产生更清晰的集合分布。我们还比较了中位数聚合和分位数的平均聚合。
When multiple redundant probabilistic judgments are obtained from subject matter experts, it is common practice to aggregate their differing views into a single probability or distribution. Although many methods have been proposed for mathematical aggregation, no single procedure has gained universal acceptance. The most widely used procedure is simple arithmetic averaging, which has both desirable and undesirable properties. Here we propose an alternative for aggregating distribution functions that is based on the median cumulative probabilities at fixed values of the variable. It is shown that aggregating cumulative probabilities by medians is equivalent, under certain conditions, to aggregating quantiles. Moreover, the median aggregate has better calibration than mean aggregation of probabilities when the experts are independent and well calibrated and produces sharper aggregate distributions for well-calibrated and independent experts when they report a common location-scale distribution. We also compare median aggregation to mean aggregation of quantiles.