Empirical Evaluation of Prior Beliefs About Frequencies: Methodology and a Case Study in Congenital Heart Disease
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频率先验信念的经验评估：方法与先天性心脏病案例
- 研究问题
- 随着离散变量样本逐步到来，如何比较专家对其分布的原始先验判断与观测数据，并及时发现不合适的主观概率输入？
- 方法与思路
- 作者讨论非序贯与序贯的贝叶斯因子和显著性检验，将其联系于观测数据预测概率的对数标准化，并构造贝叶斯差异统计量。
- 材料陈述的贡献
- 摘要称，该统计量提供依据数据折减专家判断的正式方式；先天性心脏病案例中判断总体较好，并建议自动监测与适应。
- 阅读关注点
- 应核对差异统计量的定义、不同标准化的解释、序贯检验规则及折减机制，并查看专家判断质量的具体评估依据。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；摘要未说明序贯检验的校准、折减规则和案例数值，不能据此判断普遍适用性。
原文摘要
We consider the problem of critiquing prior beliefs concerning the distribution of a discrete random variable in the light of a sequentially obtained sample. A topical application concerns a probabilistic expert system for the diagnosis of congenital heart disease, which requires specification of a large number of conditional probabilities that are initially imprecisely estimated by a suitable “expert.” These prior beliefs may be formally updated as data become available, but it would seem essential to contrast the original expert assessments with the data obtained to quickly identify inappropriate subjective inputs. We consider both Bayes factor and significance testing techniques for such a prior/data comparison, both in nonsequential and sequential forms. The common basis as alternative standardizations of the logarithm of the predictive ordinate of the observed data is emphasised, and a Bayesian discrepancy statistic with a variety of interpretations provides a formal means of discounting the expert's judgments in the light of the data. The judgments are found to be of generally high quality, and procedures for automatic monitoring and adaptation are recommended.