Confidence, Posterior Probability, and the Buehler Example
置信水平、后验概率与Buehler例子AI 解读 ↓
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置信水平、后验概率与Buehler例子
- 研究问题
- 在某些模型中置信水平可对应客观后验概率时，如何评价以投注策略为依据、质疑这种概率解释的例子？
- 方法与思路
- 作者批评常用的投注评价方式，提出修改后的平衡评价程序，并用该程序重新考察Buehler及Buehler–Feddersen策略。
- 材料陈述的贡献
- 摘要称这些策略在平衡评价下会面临较大损失，因而不足以支持所讨论的、针对客观后验概率及置信水平的反对意见。
- 阅读关注点
- 应核对平衡评价程序的定义、投注规则及损失如何计算，并区分特定模型中的概率对应与一般置信区间的解释。
- 阅读边界
- 仅据版本未注明的OpenAlex摘要；相关模型、评价规则和论证细节未提供，不能据此普遍赋予置信水平后验概率含义。
原文摘要
A confidence level is sometimes treated as a probability and accordingly given substantial "confidence." And with certain statistical models a confidence level can also be an objective posterior probability (Fraser and MacKay, 1975). An instance involving such a probability with a binary error was discussed at the Symposium on Foundations of Statistical Inference, University of Waterloo, 1970 (Godambe and Sprott, 1971, page 49). An example by Buehler (ibid., page 337) of a betting strategy and a generalization by Rubin (ibid., page 340) were subsequently presented to support a claim against the objective posterior probability and against too much "confidence." The ordinary Student confidence interval in appropriate contexts is also an objective posterior probability interval. An example by Buehler and Feddersen (1963) has been cited frequently as evidence against the validity of the objective posterior probability and against too much "confidence." This note censures the common procedure of assessment in terms of betting strategies and introduces a modified balanced procedure for such betting assessments. When assessed by this balanced procedure the Buehler and Buehler-Feddersen strategies are faced with large losses and thus do not support claims against the objective posteriors and confidence levels.