Persistent Experimenters, Stopping Rules, and Statistical Inference
Persistent Experimenters, Stopping Rules, and Statistical Inference
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持续的实验者、停止规则和统计推断
DOI：
10.1007/s10670-012-9388-1
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发表时间：
2013
期刊：
影响因子：
0.9
通讯作者：
K. Steele
中科院分区：
文献类型：
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作者：
K. Steele
本文认为，经典和贝叶斯统计之间的争论的一个关键点，是在检查所谓的“持久的实验者”-停止规则的问题，或者更准确地说，结果空间，以及它们对统计分析的影响。首先，给出了经典和贝叶斯统计检验的工作定义，这清楚地表明：（1）一旦记录了实验结果，其他可能的结果只对经典推理有影响，（2）当涉及到计划/选择检验时，完整的结果空间与经典和贝叶斯方法都相关。后一点被证明具有重要的影响。在这里，我们认为，它破坏了贝叶斯可能承认是一个令人信服的论点，反对他们的方法-贝叶斯冷漠持久的实验者和他们的可选停止规则。我们承认亲经典的“可选停止直觉”的初步呼吁，即使是那些通常有贝叶斯同情。然而，本文的最后一部分提供了三种错误理论，可以帮助贝叶斯解释他们推理中的明显异常。
This paper considers a key point of contention between classical and Bayesian statistics that is brought to the fore when examining so-called ‘persistent experimenters’—the issue of stopping rules, or more accurately, outcome spaces, and their influence on statistical analysis. First, a working definition of classical and Bayesian statistical tests is given, which makes clear that (1) once an experimental outcome is recorded, other possible outcomes matter only for classical inference, and (2) full outcome spaces are nevertheless relevant to both the classical and Bayesian approaches, when it comes to planning/choosing a test. The latter point is shown to have important repercussions. Here we argue that it undermines what Bayesians may admit to be a compelling argument against their approach—the Bayesian indifference to persistent experimenters and their optional stopping rules. We acknowledge the prima facie appeal of the pro-classical ‘optional stopping intuition’, even for those who ordinarily have Bayesian sympathies. The final section of the paper, however, provides three error theories that may assist a Bayesian in explaining away the apparent anomaly in their reasoning.