杰弗里斯-林德利悖论的历史和性质
Eric-Jan Wagenmakers1, Alexander Ly2
1University of Amsterdam, Amsterdam, The Netherlands.
概括
杰弗里斯-林德利悖论揭示了贝叶斯和频率论假设测试之间的统计推理中的核心冲突. 这种悖论凸显了对零点假设的证据对于理解统计学意义至关重要.
科学领域:
- 统计推理 统计推理
- 假设测试 假设测试
- 贝叶斯统计学贝叶斯统计学
- 频率主义统计 频率主义统计
背景情况:
- 杰弗里斯-林德利悖论强调了贝叶斯式和频率主义者对假设测试方法之间的根本分歧.
- 与常见的理解相反,这种悖论是哈罗德·杰弗里斯在20世纪30年代开发的贝叶斯方法论的核心.
研究的目的:
- 概括杰弗里斯对悖论的早期研究,并阐明他为包含术语的推理.
- 澄清先前分布在统计推理和假设测试中的作用.
- 为了证明悖论在不同统计框架中的普遍适用性.
主要方法:
- 回顾哈罗德·杰弗里斯关于杰弗里斯-林德利悖论的基础工作.
- 在贝叶斯假设测试中分析先前分布的作用.
- 关于悖论的频率主义者和贝叶斯版本的介绍.
- 证明在点假设上先前的质量对于悖论不是必不可少的.
主要成果:
- 对零点假设 () 的证据与相称,挑战恒定误差值.
- 之前的分布在选择中隐含正确,使得小参数值在下令人惊.
- 这种悖论并不取决于将先前的质量分配给点假设.
结论:
- 杰弗里斯-林德利悖论是统计推理中的一个关键概念,它影响了贝叶斯和频率论假设测试.
- 了解先前分布的作用和证据的缩放是解决悖论的关键.
- 这种悖论的含义超越了点假设,可以在贝叶斯和频率主义环境中证明.
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