混合先验的统计学意义测试:贝叶斯和频率分析的综合分析
Jakob Robnik1, Uroš Seljak1,2
1Physics Department, University of California at Berkeley, Berkeley, CA 94720, USA.
Entropy (Basel, Switzerland)
|July 8, 2023
概括
结合贝叶斯式和频率主义假设测试,在先前信息不完整时,可以提高统计能力. 这种方法在频率分析中使用贝叶斯因子,增强了对标准方法的力量,特别是在复杂的场景中,如系外行星检测.
科学领域:
- 统计 统计 统计 统计
- 天体物理学 天体物理学
- 统计力学 统计力学
背景情况:
- 假设测试通常涉及混合先验,其中一些参数具有信息先验,而另一些则没有.
- 贝叶斯方法使用贝叶斯因子,结合奥卡姆的剃须刀,而频率测试则依赖假阳性率,在先验不完整时对先前选择不那么敏感.
- 结合这两种方法提供了一个强大的方法,用于测试假设与部分的先前信息.
研究的目的:
- 为假设测试提出并验证一种混合方法,该方法利用贝叶斯式和频率主义方法.
- 证明使用贝叶斯因子作为频率分析中的测试统计数据可以提高统计能力,特别是在混合先验的情况下.
- 为这种混合方法开发一种分析形式主义,将现有定理概括,避免计算上昂贵的模拟.
主要方法:
- 该研究将贝叶斯因子 (贝叶斯) 与频率主义假设测试框架相结合.
- 它显示了贝叶斯因子的最大概率比率测试统计数据与非信息化的杰弗里先验的等价性.
- 开发了一个分析形式主义,将威尔克斯定理概括起来,适用于具有部分先前信息的场景,避免模拟.
主要成果:
- 与标准的最大概率测试相比,混合先验在频率分析中增加了统计能力.
- 开发的分析形式主义复制了线性模型和周期图中p值的现有表达式,在特定的限制内.
- 形式主义准确地复制来自数值模拟的p值在一个系外行星过境检测示例中,即使是高倍率.
结论:
- 将贝叶斯贝叶斯因子与频率分析相结合,为假设测试提供了一个强大的工具,特别是在不完整的先前知识的情况下.
- 开发的分析形式主义为复杂问题中的统计推理提供了一种计算效率高,准确的方法.
- 该研究提供了一种新的解释,将假设测试 (p值,贝叶斯因子) 与能量和竞争等统计力学概念联系起来.
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