常见假设测试的经验贝叶斯因子
1Department of Population Health Sciences, University of Leicester, Leicester, United Kingdom.
PloS one
|February 22, 2024
概括
这项研究引入了一个经验性的贝叶斯因子,以解决解释复合假设的模糊先前知识的挑战. 它为统计证据的解释提供了一个客观的框架,弥合了贝叶斯式和频率主义的方法.
科学领域:
- 统计 统计 统计 统计
- 统计推理 统计推理
- 贝叶斯统计学 贝叶斯统计学
背景情况:
- 贝叶斯因子在复合假设的模糊事先知识中扎,因为不恰当和客观的先验的局限性.
- 现有的方法可能会产生主观不合理的结果或难以解释.
- 需要强大的方法来量化统计假设测试中的证据.
研究的目的:
- 提出和评估后端贝叶斯因子作为一种解决方案,用于编码复合假设测试中模糊的先前知识.
- 开发一个经过调整的经验贝叶斯因子,与适当的贝叶斯因子相比较.
- 建立一个客观的框架来解释统计证据,并调和贝叶斯和频率主义的方法.
主要方法:
- 重温后面贝叶斯因子,使用当前数据的后面分布来计算贝叶斯因子.
- 调整后面的贝叶斯因子,以减轻对适当的贝叶斯因子进行校准时的偏差.
- 开发基于测试的经验贝叶斯因子用于标准统计测试,并扩展到多个测试场景.
- 提出基于P值和对数解释尺度的近似经验贝叶斯因子.
主要成果:
- 调整后部贝叶斯因子提供了一个可解释的尺度,与正确的贝叶斯因子相比较.
- 对于常规的正常模型,日志尺度中的偏差是参数数量的一半.
- 经验贝叶斯因子与广泛适用的信息标准 (WAIC) 有着密切的关系.
- 对于只有P值可用的情况,提出了大约10p的经验贝叶斯因子.
结论:
- 经验贝叶斯因子提供了一种可行的方法来处理复合假设测试中模糊的先前知识.
- 拟议的解释尺度 (日志基础3.73) 提供了统计证据强度的客观衡量标准.
- 这种框架促进了贝叶斯式和频率主义统计推理之间的妥协,提高了实际适用性.
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