实证贝叶斯方法,证据主义,以及它们所起的推理作用
Samidha Shetty1, Gordon Brittan2, Prasanta S Bandyopadhyay2
1Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717, USA.
Entropy (Basel, Switzerland)
|October 25, 2024
概括
基于贝叶斯经验的方法 (EBM) 为贝叶斯统计提供了一个客观的方法. 本研究将EBM与主观贝叶斯主义和证据主义进行比较,强调它们在统计推断中的独特作用.
科学领域:
- 统计 统计 统计 统计
- 科学哲学的哲学科学哲学
背景情况:
- 基于贝叶斯的经验方法 (EBM) 是客观贝叶斯主义 (OB) 中一个不断增长的方法.
- 布拉德利·埃弗朗是EBM的主要支持者.
研究的目的:
- 描述和说明EBM的特点.
- 将EBM与主观贝叶斯主义 (SB) 和证据主义进行比较.
- 为了澄清统计范式中确认和证据之间的区别.
主要方法:
- 图表示例说明了EBM的形式特征.
- 基于它们的基础哲学,对EBM,SB和证据主义进行比较分析.
- 确认/证据区分的应用在统计学悖论上.
主要成果:
- 通过说明性示例展示了EBM的核心特征.
- 在确认和证据之间制定和应用了细微的区别.
- 基率谬论和波普尔的理想证据悖论被用来证明这种区别.
结论:
- 每一个统计范式 (EBM,SB,证据主义) 都起着基本的作用.
- 对统计推理的全面理解需要整合所有范式的见解.
- 精细的哲学观点对于先进的统计推理是必不可少的.
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