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可扩展的实证贝叶斯推理和贝叶斯敏感性分析.

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概括
此摘要是机器生成的。

这项研究解决了用于估计先前分布的经验贝叶斯方法的挑战. 提出了一种新的马尔科夫链蒙特卡洛方法,用于准确和可扩展的估计,改进现有技术.

关键词:
贝叶斯模型选择选择的贝叶斯模型.多恩斯克级别的班级.马尔科夫连锁蒙特卡罗的蒙特卡罗是一个连锁城市.几何形状的形性.超参数选择的超参数选择再生模拟的再生模拟.

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科学领域:

  • 统计 统计 统计 统计
  • 计算统计学 计算统计学
  • 贝叶斯的推理是贝叶斯的推理.

背景情况:

  • 贝叶斯分析涉及观察依赖参数的数据,具有未知的先前分布.
  • 主观贝叶斯方法难以确定精确的先验,而经验贝叶斯则从数据中估计潜在分布.
  • 常见的经验贝叶斯方法最大限度地提高了边际概率,但分析评估通常是不可行的,现有的程序可能不准确或规模不佳.

研究的目的:

  • 审查和批评现有的关于在实证贝叶斯分布中估计潜在分布的文献.
  • 引入一种新的,通用的,并且在维度上可扩展的方法,用马尔科夫链蒙特卡洛 (MCMC) 来估计隐藏分布.
  • 证明拟议方法的实用性,以获得先前家族的点估计和置信区间.

主要方法:

  • 对当前实证贝叶斯估计技术的文献综述.
  • 基于马尔科夫链蒙特卡洛 (MCMC) 的新估计方法的开发.
  • 应用MCMC方法来推导后期预期和信心区间.

主要成果:

  • 现有的经验贝叶斯估计方法被发现要么不准确,要么在高维问题上计算效率低下.
  • 提出的基于MCMC的方法为估计潜分布提供了一个普遍适用的和可扩展的解决方案.
  • 该方法方便计算先前家族的点估计和全球有效的置信区间.

结论:

  • 开发的MCMC方法对经验贝叶斯估计的传统方法有显著的改进.
  • 该方法的通用性和可扩展性使其适用于广泛的统计问题.
  • 该方法提供了有价值的工具来描述预估先前分布中的不确定性.