在等级 Pitman-Yor 过程中完美采样后部
Sergio Bacallado1, Stefano Favaro2,3, Samuel Power1
1Statistical Laboratory, University of Cambridge.
Bayesian analysis
|October 25, 2023
概括
本研究介绍了对等级Pitman-Yor过程模型的完美采样器,改进了复杂统计分布的模拟. 新的算法为贝叶斯推理和各种领域的数据分析提供了重大进步.
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:
- 层次化的Pitman-Yor过程模型对于分析复杂的数据结构至关重要.
- 这些模型的当前蒙特卡洛方法,使用中国餐厅特许经营权 (CRF) 表示,需要对辅助变量进行计算密集的马尔科夫链蒙特卡洛 (MCMC) 采样.
- 对后部分布的有效模拟仍然是一个挑战.
研究的目的:
- 开发一个完美的采样器,用于中国餐厅特许经营 (CRF) 中的潜在变量,以表示层次化的皮特曼-约尔过程.
- 评估拟议的完美采样器的性能和计算效率.
- 将新算法与现有方法比较,例如吉布斯采样和公正的蒙特卡洛估计.
主要方法:
- 基于普罗普-威尔逊算法的CRF隐性变量完美采样器的开发.
- 进行了广泛的模拟,以评估完美的采样器的平均运行时间.
- 与Gibbs采样和Glynn和Rhee的不偏见的蒙特卡洛估计程序进行比较分析.
主要成果:
- 开发的完美采样器有效地为层次化的皮特曼-约尔过程采样潜变量.
- 模拟结果表明,取样器的运行时间显著,取决于参数,呈现急剧的过渡.
- 完美的采样器显示与现有方法相比具有竞争力或优异的性能.
结论:
- 完美的采样器提供了一个有价值的工具,可以从层次化的皮特曼-约尔过程模型进行准确和高效的模拟.
- 算法的性能特征为贝叶斯推理的计算挑战提供了洞察力.
- 该方法适用于现实世界的问题,正如其在微生物基因组学中的应用所说明的那样.
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