多项试点贝叶斯增量回归树的增量采样器
Yizhen Xu1, Joseph Hogan2, Michael Daniels3
1Division of Biostatistics, University of Utah.
概括
这项研究引入了多项试验贝叶斯增量回归树 (MPBART) 的新方法,可以提高马尔科夫链蒙特卡洛 (MCMC) 趋同和预测准确性. 提出的方法为现有的MPBART方法提供了更有效的替代方案.
科学领域:
- 统计数据
- 机器学习
- 计算统计
背景情况:
- 基于多变量高斯潜伏结构的多项试验 (MNP) 框架,通过不假设独立的替代方案,提供了多项后勤模型的优势.
- 贝叶斯增量回归树 (BART) 已通过多项试验器BART (MPBART) 集成到MNP中,使用崩的吉布斯采样器进行后端采样.
- 崩的吉布斯采样器的效率取决于简单的采样步骤和快速的马尔科夫链融合,这可能受到后置树的随机搜索的复杂性所挑战.
研究的目的:
- 通过提出一个新的后部树采样策略来解决MPBART的计算挑战.
- 将拟议的方法与现有的MPBART方法进行比较,包括Kindo等. " (2016) 的增强参数空间采样和Sparapani等人. " (2021) 的条件概率规范.
- 在马尔科夫链蒙特卡洛 (MCMC) 趋同和后期预测准确性方面评估拟议方法的性能.
主要方法:
- 这项研究建议在受限参数空间的条件下采样后层树,与Kindo等人形成鲜明对比. 使用增强参数空间的方法.
- 与Sparapani等人进行了比较. " (2021) 方法,该方法使用条件概率来建模多项分布.
- 使用MCMC融合诊断和后预测准确度指标来评估性能.
主要成果:
- 拟议的条件抽样方法显示了与条件概率方法相比的MCMC收率和后期预测精度.
- 这种新方法在MCMC收和预测准确性方面显著优于增强型树采样方法.
- 理论分析证实,拟议方法的混合率并不低于增强树样采样方法.
结论:
- 在MPBART中采样后层树的方法提供了更好的计算效率和预测性能.
- 这种方法为现有的MPBART方法提供了可行的替代方案,特别是优于依赖增强参数空间的方法.
- 这些发现表明,有条件的抽样策略可以在MNP框架内增强BART的实际应用.
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