贝叶斯趋势过通过近接马尔科夫链蒙特卡洛
Qiang Heng1, Hua Zhou2, Eric C Chi3
1Department of Statistics, North Carolina State University.
概括
本研究介绍了近接马尔科夫链蒙特卡洛 (MCMC) 的表征先验,自动化调整参数选择. 这种新的贝叶斯方法为复杂的统计建模提供了一种无调整的方法.
科学领域:
- 贝叶斯统计学 贝叶斯统计学
- 凸起式优化的优化
- 计算统计的计算统计.
背景情况:
- 靠近的马尔科夫链蒙特卡罗 (MCMC) 集成了贝叶斯计算和凸优化.
- 现有的近似MCMC方法需要预先指定的超参数和规范化参数.
- 在贝叶斯统计学中,不可差别的先验越来越多地被使用.
研究的目的:
- 通过引入一种新型的不可区分的priors类别来扩展近接MCMC:表写priors.
- 为自动调整参数选择开发无调整的近接MCMC方法.
- 将新方法应用于趋势过,将其从非参数设置转移到参数设置.
主要方法:
- 引入了表述式先,作为一种新的不可区分的先类.
- 利用莫罗-约西达的信封来近似不平滑的后部术语.
- 采用哈密尔顿式蒙特卡洛,一个基于梯度的MCMC采样器.
- 将框架应用于趋势过,用于后端中位数和不确定性量化.
主要成果:
- 拟议的方法以数据驱动的方式自动选择规范化参数.
- 该方法允许在贝叶斯框架内同时校准平均值,规模和规范化参数.
- 与传统的近接MCMC技术相比,该方法表现出一种无调的特性.
- 成功提供后部中位匹配和可信的间隔,用于趋势过.
结论:
- 这种新型的前面标记方法通过减少手动参数调整的需要,显著提升了近接MCMC.
- 这项工作提供了一个强大的和自动化的贝叶斯框架,用于涉及非可区分先验的统计建模.
- 该方法为分析数据提供了强大的工具,特别是在趋势过等设置中,内置不确定性估计.
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