齐格扎格路径连接了两个蒙特卡洛采样器:哈密尔顿对应的一个断片决定性马尔科夫过程的哈密尔顿对应
Akihiko Nishimura1, Zhenyu Zhang2, Marc A Suchard3
1Department of Biostatistics, Bloomberg School of Public Health, Johns Hopkins University.
Journal of the American Statistical Association
|August 11, 2025
概括
我们发现了哈密尔顿式齐克扎克和马科维式齐克扎克采样器之间的联系,用于贝叶斯计算. 通过使用动量信息,哈密尔顿式齐克扎克可以更好地探索复杂的分布,特别是与相关的参数.
科学领域:
- 计算统计学 计算统计学
- 贝叶斯的推理是贝叶斯的推理.
- 马尔科夫链 蒙特卡洛方法
背景情况:
- 断片决定性的马尔科夫过程采样器,就像齐克萨克一样,由于其不可逆转性,对贝叶斯后置计算有价值.
- 汉密尔顿蒙特卡洛 (HMC) 是一个最先进的采样器,它使用虚构的动量来导航复杂的概率分布.
研究的目的:
- 为了建立一个理论上的联系,在齐克扎格采样器和哈密尔顿蒙特卡罗的一个变体.
- 调查哈密尔顿曲线在探索复杂的目标分布中的性能,特别是那些具有高度相关的参数的目标分布.
主要方法:
- 使用拉普拉斯分布的动量开发了哈密尔顿式蒙特卡洛的变体,称为哈密尔顿式齐克扎克.
- 分析了哈密尔顿曲线的动态,并注意到它在位置-速度空间中的非马科维特性质,因为动量编码了过去的信息.
- 证明了哈密尔顿式齐克扎克与其马科维亚式对应在频繁的动量补充的极限内趋同.
主要成果:
- 证明哈密尔顿式的曲可以通过保留全部动量信息来抑制马可维式的曲的扩散行为.
- 经验性地比较了哈密尔顿式的齐克扎克和马可维式的齐克扎克在高维的截断的多变量高斯式上.
- 将采样器应用于来自贝叶斯系遗传学多变量试验模型的11235维目标分布的HIV数据.
结论:
- 哈密尔顿式齐克扎克比马科维亚式齐克扎克更好地探索具有高度相关性参数的目标分布.
- 理论见解表明,哈密尔顿式的齐克扎克是复杂贝叶斯后置计算的一个有前途的工具.
- 这项研究证实了哈密尔顿式齐克萨克在大规模,高维问题中的实际实用性.
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