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基于序贯性蒙特卡洛采样器的并行采样方法

吴江琦1, 李敬来2   

  1. 1. SJTU, 上海交通大学数学科学学院, 上海 200240;
    2. UoB, 伯明翰大学 数学学院, 英国 B15 2TT
  • 收稿日期:2021-04-10 发布日期:2022-09-09
  • 基金资助:
    国家自然科学基金(11771289)资助.

吴江琦, 李敬来. 基于序贯性蒙特卡洛采样器的并行采样方法[J]. 数值计算与计算机应用, 2022, 43(3): 281-294.

Wu Jiangqi, Li Jinglai. A PARALLEL SAMPLING METHOD BASED ON SEQUENTIAL MONTE CARLO SAMPLER[J]. Journal on Numerica Methods and Computer Applications, 2022, 43(3): 281-294.

A PARALLEL SAMPLING METHOD BASED ON SEQUENTIAL MONTE CARLO SAMPLER

Wu Jiangqi1, Li Jinglai2   

  1. 1. SJTU, School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China;
    2. UoB, School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK
  • Received:2021-04-10 Published:2022-09-09
许多科学和工程领域的问题经常会需要我们从一个给定分布中产生随机样本.在贝叶斯推断中,从后验分布中抽取样本是此类问题的一个代表性应用实例.常用的马尔可夫链蒙特卡洛方法比较难以发挥并行计算的优势,因此为了解决这个问题,在本文中我们提出了使用序贯性蒙特卡洛采样器作为在并行计算框架下对马尔可夫链蒙特卡洛方法的一个替代工具.具体而言,我们提出了序贯性蒙特卡洛采样器中两个不同的正向提议分布:高斯随机游动和朗之万正向核,并给出了相应的反向提议分布.结合数值试验,我们展示了在并行计算的条件下,序贯性蒙特卡洛采样器相比于多链条马尔可夫链蒙特卡洛方法,在计算效率上有明显的提升.
Many scientific and engineering applications require to draw samples from a given distribution. A typical example is Bayesian inference where the one needs to draw samples from the posterior distribution. The often used Markov chain Monte Carlo methods are not suitable in the parallel computing situation. In this work we propose to use the sequential Monte Carlo sampler to solve such problems. In particular we propose two forward proposal distributions:a Gaussian random walk proposal and a Langevin proposal, and we also derive the corresponding backward proposals. With numerical examples, we demonstrate that the sequential Monte Carlo sampler has a better performance than the multi-chain Markov chain Monte Carlo methods.

MR(2010)主题分类: 

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