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Multilevel Delayed Acceptance MCMC

机译：多级延迟验收 MCMC

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摘要

We develop a novel Markov chain Monte Carlo (MCMC) method that exploits a hierarchy of models of increasing complexity to efficiently generate samples from an unnormalized target distribution. Broadly, the method rewrites the multilevel MCMC approach of Dodwell et al. [SIAM/ASA J. Uncertain. Quantif., 3 (2015), pp. 1075--1108] in terms of the delayed acceptance MCMC of Christen and Fox [J. Comput. Graph. Statist., 14 (2005), pp. 795--810]. In particular, delayed acceptance is extended to use a hierarchy of models of arbitrary depth and allow subchains of arbitrary length. We show that the algorithm satisfies detailed balance and hence is ergodic for the target distribution. Furthermore, multilevel variance reduction is derived that exploits the multiple levels and subchains, and an adaptive multilevel correction to coarse-level biases is developed. Three numerical examples of Bayesian inverse problems are presented that demonstrate the advantages of these novel methods. The software and examples are available in PyMC3.
机译：我们开发一种新颖的马尔可夫链蒙特卡罗(密度)方法利用的层次结构模型增加有效生成的复杂性非规范目标样本分布。广泛地说,重写的方法获得多层次模型方法Dodwell et al .(暹罗/ ASA J。不确定的。Christen延迟获得接受的条款和福克斯(J。页795 - 810)。延长使用的层次结构模型的任意深度和允许任意子链长度。详细的平衡,因此是遍历的目标分布。减少方差就是利用了派生多级子链,一个自适应多级修正coarse-level偏见发展。逆问题给出了证明这些新方法的优点。软件和例子PyMC3中可用。

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    M. B. Lykkegaard; T. J. Dodwell; C. FoxG. MingasR. Scheichl;

  • 作者单位

    Centre for Water Systems and Institute for Data Science and AI University of Exeter, Exeter EX4 4QF, UK;

    Alan Turing Institute and Institute for Data Science and AI, University of Exeter, Exeter EX4 4QF, UK;

    Department of Physics, University of Otago, Dunedin 9016, New ZealandAlan Turing Institute, British Library, 96 Euston Road, London NW1 2DB, UKInstitute for Applied Mathematics and Interdisciplinary Center for Scientific Computing, Heidelberg University, 69120 Heidelberg, Germany;

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  • 正文语种 英语
  • 中图分类 计量学;
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