论文标题
多级延迟接受MCMC
Multilevel Delayed Acceptance MCMC
论文作者
论文摘要
我们开发了一种新颖的马尔可夫链蒙特卡洛（MCMC）方法，该方法利用了增加复杂性的模型的层次结构，以有效地从非标准化靶标分布中生成样品。从广义上讲，该方法重写了Dodwell等人的多级MCMC方法。 （2015年）就Christen＆Fox的延迟接受（DA）（2005）而言。特别是，DA扩展到使用任意深度模型的层次结构，并允许任意长度的子链。我们表明该算法满足详细的平衡，因此对于目标分布来说是奇特的。此外，得出了利用多个级别和子链的多级方差降低，并且开发了对粗级偏差的自适应多级校正。提出了贝叶斯逆问题的三个数值示例，这些示例证明了这些新方法的优势。该软件和示例可在PYMC3中找到。
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. (2015) in terms of the Delayed Acceptance (DA) MCMC of Christen & Fox (2005). In particular, DA 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, 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.
