Monte Carlo and Quasi-Monte Carlo Methods 2008
Monte Carlo and Quasi-Monte Carlo Methods 2008
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DOI：
10.1007/978-3-642-04107-5-3
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发表时间：
2009-11
期刊：
影响因子：
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通讯作者：
C. Andrieu;Arnaud Doucet;R. Holenstein
中科院分区：
文献类型：
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作者：
C. Andrieu;Arnaud Doucet;R. Holenstein
马尔可夫链蒙特卡罗（MCMC）和顺序蒙特卡罗（SMC）方法是两种最流行的算法，用于从一般的高维概率分布中采样。MCMC算法的理论收敛性在弱假设下是可以保证的，但当用于探索空间的建议分布选择不当和/或高度相关的变量独立更新时，它们的实际性能是非常不令人满意的。我们在这里展示了如何通过使用SMC技术系统地设计可能非常有效的MCMC高维提案分布。我们展示了这种新的方法如何使我们能够在复杂的情况下设计有效的MCMC算法。这是说明了一个问题的贝叶斯推理的随机动力学模型。
Markov Chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods are the two most popular classes of algorithms used to sample from general high-dimensional probability distributions. The theoretical convergence of MCMC algorithms is ensured under weak assumptions, but their practical performance is notoriously unsatisfactory when the proposal distributions used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show here how it is possible to systematically design potentially very efficient high-dimensional proposal distributions for MCMC by using SMC techniques. We demonstrate how this novel approach allows us to design effective MCMC algorithms in complex scenarios. This is illustrated by a problem of Bayesian inference for a stochastic kinetic model.