Does Waste Recycling Really Improve the Multi-Proposal Metropolis–Hastings algorithm? an Analysis Based on Control Variates
Does Waste Recycling Really Improve the Multi-Proposal Metropolis–Hastings algorithm? an Analysis Based on Control Variates
复制标题
基于控制变量的分析，废物回收真的改进了多提案 Metropolis-Hastings 算法吗？
DOI：
10.1239/jap/1261670681
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发表时间：
2009
影响因子：
1
通讯作者：
B. Jourdain
中科院分区：
文献类型：
--
作者：
Jean;B. Jourdain
物理学家引入的废物回收蒙特卡罗（WRMC）算法是（多提案）Metropolis-Hastings算法的修改版，它利用了经验平均值中的所有提案，而标准（多提案）Metropolis-Hastings算法仅使用已接受的提案。在本文中，我们将 WRMC 算法扩展到通用控制变量技术，并根据渐近方差展示控制变量的最优选择。我们还给出了一个例子，表明与物理学家的直觉相反，WRMC 算法可以具有比 Metropolis-Hastings 算法更大的渐近方差。然而，在称为玻尔兹曼算法的 Metropolis-Hastings 算法的特殊情况下，我们证明 WRMC 算法渐近优于 Metropolis-Hastings 算法。最后一个属性对于多提案 Metropolis-Hastings 算法也适用。在最后一个框架中，我们考虑 WRMC 的线性参数泛化，并使用建议提出显式最优参数的估计器。
The waste-recycling Monte Carlo (WRMC) algorithm introduced by physicists is a modification of the (multi-proposal) Metropolis–Hastings algorithm, which makes use of all the proposals in the empirical mean, whereas the standard (multi-proposal) Metropolis–Hastings algorithm uses only the accepted proposals. In this paper we extend the WRMC algorithm to a general control variate technique and exhibit the optimal choice of the control variate in terms of the asymptotic variance. We also give an example which shows that, in contradiction to the intuition of physicists, the WRMC algorithm can have an asymptotic variance larger than that of the Metropolis–Hastings algorithm. However, in the particular case of the Metropolis–Hastings algorithm called the Boltzmann algorithm, we prove that the WRMC algorithm is asymptotically better than the Metropolis–Hastings algorithm. This last property is also true for the multi-proposal Metropolis–Hastings algorithm. In this last framework we consider a linear parametric generalization of WRMC, and we propose an estimator of the explicit optimal parameter using the proposals.