Adaptive multidimensional integration: VEGAS enhanced
Adaptive multidimensional integration: VEGAS enhanced
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DOI：
10.1016/j.jcp.2021.110386
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发表时间：
2021-05-04
影响因子：
4.1
通讯作者：
Lepage, G. Peter
中科院分区：
文献类型：
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作者：
Lepage, G. Peter
我们描述了一种新的算法，VEGAS+，自适应多维Monte Carlo积分。新算法在自适应重要性采样的基础上增加了第二种自适应策略，即自适应分层采样。VEGAS和VEGAS+对于具有大峰的被整合体都是有效的，但是VEGAS+对于具有多个峰的被整合体或与整合体积的对角线对齐的其他重要结构可以有效得多。我们给出了VEGAS+比VEGAS精确2- 19倍的例子。我们还展示了如何将联合收割机VEGAS+与其他积分器，如广泛使用的MISER算法，使新的混合积分器。对于不同类型的混合，我们展示了如何使用被积样本，使用MCMC或其他方法生成，优化VEGAS+集成之前。我们给出了一个例子，其中预处理的VEGAS+比没有预处理的VEGAS+效率高100倍以上。最后，我们给出的例子中，VEGAS+是超过10倍的效率为MCMC的贝叶斯积分与D = 3和21个参数。我们解释了为什么VEGAS+在解决小型和中型问题时往往优于MCMC。(C)2021爱思唯尔公司All rights reserved.
We describe a new algorithm, VEGAS+, for adaptive multidimensional Monte Carlo integration. The new algorithm adds a second adaptive strategy, adaptive stratified sampling, to the adaptive importance sampling that is the basis for its widely used predecessor VEGAS. Both VEGAS and VEGAS+ are effective for integrands with large peaks, but VEGAS+ can be much more effective for integrands with multiple peaks or other significant structures aligned with diagonals of the integration volume. We give examples where VEGAS+ is 2-19x more accurate than VEGAS. We also show how to combine VEGAS+ with other integrators, such as the widely available MISER algorithm, to make new hybrid integrators. For a different kind of hybrid, we show how to use integrand samples, generated using MCMC or other methods, to optimize VEGAS+ before integrating. We give an example where preconditioned VEGAS+ is more than 100x as efficient as VEGAS+ without preconditioning. Finally, we give examples where VEGAS+ is more than 10x as efficient as MCMC for Bayesian integrals with D = 3 and 21 parameters. We explain why VEGAS+ will often outperform MCMC for small and moderate sized problems. (C) 2021 Elsevier Inc. All rights reserved.