Adaptive multidimensional integration: VEGAS enhanced

JOURNAL OF COMPUTATIONAL PHYSICS

卷:439

Article

Lepage, G. Peter¹ 

[1] Cornell Univ, Dept Phys, Ithaca, NY 14853 USA

关键词: Multidimensional integration;    Monte Carlo integration;    Bayesian statistics;   

DOI  :  10.1016/j.jcp.2021.110386

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free