Adaptive Multidimensional Integration: VEGAS Enhanced. 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 2-17 times 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 100 times as efficient as VEGAS+ without preconditio ing. Finally, we give examples where VEGAS+ is more than 10 times 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.
Keywords for this software
References in zbMATH (referenced in 5 articles , 1 standard article )
Showing results 1 to 5 of 5.
- Adshead, Peter; Lozanov, Kaloian D.; Weiner, Zachary J.: Non-Gaussianity and the induced gravitational wave background (2021)
- Kycia, Radosław A.; Szczurek, Antoni; Lebiedowicz, Piotr: \textscDecay: a Monte Carlo library for the decay of a particle with ROOT compatibility (2021)
- Lepage, G. Peter: Adaptive multidimensional integration: \textscvegasenhanced (2021)
- G. Peter Lepage: Adaptive Multidimensional Integration: VEGAS Enhanced (2020) arXiv
- R.A. Kycia, P. Lebiedowicz, A. Szczurek: Decay: A Monte Carlo library for the decay of a particle with ROOT compatibility (2020) arXiv