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 effectiv...
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description | 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 2-19 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. |
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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 2-19 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. 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subjects | Adaptive algorithms Adaptive sampling Algorithms Importance sampling Integrators Physics - Computational Physics Physics - High Energy Physics - Phenomenology |
title | Adaptive Multidimensional Integration: VEGAS Enhanced |
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