论文标题
自适应多维整合：维加斯增强
Adaptive Multidimensional Integration: VEGAS Enhanced
论文作者
论文摘要
我们描述了一种新的算法，拉斯维加斯+，用于自适应多维蒙特卡洛整合。新算法将第二种自适应分层抽样添加到自适应的重要性抽样中，这是其广泛使用的前任拉斯维加斯的基础。维加斯和拉斯维加斯+对于具有较大峰的积分都有效，但是对于具有多个峰的积分或其他与积分体积对角线对齐的重要结构的积分，拉斯维加斯+都可以更有效。我们提供的例子是，维加斯+的准确性比拉斯维加斯高2-19倍。我们还展示了如何将Vegas+与其他集成商（例如广泛可用的Miser算法）相结合，以制造新的混合集成剂。对于另一种混合动力，我们展示了如何使用使用MCMC或其他方法生成的Integrand样品在集成之前优化Vegas+。我们举例说明，预处理的拉斯维加斯+高于维加斯+的100倍以上，而无需预言。最后，我们给出了示例，其中Vegas+的效率是MCMC的10倍以上，对于d = 3和21个参数，贝叶斯积分的效率是MCMC。我们解释了为什么Vegas+通常在小型和中等大小的问题上表现出色。
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.
