论文标题
多级贝叶斯正交
Multilevel Bayesian Quadrature
论文作者
论文摘要
多级蒙特卡洛（Monte Carlo）是近似涉及昂贵科学模型的积分的关键工具。这个想法是利用集成剂的近似值来构建与经典蒙特卡洛相比精度提高的估计器。我们建议通过贝叶斯替代模型进一步增强多级蒙特卡洛，重点关注高斯工艺模型和相关的贝叶斯正交估计量。我们使用理论和数值实验表明，当集成剂昂贵且平滑时，以及尺寸较小或中等时，我们的方法可以显着提高准确性。我们通过案例研究结束了本文，该案例说明了我们方法对滑坡生成的海啸建模的潜在影响，在该模型中，每个集成数评估的成本通常太大，对于操作环境而言。
Multilevel Monte Carlo is a key tool for approximating integrals involving expensive scientific models. The idea is to use approximations of the integrand to construct an estimator with improved accuracy over classical Monte Carlo. We propose to further enhance multilevel Monte Carlo through Bayesian surrogate models of the integrand, focusing on Gaussian process models and the associated Bayesian quadrature estimators. We show, using both theory and numerical experiments, that our approach can lead to significant improvements in accuracy when the integrand is expensive and smooth, and when the dimensionality is small or moderate. We conclude the paper with a case study illustrating the potential impact of our method in landslide-generated tsunami modelling, where the cost of each integrand evaluation is typically too large for operational settings.
