Multilevel randomized quasi Monte Carlo Estimator for nested integration

arXiv (Cornell University)

Abstract

Nested integration problems are encountered in scientific and engineering applications such as Bayesian experimental design, financial risk assessment, and uncertainty quantification. Nested integrals, where a nonlinear function separates an outer from an inner integral, are computationally challenging, especially in high dimensions. Monte Carlo methods can be computationally demanding in this setting. A novel multilevel estimator combining deterministic and randomized quasi-Monte Carlo methods is introduced in this work to address nested integration problems efficiently. In Bayesian experimental design applications, Gaussian observation noise in the experiment introduces a singularity, and a truncation scheme is applied to ensure finite error bounds.

Authors 5

1. Arved Bartuska Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen

2. André Gustavo Carlon Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen

3. Luis Espath
4. Sebastian Krumscheid
5. Raul F. Tempone Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen