A variance reduction method based on sensitivity derivatives

Authors:
Yanzhao Cao;M. Y. Hussaini;T. Zang;A. Zatezalo
Affiliations:
Department of Mathematics, Florida A&M University, Tallahassee, FL;School of Computational Science and Information Technology, Florida State University, Tallahassee, FL;NASA Langley Research Center, Hampton, VA;School of Computational Science and Information Technology, Florida State University, Tallahassee, FL
Venue:
Applied Numerical Mathematics
Year:
2006

Citing 6
Cited 0

Monte Carlo methods. Vol. 1: basics

Monte Carlo methods. Vol. 1: basics
First- and second-order aerodynamic sensitivity derivatives via automatic differentiation with incremental iterative methods

Journal of Computational Physics
Handbook of mathematics (3rd ed.)

Handbook of mathematics (3rd ed.)
Simulation and the Monte Carlo Method

Simulation and the Monte Carlo Method
An Efficient Monte Carlo Method for Optimal Control Problems with Uncertainty

Computational Optimization and Applications
Variance Reduction Techniques for Estimating Value-at-Risk

Management Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper establishes a general theoretical framework for variance reduction based on arbitrary order derivatives of the solution with respect to the random parameters, known as sensitivity derivatives. The theoretical results are validated by two examples--the solution of the Burgers equation with viscosity as a single random parameter, and a test case involving five random variables. These examples illustrate that the first-order sensitivity derivative variance reduction method achieves an order of magnitude improvement in accuracy for both Monte Carlo and stratified sampling schemes. The second-order sensitivity derivative method improves the accuracy by another order of magnitude relative to the first-order method. Coupling it with stratified sampling yields yet another order of magnitude improvement in accuracy.