Double-Loop Quasi-Monte Carlo Estimator for Nested Integration

Keskeiset käsitteet

Introducing a novel DLQMC estimator for nested integration problems to improve efficiency and reduce computational costs.

Tiivistelmä

1. Introduction

Evaluating Expected Information Gain (EIG) is crucial in computational science and statistics.
Techniques based on Quasi-Monte Carlo (QMC) methods have focused on enhancing inner integral approximation efficiency.
A novel approach, DLQMC estimator, extends efforts to address inner and outer expectations simultaneously.
2. Brief Overview of Monte Carlo and Randomized Quasi-Monte Carlo Integration

MC method approximates integrals using random points.
QMC method achieves better convergence rates for certain integrands.
RQMC method improves efficiency while maintaining a low-discrepancy structure.
3. Nested Integration

DLQMC estimator defined for nested integrals.
DLMC estimator for nested integrals has limitations due to bias and variance.
DLQMC estimator aims to reduce required samples and improve efficiency.
4. Numerical Results

DLQMC estimator's bias and variance analyzed.
Optimal work for DLQMC estimator derived for specified error tolerance.

Tilastot

"The total work of the optimized DLQMC estimator for a specified error tolerance TOL > 0 is given by W ∗ DLQ ∝ TOL−(2/(1+β) + 1/(1+δ + γη))"

Lainaukset

"The DLQMC estimator for nested integration problems to improve efficiency and reduce computational costs."
"DLQMC estimator aims to reduce required samples and improve efficiency."

Tärkeimmät oivallukset

Double-loop quasi-Monte Carlo estimator for nested integration

by Arve... klo arxiv.org 02-29-2024

https://arxiv.org/pdf/2302.14119.pdf

Syvällisempiä Kysymyksiä

질문 1

DLQMC 추정자를 다른 계산 문제에 어떻게 적용할 수 있습니까?
답변 1 여기에

질문 2

실제 응용 프로그램에서 DLQMC 추정자의 잠재적인 제한 사항은 무엇입니까?
답변 2 여기에

질문 3

DLQMC의 원칙을 확장하여 다른 계산 알고리즘을 최적화하는 방법은 무엇입니까?
답변 3 여기에