แนวคิดหลัก
Introducing a novel DLQMC estimator for nested integration problems to improve efficiency and reduce computational costs.
บทคัดย่อ
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.
สถิติ
"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))"
คำพูด
"The DLQMC estimator for nested integration problems to improve efficiency and reduce computational costs."
"DLQMC estimator aims to reduce required samples and improve efficiency."