Uniform design over general input domains with applications to target region estimation in computer experiments

Authors:
S. C. Chuang;Y. C. Hung
Affiliations:
Graduate Institute of Statistics, National Central University, Jhongli 32049, Taiwan;Department of Statistics, National Chengchi University, Taipei 11605, Taiwan
Venue:
Computational Statistics & Data Analysis
Year:
2010

Citing 12
Cited 3

Empirical model-building and response surface

Empirical model-building and response surface
The nature of statistical learning theory

The nature of statistical learning theory
Support-Vector Networks

Machine Learning
A generalized discrepancy and quadrature error bound

Mathematics of Computation
An improvement of the standard genetic algorithm fighting premature convergence in continuous optimization

Advances in Engineering Software
Efficient Global Optimization of Expensive Black-Box Functions

Journal of Global Optimization
Automatic Capacity Tuning of Very Large VC-Dimension Classifiers

Advances in Neural Information Processing Systems 5, [NIPS Conference]
Centered L2-discrepancy of random sampling and Latin hypercube design, and construction of uniform designs

Mathematics of Computation
Queueing Dynamics and Maximal Throughput Scheduling in Switched Processing Systems

Queueing Systems: Theory and Applications
Asymptotic behaviors of support vector machines with Gaussian kernel

Neural Computation
Modeling, scheduling, and simulation of switched processing systems

ACM Transactions on Modeling and Computer Simulation (TOMACS)
Dynamic scheduling for switched processing systems with substantial service-mode switching times

Queueing Systems: Theory and Applications

Optimized U-type designs on flexible regions

Computational Statistics & Data Analysis
Contour estimation via two fidelity computer simulators under limited resources

Computational Statistics
Discrete particle swarm optimization for constructing uniform design on irregular regions

Computational Statistics & Data Analysis

Quantified Score

Hi-index	0.03

Visualization

Abstract

The power of uniform design (UD) has received great attention in the area of computer experiments over the last two decades. However, when conducting a typical computer experiment, one finds many non-rectangular types of input domains on which traditional UD methods cannot be adequately applied. In this study, we propose a new UD method that is suitable for any type of design area. For practical implementation, we develop an efficient algorithm to construct a so-called nearly uniform design (NUD) and show that it approximates very well the UD solution for small sizes of experiment. By utilizing the proposed UD method, we also develop a methodology for estimating the target region of computer experiments. The methodology is sequential and aims to (i) provide adaptive models that predict well the output measures related to the experimental target; and (ii) minimize the number of experimental trials. Finally, we illustrate the developed methodology on various examples and show that, given the same experimental budget, it outperforms other approaches in estimating the prespecified target region of computer experiments.