Non-uniform space filling (NUSF) designs

Abstract

Space-filling designs are a convenient and effective approach for exploring the input space for experiments. However, standard choices for these designs strive to provide uniform density of points throughout the region of interest. There are numerous situations where flexibility to adapt the density of points to match specific design objectives would be advantageous to maximize the efficiency of the design. In this paper, we propose non-uniform space-filling (NUSF) designs to achieve a user-specified desired density distribution of design points across the input space and demonstrate how to implement NUSF designs in different ways to provide the experimenters with flexibility to match their goals. The approach is flexible for a variety of scenarios where the experimenter wishes to control the density of points throughout the region while still preserving the space-filling characteristic. Details are provided about how to translate a problem into an appropriate weight structure to generate several designs which can then be compared using graphical methods, including the Closest Distance by Weight plot, to determine if the desired characteristics have been achieved. The methods are demonstrated with two real examples with different requirements for design point placement.

Keywords:

• Closest Distance by Weight plot
• computer experiments
• data competitions
• point exchange
• unequal density of design points
• weighted distance metric

Additional information

Notes on contributors

Lu Lu

Dr. Lu Lu is an Assistant Professor of Statistics in the Department of Mathematics and Statistics at the University of South Florida in Tampa. She was a postdoctoral research associate in the Statistics Sciences Group at Los Alamos National Laboratory. She earned a doctorate in Statistics from Iowa State University in Ames, IA. Her research interests include reliability analysis, design of experiments, response surface methodology, survey sampling, multiple objective/response optimization.

Christine M. Anderson-Cook

Dr. Christine M. Anderson-Cook is a Research Scientist in the Statistical Sciences Group at Los Alamos National Laboratory. Her research areas include reliability, design of experiments, multiple criterion optimization, and response surface methodology. She is a Fellow of the American Statistical Association and the American Society for Quality.

Towfiq Ahmed

Dr. Towfiq Ahmed is a Research Scientist in the Theoretical and Computational Condense Matter Physics Group at Los Alamos National Laboratory. His research interests include materials physics, computational physics, and quantum physics.