Title: Prediction variance properties of bridge designs

Authors: Kathryn Kennedy; Rachel T. Silvestrini; Douglas C. Montgomery; Bradley Jones

Addresses: School of Computing, Informatics and Decision Systems Engineering, Arizona State University, Tempe, AZ 85287, USA ' Industrial and Systems Engineering Department, Rochester Institute of Technology, Rochester, NY 14623-5603, USA ' School of Computing, Informatics and Decision Systems Engineering, Arizona State University, Tempe, AZ 85287, USA ' SAS Institute, SAS Campus Dr., Cary, NC 27513, USA

Abstract: Bridge designs are compromise designs between D-optimal designs and Latin hypercube designs. Bridge designs are a good choice of experiments for computer simulation models with only small variance in the output response. This can occur in a wide range of computer experiments because variance reduction techniques are widely used in these studies. We expect that people will use results from bridge designs to fitting low order polynomial regression models. Bridge designs do not contain replicates, either in the original design or in projection, so they are also potentially good choices for other modelling strategies such as Gaussian process models. We compare bridge designs to D-optimal, I-optimal and Latin hypercube designs in terms of their theoretical prediction variance for experiments with 2-5 factors and polynomial models of order 2-5. The empirical results are also provided using test functions for Gaussian process models. We find that bridge designs are good choices for computer experiments when the underlying model is hypothesised to be a second or third-order polynomial, or a fourth-order polynomial of up to four factors. They also perform well in fitting Gaussian process models.

Keywords: optimal design; Latin hypercube design; computer experiments; prediction variance; bridge design; simulation; polynomial regression models; Gaussian process models; modelling.

DOI: 10.1504/IJEDPO.2015.072811

International Journal of Experimental Design and Process Optimisation, 2015 Vol.4 No.3/4, pp.234 - 255

Received: 20 Dec 2014
Accepted: 22 May 2015

Published online: 03 Nov 2015 *

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