Polar Gaussian Processes and Experimental Designs in Circular Domains
- 1 January 2016
- journal article
- research article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM/ASA Journal on Uncertainty Quantification
- Vol. 4 (1), 1014-1033
- https://doi.org/10.1137/15m1032740
Abstract
Predicting on circular domains is a central issue that can be addressed by Gaussian process (GP) regression. However, usual GP models do not take into account the geometry of the disk in their covariance structure (or kernel), which may be a drawback at least for industrial processes involving a rotation or a diffusion from the center of the disk. We introduce so-called polar GPs defined on the space of polar coordinates. Their kernels are obtained as a combination of a kernel for the radius and a kernel for the angle, based on either chordal or geodesic distances on the circle. Their efficiency is illustrated on two industrial applications. We further consider the problem of designing experiments on the disk. Two new Latin hypercube designs are obtained, by defining a valid maximin criterion for polar coordinates. Finally, an extension of the whole methodology to higher dimensions is investigated.Keywords
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This publication has 17 references indexed in Scilit:
- Numerical studies of space-filling designs: optimization of Latin Hypercube Samples and subprojection propertiesJournal of Simulation, 2013
- Strictly and non-strictly positive definite functions on spheresBernoulli, 2013
- ANOVA kernels and RKHS of zero mean functions for model-based sensitivity analysisJournal of Multivariate Analysis, 2013
- The effect of the nugget on Gaussian process emulators of computer modelsComputational Statistics & Data Analysis, 2012
- Gaussian Surrogates for Computer Models With Time-Varying Inputs and OutputsTechnometrics, 2012
- Cases for the nugget in modeling computer experimentsStatistics and Computing, 2010
- Optimal designs for statistical analysis with Zernike polynomialsStatistics, 2007
- Exploratory designs for computational experimentsJournal of Statistical Planning and Inference, 1995
- Generating random vectors uniformly distributed inside and on the surface of different regionsEuropean Journal of Operational Research, 1982
- Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkontrastmethodePhysica, 1934