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International Journal for Uncertainty Quantification

Impact factor: 1.000

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2011003369
pages 25-38

VISUALIZATION OF COVARIANCE AND CROSS-COVARIANCE FIELDS

Chao Yang
School of Computing, University of Utah, Salt Lake City, UT 84112, USA
Dongbin Xiu
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907, USA; Ohio State University Columbus, Ohio, USA
Mike Kirby
Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, Utah, 84112, USA

ABSTRACT

We present a numerical technique to visualize covariance and cross-covariance fields of a stochastic simulation. The method is local in the sense that it demonstrates the covariance structure of the solution at a point with its neighboring locations. When coupled with an efficient stochastic simulation solver, our framework allows one to effectively concurrently visualize both the mean and (cross-)covariance information for two-dimensional (spatial) simulation results. Most importantly, the visualization provides the scientist a means to identify the interesting correlation structure of the solution field. The mathematical setup is discussed, along with several examples to demonstrate the efficacy of this approach.