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Systematic sampling of Gaussian random processes and fields
Author(s) -
Veneziano Daniele,
Queiroz Celso S.
Publication year - 1979
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr015i003p00703
Subject(s) - variance reduction , gaussian , sampling (signal processing) , mathematics , random field , simple random sample , parametric statistics , statistics , mathematical optimization , filter (signal processing) , computer science , monte carlo method , physics , population , demography , quantum mechanics , sociology , computer vision
Linear observation of Gaussian random functions always results in reduction of uncertainty and since the posterior central moments are precomputable, optimal linear sampling schemes for variance reduction are nonsequential. In particular, systematic sampling of homogeneous Gaussian processes and fields, the latter on rectangular grids, leads to simple variance‐updating equations. Cases when measurements are noisy, when linear transformations of the uncertain function are observed or estimated, and when nonparametric uncertainty is superposed to a random parametric trend lead to simple variants of the direct observation/estimation model. The basic analytical tool is the Kolmogorov‐Wiener filter, either in the frequency or in the space domain. Application areas include the design of rainfall collection networks, inference of soil properties for geotechnical use, mineral exploration, biological and environmental sampling, materials testing, and quality control.