Estimation of spatial covariance structures by adjoint state maximum likelihood cross validation, 1. Theory

F. J. Samper, Shlomo P Neuman

Research output: Contribution to journalArticle

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A series of three papers describes a cross-validation method to estimate the spatial covariance structure of intrinsic or nonintrinsic random functions from point or spatially averaged data that may be corrupted by noise. Any number of relevant parameters, including nugget effect, can be estimated. The theory, described in this paper, is based on a maximum likelihood approach which treats the cross-validation errors as Gaussian. Various a posteriori statistical tests are used to verify this hypothesis and to show that in many cases, correlation between these errors is weak. The log likelihood criterion is optimized through a combination of conjugate gradient algorithms. An adjoint state theory is used to efficiently calculate the gradient of the estimation criterion, optimize the step size downgradient, and compute a lower bound for the covariance matrix of the estimation errors. Issues related to the identifiability, stability, and uniqueness of the resulting adjoint state maximum likelihood cross-validation method are discussed. -from Authors

Original languageEnglish (US)
Pages (from-to)351-362
Number of pages12
JournalWater Resources Research
Issue number3
Publication statusPublished - 1989
Externally publishedYes


ASJC Scopus subject areas

  • Aquatic Science
  • Environmental Science(all)
  • Environmental Chemistry
  • Water Science and Technology

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