Inference of spatial indicator convariance parameters by maximum likelihood using MLREML
Computers & Geosciences
A More Portable Fortran Random Number Generator
ACM Transactions on Mathematical Software (TOMS)
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A probabilistic solution to the problem of spatial interpolation of a variable at an unsampled location consists of estimating the local cumulative distribution function (cdf) of the variable at that location from values measured at neighbouring locations. As this distribution is conditional to the data available at neighbouring locations it incorporates the uncertainty of the value of the variable at the unsampled location. Geostatistics provides a non-parametric solution to such problems via the various forms of indicator kriging. In a least squares sense indicator cokriging is theoretically the best estimator but in practice its use has been inhibited by problems such as an increased number of violations of order relations constraints when compared with simpler forms of indicator kriging. In this paper, we describe a methodology and an accompanying computer program for estimating a vector of indicators by simple indicator cokriging, i.e. simultaneous estimation of the cdf for K different thresholds, {F(u,z"k),k=1,...,K}, by solving a unique cokriging system for each location at which an estimate is required. This approach produces a variance-covariance matrix of the estimated vector of indicators which is used to fit a model to the estimated local cdf by logistic regression. This model is used to correct any violations of order relations and automatically ensures that all order relations are satisfied, i.e. the estimated cumulative distribution function, F@^(u,z"k), is such that:F@^(u,z"k)@?[0,1],@?z"k,andF@^(u,z"k)=