Application of Best Linear Unbiased Prediction to Interpolation of Random Fields and to Network Design

摘要

The practical problem of monitoring air pollutant concentration over a geographical area, or of estimating the mining resources in a region or a field can both be formulated as a problem of interpolation of random field. Given a real-valued random field (Z(X),x an element of R to the m power) the basic problem is to interpolate Z over an area A from measurements taken at n stations x1 ,x2,..,xn, when the distribution of Z is only partially specified. The second problem is the choice of the network of stations. After deriving the form of the best linear unbiased predictor of Z we prove a general updating theorem which is useful both practically to quicken the computation of the new estimated map, and theoretically to study the problem of network design. Then we use this theorem to prove that when Z is a smooth random field (essentially differentiable in quadratic mean) the variance of estimation error of Z(x) is a discontinuous function of the arguments x1,x2,...,xn. We discuss the practical consequences of this result in the design of networks of stations. (Author)