An Introduction to Model-Based Geostatistics

The term geostatistics identifies the part of spatial statistics which is concerned with continuous spatial variation, in the following sense. The scientific focus is to study a spatial phenomenon, s(x)say, which exists throughout a continuous spatial region A ⊂ ℝ2 and can be treated as if it were a realisation of a stochastic process S(·) = {S(x): x ∈ A}. In general, S(·) is not directly observable. Instead, the available data consist of measurements Y 1,..., Y n taken at locations x 1,..., x n sampled within A, and Y i is a noisy version of S(x i ). We shall assume either that the sampling design for x 1,..., x n is deterministic or that it is stochastic but independent of the process S(·), and all analyses are carried out conditionally on x 1,...,x n .

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