In rather formal terms, the situation with which this paper is concerned may be described as follows. We are given a fixed system of n sites, labelled by the first n positive integers, and an associated vector x of observations, Xi, . . ., Xn, which, in turn, is presumed to be a realization of a vector X of (dependent) random variables, Xi, . . ., X.. In practice, the sites may represent points or regions in space and the random variables may be either continuous or discrete. The main statistical objectives are the following: firstly, to provide a means of using the available concomitant information, particularly the configuration of the sites, to attach a plausible probability distribution to the random vector X; secondly, to estimate any unknown parameters in the distribution from the realization x; thirdly, where possible, to quantify the extent of disagreement between hypothesis and observation.
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