In this paper we propose fast approximate methods for computing posterior marginals in spatial generalized linear mixed models. We consider the common geostatistical special case with a high dimensional latent spatial variable and observations at only a few known registration sites. Our methods of inference are deterministic, using no random sampling. We present two methods of approximate inference. The first is very fast to compute and via examples we find that this approximation is ’practically sufficient’. By this expression we mean that the results obtained by this approximate method do not show any bias or dispersion effects that might affect decision making. The other approximation is an improved version of the first one, and via examples we demonstrate that the inferred posterior approximations of this improved version are ’practically exact’. By this expression we mean that one would have to run Markov chain Monte Carlo simulations for longer than is typically done to detect any indications of bias or dispersion error effects in the approximate results. The two methods of approximate inference can help to expand the scope of geostatistical models, for instance in the context of model choice, model assessment, and sampling design. The

Decisions involving selection of sites over a lateral domain with a spatially correlated distinction of interest are common in several realms. In this paper we use the decision-analytic notion of value of information on models common to spatial statistics. We formulate methods to evaluate monetary values associated with experiments performed in the spatial decision making context, including the prior value, the value of perfect information, and the value of the experiment. The prior for the spatial distinction of interest is assumed to be a Markov random field where the value at each spatial site belongs to a finite set of states. The likelihood distribution can take any form depending on the experiment one decides to acquire. Typical experiment types are binary registration or a Gaussian measurement at selected spatial sites. We demonstrate how to efficiently compute the value of an experiment for Markov random fields of moderate size. The most computationally demanding task is solving an integral over the result of the experiment under evaluation, which we accomplish using Monte Carlo integration. We explore and compare some measures for the worth of an experiment in our problem context. Our methods are illustrated on two examples. One is relevant to conservation biology,