Multi-parameter automodels and their applications

Motivated by the modelling of non-Gaussian data or positivelycorrelated data on a lattice, extensions of Besag's automodelsto exponential families with multi-dimensional parameters havebeen proposed recently. We provide a multiple-parameter analogueof Besag's one-dimensional result that gives the necessary formof the exponential families for the Markov random field's conditionaldistributions. We propose estimation of parameters by maximumpseudolikelihood and give a proof of the consistency of theestimators for the multi-parameter automodel. The methodologyis illustrated with examples, in particular the building ofa cooperative system with beta conditional distributions. Wealso indicate future applications of these models to the analysisof mixed-state spatial data.