Recursions on the marginals and exact computation of the normalizing constant for Gibbs processes

This paper presents different recursive formulas for computing the marginals and the normalizing constant of a Gibbs distribution <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\pi $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">π</mi> </math> </EquationSource> </InlineEquation>. The common thread is the use of the underlying Markov properties of such processes. The procedures are illustrated with several examples, particularly the Ising model. Copyright Springer-Verlag Berlin Heidelberg 2014