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

TL;DR

This paper introduces recursive formulas leveraging Markov properties to compute marginals and the normalizing constant of Gibbs distributions, with applications demonstrated on models like the Ising model.

Contribution

It provides novel recursive methods for exact computation of marginals and normalizing constants in Gibbs processes, enhancing analytical capabilities.

Findings

Recursive formulas successfully compute marginals and normalizing constants.

Methods are illustrated with examples including the Ising model.

Approach leverages Markov properties for efficient calculations.

Abstract

This paper presents different recursive formulas for computing the marginals and the normalizing constant of a Gibbs distribution $\pi$: 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.