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Forward recursions and normalizing constant

Xavier Guyon 1, 2, Cécile Hardouin 1, 2

(2009-12-01)

Maximum likelihood parameter estimation is frequently replaced by various techniques because of its intractable normalizing constant. In the same way, the literature displays various alternatives for distributions involving such unreachable constants. In this paper, we consider a Gibbs distribution $\pi $ and present a recurrence formula allowing a recursive calculus of the marginals of $\pi $ and in the same time its normalizing constant$.$ The numerical performance of this algorithm is evaluated for several examples, particularly for an Ising model on a lattice.

1:	Statistique Appliquée et MOdélisation Stochastique (SAMOS)
	Université Paris I - Panthéon-Sorbonne
2:	Centre d'économie de la Sorbonne (CES)
	CNRS : UMR8174 – Université Paris I - Panthéon-Sorbonne

Subject

:

Mathematics/Statistics Statistics/Statistics Theory

Keyword(s): Gibbs distribution – interaction potential – Markov Chain – Markov field – marginal law – normalizing constant – Ising model.

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From: Cécile Hardouin <>

Submitted on: Tuesday, 1 December 2009 16:17:40

Updated on: Thursday, 17 November 2011 14:46:32