Estimation of the Ising field parameter from incomplete and noisy data

Abstract : The present paper deals with the estimation problem of the Ising field parameter and extends a previous one [Giovannelli 2010]. It proposes an estimate from indirect observation (incomplete and noisy), whereas the previous paper proposed an estimate from direct observation (complete and noiseless). Both of them are based on an explicit expression for the partition function, known for a long time [Onsager 1944] but, to the best of our knowledge, never used for parameter estimation (except in our previous paper. Both of them are developed in a Bayesian framework. In our previous study (direct observation), the posterior law is explicit but in the present case (indirect observation) the posterior law is not explicit due to the hidden structure. The proposed approach relies on a full Bayesian strategy and a stochastic sampling algorithm (Gibbs sampler including a Metropolis-Hastings step) for posterior exploration. The paper proposes a numerical evaluation of the proposed method.
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https://hal.archives-ouvertes.fr/hal-00669079
Contributor : Jean-François Giovannelli <>
Submitted on : Saturday, February 11, 2012 - 8:42:47 AM
Last modification on : Thursday, April 5, 2018 - 12:30:05 PM

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  • HAL Id : hal-00669079, version 1

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Jean-François Giovannelli. Estimation of the Ising field parameter from incomplete and noisy data. ICIP, Sep 2011, Bruxelles, Belgium. pp.1893-1896. ⟨hal-00669079⟩

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