Summary
Gaussian fields are considered as Gibbsian fields. Thermodynamic functions are calculated for them and the variational principle is proved. As an application we get an approximation of log likelihood and an information theoretic interpretation of the asymptotic behaviour of the maximum likelihood estimator for Gaussian Markov fields.
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Künsch, H. Thermodynamics and statistical analysis of Gaussian random fields. Z. Wahrscheinlichkeitstheorie verw Gebiete 58, 407–421 (1981). https://doi.org/10.1007/BF00542645
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DOI: https://doi.org/10.1007/BF00542645