Künsch, H. Thermodynamics and statistical analysis of Gaussian random fields. (English) Zbl 0458.60053 Z. Wahrscheinlichkeitstheor. Verw. Geb. 58, 407-421 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 16 Documents MSC: 60G60 Random fields 62A01 Foundations and philosophical topics in statistics 62M09 Non-Markovian processes: estimation 80A17 Thermodynamics of continua Keywords:Gaussian random fields; Gibbsian fields; variational principle; asymptotic behaviour of maximum likelihood estimators × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Akaike, H.; Petrov, B. N.; Csaki, F., Information theory and an extension of the maximum likelihood principle, 267-281 (1973), Budapest: Akademiai Kiado, Budapest · Zbl 0283.62006 [2] Anderson, T. W., The statistical analysis of time series (1971), New York: Wiley, New York · Zbl 0225.62108 [3] Besag, J., Spatial interaction and the statistical analysis of lattice systems, J. Roy. Statist. Soc. Ser. B, 36, 192-236 (1974) · Zbl 0327.60067 [4] Besag, J., Errors-in-variables estimation for Gaussian lattice schemes, J. Roy. Statist. Soc. Ser. B, 39, 73-78 (1977) · Zbl 0355.62027 [5] Besag, J.; Moran, P. A.P., On the estimation and testing of spatial interaction for Gaussian lattice processes, Biometrika, 62, 555-562 (1975) · Zbl 0388.62082 [6] Dempster, A. P., Covariance selection, Biometrics, 28, 157-175 (1972) [7] Dobrushin, R. L.; Dobrushin, R. L.; Sinai, Ya. G., Gaussian random fields — Gibbsian point of view, Multicomponent random systems, 119-151 (1980), New York: M. Dekker, New York · Zbl 0499.60046 [8] Dunford, N.; Schwartz, J. T., Linear Operators I (1958), New York: Interscience, New York · Zbl 0084.10402 [9] Föllmer, H., On entropy and information gain in random fields, Z. Wahrscheinlichkeitstheorie verw. Geb., 26, 207-217 (1973) · Zbl 0258.60029 [10] Guyon, X.: Parameter estimation for stationary processes on ℤ^d. [To appear ] · Zbl 0485.62107 [11] Künsch, H., Gaussian Markov random fields, J. Fac. Sci. Univ. Tokyo Sec. 1A Math., 26, 53-73 (1979) · Zbl 0408.60038 [12] Künsch, H.: Almost sure entropy and the variational principle for random fields with unbounded state space. [To appear in Z. Wahrscheinlichkeitstheorie verw. Geb.] · Zbl 0473.60049 [13] Nguyen, X. X.; Zessin, H., Ergodic theorems for spatial processes, Z. Wahrscheinlichkeitstheorie verw. Geb., 48, 133-158 (1979) · Zbl 0397.60080 [14] Pirlot, M., A strong variational principle for continuous spin systems, J. Appl. Probability, 17, 47-58 (1980) · Zbl 0431.60097 [15] Preston, C., Random fields, Lecture Notes in Math. 534 (1976), Berlin — Heidelberg — New York: Springer, Berlin — Heidelberg — New York · Zbl 0335.60074 [16] Rosanov, Yu. A., On Gaussian fields with given conditional distributions, Theory Probability Appl., 12, 381-391 (1967) · Zbl 0212.20101 [17] Spitzer, F., Champs de Markov Gaussiens, Ecole d’été de probabilité Saint Flour III, Lecture Notes in Math. 390, 179-185 (1974), Berlin — Heidelberg — New York: Springer, Berlin — Heidelberg — New York [18] TjØstheim, D., Statistical spatial series modeling, Adv. Appl. Probability, 10, 130-154 (1978) · Zbl 0383.62060 [19] Whittle, P., On stationary processes in the plane, Biometrika, 41, 450-462 (1954) · Zbl 0058.35601 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.