Geodesic
Marginal problem, statistical estimation, and Möbius formula
Kybernetika, Tome 43 (2007) no. 5, pp. 619-631.

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A solution to the marginal problem is obtained in a form of parametric exponential (Gibbs–Markov) distribution, where the unknown parameters are obtained by an optimization procedure that agrees with the maximum likelihood (ML) estimate. With respect to a difficult performance of the method we propose also an alternative approach, providing the original basis of marginals can be appropriately extended. Then the (numerically feasible) solution can be obtained either by the maximum pseudo-likelihood (MPL) estimate, or directly by Möbius formula.
Classification : 60G60, 62F10, 62G07, 62H12, 93E12, 93E25
Keywords: Gibbs distributions; maximum entropy; pseudo-likelihood; Möbius formula 
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     author = {Jan\v{z}ura, Martin},
     title = {Marginal problem, statistical estimation, and {M\"obius} formula},
     journal = {Kybernetika},
     pages = {619--631},
     publisher = {mathdoc},
     volume = {43},
     number = {5},
     year = {2007},
     mrnumber = {2376327},
     zbl = {1138.93059},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2007__43_5_a2/}
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Janžura, Martin. Marginal problem, statistical estimation, and Möbius formula. Kybernetika, Tome 43 (2007) no. 5, pp. 619-631. http://geodesic.mathdoc.fr/item/KYB_2007__43_5_a2/