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Entropy2016,18, 383 14. Chua,C.B.RelatinghomogeneousconesandpositivedeïŹniteconesviaT-algebras.SIAMJ.Optim. 2003, 14, 500–506. 15. Ishi,H.Onsymplectic representationsofnormal j-algebras and their application toXu’s realizationsof Siegeldomains.Differ.Geom.Appl. 2006,24, 588–612. 16. Yamasaki,T.;Nomura,T.Realizationofhomogeneouscones throughorientedgraphs.KyushuJ.Math. 2015, 69, 11–48. 17. Ishi,H.Homogeneousconesandtheirapplications tostatistics. InModernMethodsofMultivariateStatistics; Graczyk,P.,Hassairi,A,Eds.;Hermann: Paris,France,2014;pp. 135–154. 18. Ishi,H.Matrixrealizationofhomogeneouscones. InGeometricScienceof Information;Nielsen,F.,Barbaresco,F., Eds.; (LectureNotes inComputer Science); Springer International Publishing: Basel, Switzerland, 2015; Volume9389,pp. 248–256. 19. Lauritzen,S.L.GraphicalModels;ClarendonPress:Oxford,UK,1996. 20. Faraut, J.;KorĂĄnyi,A.Analysis onSymmetricCones;ClarendonPress:Oxford,UK;1994. 21. Graczyk,P.; Ishi,H.RieszmeasuresandWishart lawsassociatedwithquadraticmaps. J.Math. Soc. Jpn. 2014,66, 317–348. 22. Shima,H.HomogeneousHessianmanifolds.Ann. Inst. Fourier1980,30, 91–128. 23. GĂŒler, O.; Tunçel, L. Characterization of the barrier parameter of homogeneous convex cones. Math.Program.A1988,81, 55–76. 24. Andersson, S.A.; Wojnar, G.G. Wishart distributions on homogeneous cones. J. Theor. Probab. 2004, 17, 781–818. 25. Graczyk,P.; Ishi,H.;KoƂodziejek,B.Wishartexponential familiesandvariance functiononhomogeneous cones.HAL2016, submittedforpublication. 26. Ishi,H.Onaclassofhomogeneousconesconsistingofreal symmetricmatrices. JosaiMath.Monogr. 2013, 6, 71–80. 27. Roverato,A.Choleskydecompositionofahyper inverseWishartmatrix.Biometrika2000,87, 99–112. 28. Graczyk,P.; Ishi,H.;Mamane, S.Wishart exponential familiesoncones related toAn graphs.HAL2016, submittedforpublication. c©2016bytheauthors. LicenseeMDPI,Basel,Switzerland. Thisarticle isanopenaccess articledistributedunder the termsandconditionsof theCreativeCommonsAttribution (CCBY) license (http://creativecommons.org/licenses/by/4.0/). 250
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Differential Geometrical Theory of Statistics
Title
Differential Geometrical Theory of Statistics
Authors
Frédéric Barbaresco
Frank Nielsen
Editor
MDPI
Location
Basel
Date
2017
Language
English
License
CC BY-NC-ND 4.0
ISBN
978-3-03842-425-3
Size
17.0 x 24.4 cm
Pages
476
Keywords
Entropy, Coding Theory, Maximum entropy, Information geometry, Computational Information Geometry, Hessian Geometry, Divergence Geometry, Information topology, Cohomology, Shape Space, Statistical physics, Thermodynamics
Categories
Naturwissenschaften Physik
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