Page - 250 - in Differential Geometrical Theory of Statistics
Image of the Page - 250 -
Text of the Page - 250 -
Entropy2016,18, 383
14. Chua,C.B.RelatinghomogeneousconesandpositivedeïŹniteconesviaT-algebras.SIAMJ.Optim. 2003,
14, 500â506.
15. Ishi,H.Onsymplectic representationsofnormal j-algebras and their application toXuâs realizationsof
Siegeldomains.Differ.Geom.Appl. 2006,24, 588â612.
16. Yamasaki,T.;Nomura,T.Realizationofhomogeneouscones throughorientedgraphs.KyushuJ.Math. 2015,
69, 11â48.
17. Ishi,H.Homogeneousconesandtheirapplications tostatistics. InModernMethodsofMultivariateStatistics;
Graczyk,P.,Hassairi,A,Eds.;Hermann: Paris,France,2014;pp. 135â154.
18. Ishi,H.Matrixrealizationofhomogeneouscones. InGeometricScienceof Information;Nielsen,F.,Barbaresco,F.,
Eds.; (LectureNotes inComputer Science); Springer International Publishing: Basel, Switzerland, 2015;
Volume9389,pp. 248â256.
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, 317â348.
22. Shima,H.HomogeneousHessianmanifolds.Ann. Inst. Fourier1980,30, 91â128.
23. GĂŒler, O.; Tunçel, L. Characterization of the barrier parameter of homogeneous convex cones.
Math.Program.A1988,81, 55â76.
24. Andersson, S.A.; Wojnar, G.G. Wishart distributions on homogeneous cones. J. Theor. Probab. 2004,
17, 781â818.
25. Graczyk,P.; Ishi,H.;KoĆodziejek,B.Wishartexponential familiesandvariance functiononhomogeneous
cones.HAL2016, submittedforpublication.
26. Ishi,H.Onaclassofhomogeneousconesconsistingofreal symmetricmatrices. JosaiMath.Monogr. 2013,
6, 71â80.
27. Roverato,A.Choleskydecompositionofahyper inverseWishartmatrix.Biometrika2000,87, 99â112.
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
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