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Entropy2016,18, 433 44. Hess,H.Connectionsonsymplecticmanifoldsandgeometricquantization. InDifferentialGeometryMethods inMaththematicalPhysics;LecturesNotes836;Springer: Berlin/Heidelberg,Germany,1980;pp. 153–166 45. NguiffoBoyom,M.Structures localementplatesdanscertainesvariétéssymplectiques.Math. Scand. 1995, 76, 61–84. (InFrench) 46. Kamber,F.;Tondeur,P.H.DeRham-HodgeTheory forRiemannianfoliations.Math.Ann. 1987,277, 415–431. 47. Byande, P.M.De Structures Affines à la Géométrie de L’information; ÉditionsUniversitaires Européennes: Saarbrücken,Germany,2012. (InFrench) 48. Chentsov,N.N.StatisticalDecisionRulesandOptimal Inference;AmericanMathematicalSociety: Providence, RI,USA,1982. 49. Petrie,T.;Handal, J.Connections,DefiniteFormsandFour-Manifolds;OxfordMathematcalMonograph,Oxford SciencePublications;ClarendonPress:Oxford,UK,1990. 50. Guillemin,V.; Sternberg, S.Analgebraicmodel for transitivedifferentialgeometry. Bull. Am. Math. Soc. 1964,70, 16–47. 51. Singer, I.M.;Sternberg,S.The infintegroupsandlieandCartan. J.Anal.Math. Jerus. 1965,15, 1–144. 52. Shima,H.TheGeometryofHessianStructures;WorldScientific: Singapore,2007. 53. Barbaresco,F.SymplecticStructureof InformationGeometry: Fisher InformationandEuler-PoincareEquationof SouriauLieGroupThermodynamics;Nielsen,F.,Barbaresco,F.,Eds.;Springer: Berlin/Heidelberg,Germany, 2015;pp. 529–540. 54. Matsuzoe,H.;Henmi,M.HessianStructuresonDeformedExponentialFamilies;Nielsen,F.,Barbaresco,F.,Eds.; Springer: Berlin/Heidelberg,Germany,2013;Volume8085,pp. 275–282. 55. Barbaresco,F.Koszul InformationGeometryandSouriauGeometricTemperature/CapacityofLieGroup Thermodynamics.Entropy2014,16, 4521–4565. 56. Nijenhuis, A.; Richardson,W.Commutative algebra cohomology anddeformation of Lie algebras and associativealgebras. J.Algebra1968,9, 42–53. 57. Chevallier, E.; Barbaresco, F.; Angulo, J. Kernel Density Estimation on Siegel SpaceApplied to Radar Processing.Entropy2016,18, 396. 58. Chevallier,E.;Barbaresco,F.;Angulo, J.Probabilitydensityestimationonhyperbolic spaceapplied toradar processing. InGeometricScienceof Information; Springer: Berlin/Heidelberg,Germany,2015;pp. 753–761. 59. Eilenberg,S.HomologyofspaceswithoperatorsgroupI.Trans.Am.Math. Soc. 1947,62, 378–417. 60. NguiffoBoyom,M.;Wolak,R.TransverseHessianmetrics informationgeometry. InProceedingsof the34th InternationalWorkshoponBayesian InferenceandMaximumEntropyMethods inScienceandEngineering, Amboise,France,21–26September2014. 61. NguiffoBoyom,M.;Wolak,R.A.TransverselyHessian foliationsand informationgeometry. Int. J.Math. 2016,27,doi:10.1142/S0129167X16500920. 62. Zeghib,A.OnGromovtheoryofrigid transformationgroups,adualapproach.Ergod. TheoreyDyn. Syst. 2000,20, 935–946. 63. Kamber, F.; Tondeur, P.H. InvariantOperators and the Cohomology of Lie Algebra Sheaves; Memoirs of the AmericanMatheamticalSociety: Providence,RI,USA,1971. 64. Kumpera,A.;Spencer,D.LieEquation;PrincetonUniversityPress: Princeton,NJ,USA,1972. 65. Guts,A.K. (OmskStateUniversity). Privatecommunication. c©2016bytheauthor. LicenseeMDPI,Basel,Switzerland.Thisarticle isanopenaccess articledistributedunder the termsandconditionsof theCreativeCommonsAttribution (CCBY) license (http://creativecommons.org/licenses/by/4.0/). 234
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Differential Geometrical Theory of Statistics
Titel
Differential Geometrical Theory of Statistics
Autoren
Frédéric Barbaresco
Frank Nielsen
Herausgeber
MDPI
Ort
Basel
Datum
2017
Sprache
englisch
Lizenz
CC BY-NC-ND 4.0
ISBN
978-3-03842-425-3
Abmessungen
17.0 x 24.4 cm
Seiten
476
Schlagwörter
Entropy, Coding Theory, Maximum entropy, Information geometry, Computational Information Geometry, Hessian Geometry, Divergence Geometry, Information topology, Cohomology, Shape Space, Statistical physics, Thermodynamics
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Differential Geometrical Theory of Statistics