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Entropy2016,18, 386 180. Letac,G.Lectures onNaturalExponential Families andTheirVarianceFunctions,Volume50ofMonograïŹasde Matematica (MathematicalMonographs); InstitutodeMatematicaPura eAplicada (IMPA):Riode Janeiro, Brazil, 1992. 181. Letac,G.Les famillesexponentiellesstatistiques invariantespar lesgroupesduCĂŽneetduparaboloĂŻdede revolution. In Journal ofAppliedProbability,Volume31,Studies inAppliedProbability;Takacs,L.,Galambos, J., Gani, J.,Eds.;AppliedProbabilityTrust: ShefïŹeld,UK,1994;pp.71–95. 182. Barndorff-Nielsen,O.E.Differential geometryandstatistics: Somemathematical aspects. Indian J.Math. 1987,29, 335–350. 183. Barndorff-Nielsen,O.E.; Jupp,P.E.Yokesandsymplectic structures. J.Stat. Plan Inference1997,63, 133–146. [CrossRef] 184. Barndorff-Nielsen,O.E.; Jupp,P.E.Statistics,yokesandsymplecticgeometry.Annalesde laFacultĂ©des sciences deToulouse:MathĂ©matiques1997,6, 389–427. [CrossRef] 185. Barndorff-Nielsen,O.E. Information andExponential Families in Stattistical Theory;Wiley: NewYork,NY, USA,2014. 186. Jespersen,N.C.B.Onthestructureof transformationmodels.Ann. Stat. 1999,17, 195–208. 187. Skovgaard,L.T.ARiemanniangeometryof themultivariatenormalmodel.Scand. J.Stat. 1984,11, 211–223. 188. Han,M.;Park,F.C.DTIsegmentationandïŹber trackingusingmetricsonmultivariatenormaldistributions. J.Math. ImagingVis. 2014,49, 317–334. [CrossRef] 189. Imai,T.;Takaesu,A.;Wakayama,M.Remarksongeodesics formultivariatenormalmodels. J.Math. Ind. 2011,3, 125–130. 190. Inoue,H.Grouptheoretical studyongeodesics for theellipticalmodels. InGeometricScienceof Information Proceedings;LectureNotes inComputerScience;Springer: Berlin/Heidelberg,Germany,2015;Volume9389, pp.605–614. 191. PiltĂ©,M.;Barbaresco,F.Trackingqualitymonitoringbasedoninformationgeometryandgeodesic shooting. InProceedingsof the17th InternationalRadarSymposium(IRS),Krakow,Poland,10–12May2016;pp.1–6. 192. Eriksen,P.S. (k, 1)Exponential transformationmodels.Scand. J.Stat. 1984,11, 129–145. 193. Eriksen,P.GeodesicsConnectedwith theFisherMetric on theMultivariateNormalManifold; TechnicalReport 86-13; InstituteofElectronicSystems,AalborgUniversity:Aalborg,Denmark,1986. 194. Eriksen,P.S.GeodesicsconnectedwiththeFishermetriconthemultivariatenormalmanifold. InProceedings of theGSTWorkshop,Lancaster,UK,28–31October1987. 195. Feragen,A.; Lauze,F.;Hauberg, S.Geodesic exponential kernels:Whencurvatureand linearity conïŹ‚ict. InProceedingsof the IEEEConferenceonComputerVisionandPatternRecognition(CVPR),8–10June2015; pp.3032–3042. 196. Besse,A.L.EinsteinManifolds,ErgebnissederMathematikund ihreGrenzgebiete; Springer: Berlin/Heidelberg, Germany,1986. 197. Tumpach,A.B. InïŹnite-dimensionalhyperkĂ€hlermanifoldsassociatedwithHermitian-symmetric afïŹne coadjointorbits.Ann. Inst. Fourier2009,59, 167–197. [CrossRef] 198. Tumpach, A.B. ClassiïŹcation of inïŹnite-dimensional Hermitian-symmetric afïŹne coadjoint orbits. ForumMath. 2009,21, 375–393. [CrossRef] 199. Tumpach,A.B. VariĂ©tĂ©s KĂ€hlĂ©riennes etHyperkĂ€hlĂ©riennes deDimension InïŹnie. Ph.D. Thesis, Ecole Polytechnique,Paris,France,26 July2005. 200. Neeb, K.-H. InïŹnite-dimensional groups and their representations. In Lie Theory; BirkhĂ€user: Basel, Switzerland,2004. 201. Gauduchon,P.Calabi’sExtremalKĂ€hlerMetrics:AnElementary Introduction.Availableonline: germanio. math.uniïŹ.it/wp-content/uploads/2015/03/dercalabi.pdf (accessedon27October2016). 202. Biquard,O.;Gauduchon,P.HyperkĂ€hlerMetricsonCotangentBundlesofHermitianSymmetricSpaces. Availableonline: https://www.math.ens.fr/~biquard/aarhus96.pdf (accessedon27October2016). 203. Biquard,O.; Gauduchon, P. LamĂ©trique hyperkĂ€hlĂ©rienne des orbites coadjointes de type symĂ©trique d’ungroupedeLiecomplexesemi-simple.ComptesRendusde l’AcadĂ©miedesSciences1996,323, 1259–1264. (InFrench) 204. Biquard,O.;Gauduchon,P.GĂ©omĂ©triehyperkĂ€hlĂ©riennedesespaceshermitienssymĂ©triquescomplexiïŹĂ©s. SĂ©minairedeThĂ©orieSpectrale etGĂ©omĂ©trie1998,16, 127–173. [CrossRef] 118
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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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