Page - 323 - in Differential Geometrical Theory of Statistics
Image of the Page - 323 -
Text of the Page - 323 -
Entropy2017,19, 7
Acknowledgments: This researchwaspartiallysupportedbyJSPS(JapanSociety for thePromotionofScience),
KAKENHI(Grants-in-AidforScientificResearch)GrantNumbers JP26108003andJP15K04842.
Conflictsof Interest:Theauthordeclaresnoconflictof interest.
References
1. Tsallis,C. Introduction toNonextensiveStatisticalMechanics:ApproachingaComplexWorld; Springer:NewYork,
NY,USA,2009.
2. Naudts, J. GeneralisedThermostatistics; Springer: London,UK,2011.
3. Kaniadakis,G. Theoretical foundations andmathematical formalismof thepower-law tailed statistical
distributions. Entropy2013,15, 3983–4010.
4. Beck, C.; Schlögl, F. Thermodynamics of Chaotic Systems: An Introduction; CambridgeUniversity Press:
Cambridge,UK,1993.
5. Naudts, J. Estimators, escortprobabilities, andφ-exponential families instatisticalphysics. J. Inequal. Pure
Appl.Math. 2004,5, 102.
6. Matsuzoe,H.;Henmi,M.Hessianstructuresanddivergence functionsondeformedexponential families.
InGeometricTheory of Information, Signals andCommunicationTechnology;Nielsen, F., Ed.; Springer: Basel,
Switzerland,2014;pp. 57–80.
7. Sakamoto,M.;Matsuzoe,H.Ageneralizationof independenceandmultivariateStudent’s t-distributions.
InGeometricScienceof Information,ProceedingsofSecondInternationalConferenceonGeometricScienceof
Information(GSI2015),Palaiseau,France,28–30October2015;Volume9389,pp. 740–749.
8. Matsuzoe,H.;Wada,T. Deformedalgebrasandgeneralizationsof independenceondeformedexponential
families. Entropy2015,17, 5729–5751.
9. Wada,T.;Matsuzoe,H.;Scarfone,A.M. Dualistichessianstructuresamongthe thermodynamicpotentials in
theκ-Thermostatistics. Entropy2015,17, 7213–7229.
10. Matsuzoe,H. Statisticalmanifoldsandgeometryofestimating functions. InProspects ofDifferentialGeometry
andItsRelatedFields,Proceedingsofthe3rdInternationalColloquiumonDifferentialGeomentryandItsRelatedFields,
VelikoTarnovo,Bulgaria, 3–7September2012;Adachi,T.,Hashimoto,H.,Hristov,M.J.,Eds.;WorldScientific:
Hackensack,NJ,USA,2013;pp. 187–202.
11. Matsuzoe,H.;Henmi,M. Hessian structures ondeformedexponential families. InGeometric Science of
Information,ProceedingsofFirst InternationalConferenceonGeometricScienceof Information (GSI2013),Paris,
France,28–30August2013; Springer: Berlin/Heidelberg,Germany,2015;Volume8085,pp. 275–282.
12. Eguchi,S.;Komori,O. Pathconnectednessonaspaceofprobabilitydensity functions. InGeometricScience
of Information, Proceedings of Second InternationalConference onGeometric Science of Information (GSI 2015),
Palaiseau,France, 28–30October2015; Springer: Berlin/Heidelberg,Germany,2015;Volume9389,pp.615–624.
13. Scarfone, A.M.; Matsuzoe, H.; Wada, T. Consistency of the structure of Legendre transform in
thermodynamicswith theKolmogorov-Nagumoaverage. Phys. Lett. A2016,380, 3022–3028.
14. Tsallis,C.Whatare thenumbers thatexperimentsprovide? Quim.Nova1994,17, 468–471.
15. Zhang, J. Onmonotoneembedding in informationgeometry. Entropy2015,17, 4485–4499.
16. TanakaM.Meaningofanescortdistributionandτ-transformation. J.Phys. Conf. Ser. 2010,201, 012007.
17. Murata, N.; Takenouchi, T.; Kanamori, T.; Eguchi, S. Information geometry ofU-boost and Bregman
divergence. NeuralComput. 2004,16, 1437–1481.
18. Kurose,T. Onthedivergencesof1-conformallyflatstatisticalmanifolds. TôhokuMath. J.1994,46, 427–433.
19. Matsuzoe,H. Statisticalmanifoldsandaffinedifferentialgeometry. Adv. Stud. PureMath. 2010,57, 303–321.
20. Lauritzen,S.L. Statisticalmanifolds. InDifferentialGeometry inStatistical Inferences;Gupta,S.S.,Ed.; IMS
Lecture Notes Monograph Series 10; Institute of Mathematical Statistics: Hayward, CA, USA, 1987;
pp.96–163.
21. Amari,S.;Nagaoka,H.Methodof InformationGeometry;TranslationsofMathematicalMonographs;American
MathematicalSociety: Providence,RI,USA;OxfordUniversityPress:Oxford,UK,2000.
22. Amari,S. InformationGeometryandItsApplications; Springer: Tokyo, Japan,2016.
23. Amari,S.;Ohara,A.;Matsuzoe,H. Geometryofdeformedexponential families: Invariant,dually-flatand
conformalgeometry. PhysicaA2012,391, 4308–4319.
323
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