Methods of information geometry:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Japanese |
| Published: |
Providence, RI
American Math. Soc. [u.a.]
2000
|
| Series: | Translations of mathematical monographs
191 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | X, 206 S. graph. Darst. |
| ISBN: | 0821805312 9780821843024 |
Staff View
MARC
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| 245 | 1 | 0 | |a Methods of information geometry |c Shun-ichi Amari ; Hiroshi Nagaoka |
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Record in the Search Index
| _version_ | 1804128704313425920 |
|---|---|
| adam_text | TRANSLATIONS OF MATHEMATICAL MONOGRAPHS VOLUME 191 METHODS OF
INFORMATION GEOMETRY SHUN-ICHI AMARI HIROSHI NAGAOKA TRANSLATED BY
DAISHI HARADA IAMS OXFORD AMERICAN MATHEMATICAL SOCIETY UNIVERSITY PRESS
CONTENTS PREFACE VII PREFACE TO THE ENGLISH EDITION IX 1 ELEMENTARY
DIFFERENTIAL GEOMETRY 1 1.1 DIFFERENTIABLE MANIFOLDS 1 1.2 TANGENT
VECTORS AND TANGENT SPACES 5 1.3 VECTOR FIELDS AND TENSOR FIELDS 8 1.4
SUBMANIFOLDS 10 1.5 RIEMANNIAN METRICS 11 1.6 AFFINE CONNECTIONS AND
COVARIANT DERIVATIVES 13 1.7 FLATNESS 17 1.8 AUTOPARALLEL SUBMANIFOLDS
19 1.9 PROJECTION OF CONNECTIONS AND EMBEDDING CURVATURE 22 1.10
RIEMANNIAN CONNECTION 23 2 THE GEOMETRIC STRUCTURE OF STATISTICAL MODELS
25 2.1 STATISTICAL MODELS 25 2.2 THE FISHER METRIC 28 2.3 THE
A-CONNECTION 32 2.4 CHENTSOV S THEOREM AND SOME HISTORICAL REMARKS 37
2.5 THE GEOMETRY OF V(X) 40 2.6 A-AFFINE MANIFOLDS AND A-FAMILIES 45 3
DUAL CONNECTIONS 51 3.1 DUALITY OF CONNECTIONS 51 3.2 DIVERGENCES:
GENERAL CONTRAST FUNCTIONS 53 3.3 DUALLY FLAT SPACES 58 3.4 CANONICAL
DIVERGENCE 61 3.5 THE DUALISTIC STRUCTURE OF EXPONENTIAL FAMILIES 65 3.6
THE DUALISTIC STRUCTURE OF A-AFFINE MANIFOLDS AND A-FAMILIES ... 70 3.7
MUTUALLY DUAL FOLIATIONS 75 3.8 A FURTHER LOOK AT THE TRIANGULAR
RELATION 77 VI CONTENTS 4 STATISTICAL INFERENCE AND DIFFERENTIAL
GEOMETRY 81 4.1 ESTIMATION BASED ON INDEPENDENT OBSERVATIONS 81 4.2
EXPONENTIAL FAMILIES AND OBSERVED POINTS 85 4.3 CURVED EXPONENTIAL
FAMILIES 87 4.4 CONSISTENCY AND FIRST-ORDER EFFICIENCY 89 4.5
HIGHER-ORDER ASYMPTOTIC THEORY OF ESTIMATION 94 4.6 ASYMPTOTICS OF
FISHER INFORMATION 97 4.7 HIGHER-ORDER ASYMPTOTIC THEORY OF TESTS 100
4.8 THE THEORY OF ESTIMATING FUNCTIONS AND FIBER BUNDLES 107 4.8.1 THE
FIBER BUNDLE OF LOCAL EXPONENTIAL FAMILIES 107 4.8.2 HILBERT BUNDLES AND
ESTIMATING FUNCTIONS 109 5 THE GEOMETRY OF TIME SERIES AND LINEAR
SYSTEMS 115 5.1 THE SPACE OF SYSTEMS AND TIME SERIES 115 5.2 THE FISHER
METRIC AND THE A-CONNECTION ON THE SYSTEM SPACE . . 118 5.3 THE GEOMETRY
OF FINITE-DIMENSIONAL MODELS 123 5.4 STABLE SYSTEMS AND STABLE FEEDBACK
127 6 MULTITERMINAL INFORMATION THEORY AND STATISTICAL INFERENCE 133 6.1
STATISTICAL INFERENCE FOR MULTITERMINAL INFORMATION 133 6.2 0-RATE
TESTING 136 6.3 0-RATE ESTIMATION 140 6.4 INFERENCE FOR GENERAL
MULTITERMINAL INFORMATION 142 7 INFORMATION GEOMETRY FOR QUANTUM SYSTEMS
145 7.1 THE QUANTUM STATE SPACE 145 7.2 THE GEOMETRIC STRUCTURE INDUCED
FROM A QUANTUM DIVERGENCE . . 150 7.3 THE GEOMETRIC STRUCTURE INDUCED
FROM A GENERALIZED COVARIANCE . 154 7.4 APPLICATIONS TO QUANTUM
ESTIMATION THEORY 159 8 MISCELLANEOUS TOPICS 167 8.1 THE GEOMETRY OF
CONVEX ANALYSIS, LINEAR PROGRAMMING AND GRADI- ENT FLOWS 167 8.2
NEURO-MANIFOLDS AND NONLINEAR SYSTEMS 170 8.3 LIE GROUPS AND
TRANSFORMATION MODELS IN INFORMATION GEOMETRY . 172 8.4 MATHEMATICAL
PROBLEMS POSED BY INFORMATION GEOMETRY 175 GUIDE TO THE BIBLIOGRAPHY 181
BIBLIOGRAPHY 187 INDEX 203
|
| any_adam_object | 1 |
| author | Amari, Shun'ichi 1936- Nagaoka, Hiroshi |
| author_GND | (DE-588)1055752951 |
| author_facet | Amari, Shun'ichi 1936- Nagaoka, Hiroshi |
| author_role | aut aut |
| author_sort | Amari, Shun'ichi 1936- |
| author_variant | s a sa h n hn |
| building | Verbundindex |
| bvnumber | BV013869294 |
| callnumber-first | Q - Science |
| callnumber-label | QA276 |
| callnumber-raw | QA276 |
| callnumber-search | QA276 |
| callnumber-sort | QA 3276 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 370 ST 515 |
| ctrlnum | (OCoLC)248089639 (DE-599)BVBBV013869294 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV013869294 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:53:28Z |
| institution | BVB |
| isbn | 0821805312 9780821843024 |
| language | English Japanese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009486666 |
| oclc_num | 248089639 |
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| physical | X, 206 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | American Math. Soc. [u.a.] |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Amari, Shun'ichi 1936- Verfasser (DE-588)1055752951 aut Joho kika no hoho Methods of information geometry Shun-ichi Amari ; Hiroshi Nagaoka Providence, RI American Math. Soc. [u.a.] 2000 X, 206 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 191 Hier auch später erschienene, unveränderte Nachdrucke Aus dem Japan. übers. Differentialgeometrie - Statistik Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s Statistik (DE-588)4056995-0 s DE-604 Nagaoka, Hiroshi Verfasser aut Translations of mathematical monographs 191 (DE-604)BV000002394 191 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009486666&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Amari, Shun'ichi 1936- Nagaoka, Hiroshi Methods of information geometry Translations of mathematical monographs Differentialgeometrie - Statistik Differentialgeometrie (DE-588)4012248-7 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4056995-0 |
| title | Methods of information geometry |
| title_alt | Joho kika no hoho |
| title_auth | Methods of information geometry |
| title_exact_search | Methods of information geometry |
| title_full | Methods of information geometry Shun-ichi Amari ; Hiroshi Nagaoka |
| title_fullStr | Methods of information geometry Shun-ichi Amari ; Hiroshi Nagaoka |
| title_full_unstemmed | Methods of information geometry Shun-ichi Amari ; Hiroshi Nagaoka |
| title_short | Methods of information geometry |
| title_sort | methods of information geometry |
| topic | Differentialgeometrie - Statistik Differentialgeometrie (DE-588)4012248-7 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Differentialgeometrie - Statistik Differentialgeometrie Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009486666&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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