Differential geometry and statistics:
Ever since the introduction by Rao in 1945 of the Fisher information metric on a family of probability distributions, there has been interest among statisticians in the application of differential geometry to statistics. This interest has increased rapidly in the last couple of decades with the work...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Chapman & Hall
1993
|
| Edition: | 1. ed. |
| Series: | Monographs on statistics and applied probability
48 |
| Subjects: | |
| Summary: | Ever since the introduction by Rao in 1945 of the Fisher information metric on a family of probability distributions, there has been interest among statisticians in the application of differential geometry to statistics. This interest has increased rapidly in the last couple of decades with the work of a large number of researchers. Until now an impediment to the spread of these ideas into the wider community of statisticians has been the lack of a suitable text introducing the modern coordinate free approach to differential geometry in a manner accessible to statisticians. Differential Geometry and Statistics aims to fill this gap. The authors bring to this book extensive research experience in differential geometry and its application to statistics. The book commences with the study of the simplest differentiable manifolds - affine spaces and their relevance to exponential families, and goes on to the general theory, the Fisher information metric, the Amari connections and asymptotics It culminates in the theory of vector bundles, principal bundles and jets and their applications to the theory of strings - a topic presently at the cutting edge of research in statistics and differential geometry |
| Item Description: | Literaturverz. S. 264 - 266 |
| Physical Description: | XIII, 272 S. |
| ISBN: | 0412398605 |
Staff View
MARC
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| 500 | |a Literaturverz. S. 264 - 266 | ||
| 520 | 3 | |a Ever since the introduction by Rao in 1945 of the Fisher information metric on a family of probability distributions, there has been interest among statisticians in the application of differential geometry to statistics. This interest has increased rapidly in the last couple of decades with the work of a large number of researchers. Until now an impediment to the spread of these ideas into the wider community of statisticians has been the lack of a suitable text introducing the modern coordinate free approach to differential geometry in a manner accessible to statisticians. Differential Geometry and Statistics aims to fill this gap. The authors bring to this book extensive research experience in differential geometry and its application to statistics. The book commences with the study of the simplest differentiable manifolds - affine spaces and their relevance to exponential families, and goes on to the general theory, the Fisher information metric, the Amari connections and asymptotics | |
| 520 | |a It culminates in the theory of vector bundles, principal bundles and jets and their applications to the theory of strings - a topic presently at the cutting edge of research in statistics and differential geometry | ||
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Record in the Search Index
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| author | Murray, Michael K. Rice, John W. |
| author_facet | Murray, Michael K. Rice, John W. |
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| author_sort | Murray, Michael K. |
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| bvnumber | BV009534575 |
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| ctrlnum | (OCoLC)27266305 (DE-599)BVBBV009534575 |
| 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 | Mathematik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV009534575 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:36:40Z |
| institution | BVB |
| isbn | 0412398605 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006296258 |
| oclc_num | 27266305 |
| open_access_boolean | |
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| physical | XIII, 272 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Chapman & Hall |
| record_format | marc |
| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spelling | Murray, Michael K. Verfasser aut Differential geometry and statistics Michael K. Murray and John W. Rice 1. ed. London [u.a.] Chapman & Hall 1993 XIII, 272 S. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 48 Literaturverz. S. 264 - 266 Ever since the introduction by Rao in 1945 of the Fisher information metric on a family of probability distributions, there has been interest among statisticians in the application of differential geometry to statistics. This interest has increased rapidly in the last couple of decades with the work of a large number of researchers. Until now an impediment to the spread of these ideas into the wider community of statisticians has been the lack of a suitable text introducing the modern coordinate free approach to differential geometry in a manner accessible to statisticians. Differential Geometry and Statistics aims to fill this gap. The authors bring to this book extensive research experience in differential geometry and its application to statistics. The book commences with the study of the simplest differentiable manifolds - affine spaces and their relevance to exponential families, and goes on to the general theory, the Fisher information metric, the Amari connections and asymptotics It culminates in the theory of vector bundles, principal bundles and jets and their applications to the theory of strings - a topic presently at the cutting edge of research in statistics and differential geometry Geometri, Diferensiyel Géométrie différentielle ram Matematiksel istatistik Meetkunde gtt Statistiek gtt Statistique mathématique ram application statistique inriac courbure inriac géométrie différentielle inriac statistique inriac Statistik Geometry, Differential Mathematical statistics 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 Rice, John W. Verfasser aut Monographs on statistics and applied probability 48 (DE-604)BV002494005 48 |
| spellingShingle | Murray, Michael K. Rice, John W. Differential geometry and statistics Monographs on statistics and applied probability Geometri, Diferensiyel Géométrie différentielle ram Matematiksel istatistik Meetkunde gtt Statistiek gtt Statistique mathématique ram application statistique inriac courbure inriac géométrie différentielle inriac statistique inriac Statistik Geometry, Differential Mathematical statistics Differentialgeometrie (DE-588)4012248-7 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4056995-0 |
| title | Differential geometry and statistics |
| title_auth | Differential geometry and statistics |
| title_exact_search | Differential geometry and statistics |
| title_full | Differential geometry and statistics Michael K. Murray and John W. Rice |
| title_fullStr | Differential geometry and statistics Michael K. Murray and John W. Rice |
| title_full_unstemmed | Differential geometry and statistics Michael K. Murray and John W. Rice |
| title_short | Differential geometry and statistics |
| title_sort | differential geometry and statistics |
| topic | Geometri, Diferensiyel Géométrie différentielle ram Matematiksel istatistik Meetkunde gtt Statistiek gtt Statistique mathématique ram application statistique inriac courbure inriac géométrie différentielle inriac statistique inriac Statistik Geometry, Differential Mathematical statistics Differentialgeometrie (DE-588)4012248-7 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Geometri, Diferensiyel Géométrie différentielle Matematiksel istatistik Meetkunde Statistiek Statistique mathématique application statistique courbure géométrie différentielle statistique Statistik Geometry, Differential Mathematical statistics Differentialgeometrie |
| volume_link | (DE-604)BV002494005 |
| work_keys_str_mv | AT murraymichaelk differentialgeometryandstatistics AT ricejohnw differentialgeometryandstatistics |