Algebraic statistics: computational commutative algebra in statistics
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall / CRC
2001
|
| Schriftenreihe: | Monographs on statistics and applied probability
89 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 160 S. |
| ISBN: | 1584882042 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | ALGEBRAIC STATISTICS COMPUTATIONAL COMMUTATIVE ALGEBRA IN STATISTICS
GIOVANNI PISTONE EVA RICCOMAGNO HENRY P. WYNN CHAPMAN & HALL/CRC BOCA
RATON LONDON NEW YORK WASHINGTON, D.C. CONTENTS LIST OF FIGURES IX LIST
OF TABLES XI PREFACE XIII NOTATION XV 1 INTRODUCTION 1 1.1 OUTLINE 1 1.2
COMPUTER ALGEBRA 5 1.3 AN EXAMPLE: THE 2 3 1 FRACTIONAL FACTORIAL
DESIGN 10 2 ALGEBRAIC MODELS 15 2.1 MODELS 16 2.2 POLYNOMIAL IDEALS 17
2.3 TERM-ORDERINGS 19 2.4 DIVISION ALGORITHM 22. 2.5 HILBERT BASIS
THEOREM 23 2.6 VARIETIES AND EQUATIONS 25 2.7 GROBNER BASES 27 2.8
PROPERTIES OF A GROBNER BASIS 29 2.9 ELIMINATION THEORY 31 2.10
POLYNOMIAL FUNCTIONS AND QUOTIENTS BY IDEALS 33 2.11 HILBERT FUNCTION 35
2.12 FURTHER TOPICS 36 3 GROBNER BASES IN EXPERIMENTAL DESIGN 43 3.1
DESIGNS AND DESIGN IDEALS 43 3.2 COMPUTING THE GROBNER BASIS OF A DESIGN
44 3.3 OPERATIONS WITH DESIGNS 47 3.4 EXAMPLES 48 3.5 SPAN OF A DESIGN
50 3.6 MODELS AND IDENTIFIABILITY: QUOTIENTS 53 CONTENTS 3.7 CONFOUNDING
OF MODELS 54 3.8 FURTHER EXAMPLES 56 3.9 THE FAN OF AN EXPERIMENTAL
DESIGN 60 3.10 MINIMAL AND MAXIMAL FAN DESIGNS 63 3.11 HILBERT FUNCTIONS
AND FANS FOR GRADED ORDERING 65 3.12 SUBSETS AND ALGORITHMS 66 3.13
REGRESSION ANALYSIS 71 3.14 NON-POLYNOMIAL MODELS 72 4 TWO-LEVEL
FACTORS: LOGIC, RELIABILITY, DESIGN 75 4.1 THE BINARY CASE: BOOLEAN
REPRESENTATIONS 75 V 4.2 GROBNER BASES AND BOOLEAN IDEALS 78 4.3 LOGIC
AND LEARNING 80 4.4 RELIABILITY: COHERENT SYSTEMS AS MINIMAL FAN DESIGNS
81 4.5 INCLUSION-EXCLUSION AND TUBE THEORY 83 4.6 TWO-LEVEL FACTORIAL
DESIGN: CONTRASTS AND ORTHOGONALITY 90 5 PROBABILITY 95 5.1 RANDOM
VARIABLES ON A FINITE SUPPORT 96 5.2 THE RING OF RANDOM VARIABLES 97 5.3
MATRIX REPRESENTATION OF C(D,FC) 99 5.4 UNIFORM PROBABILITY 101 5.5
PROBABILITY DENSITIES 103 5.6 IMAGE PROBABILITY AND MARGINALISATION 106
5.7 CONDITIONAL EXPECTATION 108 5.8 ALGEBRAIC REPRESENTATION OF
EXPONENTIALS 111 5.9 EXPONENTIAL FORM OF A PROBABILITY 113 6 STATISTICAL
MODELING 119 6.1 INTRODUCTION 119 6.2 STATISTICAL MODELS 120 6.3
GENERATING FUNCTIONS AND EXPONENTIAL SUBMODELS 128 6.4 LIKELIHOODS AND
SUFFICIENT STATISTICS 131 6.5 SCORE FUNCTION AND INFORMATION 135 6.6
ESTIMATION: LATTICE CASE 136 6.7 FINITELY GENERATED CUMULANTS 138 6.8
ESTIMATING FUNCTIONS 139 6.9 AN EXTENDED EXAMPLE 140 6.10 ORTHOGONALITY
AND TORIC IDEALS 149 REFERENCES 155 INDEX 159
|
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| author | Pistone, Giovanni Riccomagno, Eva Wynn, Henry P. 1945- |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)45121691 (DE-599)BVBBV013845956 |
| dewey-full | 519.5 519.521 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 519.5 21 |
| dewey-search | 519.5 519.5 21 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:53:04Z |
| institution | BVB |
| isbn | 1584882042 |
| language | English |
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| physical | XVII, 160 S. |
| publishDate | 2001 |
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| publishDateSort | 2001 |
| publisher | Chapman & Hall / CRC |
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| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spelling | Pistone, Giovanni Verfasser (DE-588)139663312 aut Algebraic statistics computational commutative algebra in statistics Giovanni Pistone ; Eva Riccomagno ; Henry P. Wynn Boca Raton [u.a.] Chapman & Hall / CRC 2001 XVII, 160 S. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 89 Mathematical statistics Algebra Statistik (DE-588)4056995-0 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 s Algorithmus (DE-588)4001183-5 s Statistik (DE-588)4056995-0 s DE-604 Riccomagno, Eva Verfasser (DE-588)1175133000 aut Wynn, Henry P. 1945- Verfasser (DE-588)139664033 aut Monographs on statistics and applied probability 89 (DE-604)BV002494005 89 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009470263&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pistone, Giovanni Riccomagno, Eva Wynn, Henry P. 1945- Algebraic statistics computational commutative algebra in statistics Monographs on statistics and applied probability Mathematical statistics Algebra Statistik (DE-588)4056995-0 gnd Algorithmus (DE-588)4001183-5 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4001183-5 (DE-588)4164821-3 |
| title | Algebraic statistics computational commutative algebra in statistics |
| title_auth | Algebraic statistics computational commutative algebra in statistics |
| title_exact_search | Algebraic statistics computational commutative algebra in statistics |
| title_full | Algebraic statistics computational commutative algebra in statistics Giovanni Pistone ; Eva Riccomagno ; Henry P. Wynn |
| title_fullStr | Algebraic statistics computational commutative algebra in statistics Giovanni Pistone ; Eva Riccomagno ; Henry P. Wynn |
| title_full_unstemmed | Algebraic statistics computational commutative algebra in statistics Giovanni Pistone ; Eva Riccomagno ; Henry P. Wynn |
| title_short | Algebraic statistics |
| title_sort | algebraic statistics computational commutative algebra in statistics |
| title_sub | computational commutative algebra in statistics |
| topic | Mathematical statistics Algebra Statistik (DE-588)4056995-0 gnd Algorithmus (DE-588)4001183-5 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| topic_facet | Mathematical statistics Algebra Statistik Algorithmus Kommutative Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009470263&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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