Verfügbarkeit: Lectures on algebraic statistics | Technische Universität München

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Bibliographische Detailangaben
Beteiligte Personen:	Drton, Mathias 1975- (VerfasserIn), Sturmfels, Bernd 1962- (VerfasserIn), Sullivant, Seth (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Basel [u.a.] Birkhäuser 2009
Schriftenreihe:	Oberwolfach seminars 39
Schlagwörter:	Algebra Mathematical statistics Algebraische Methode Statistik Oberwolfach Konferenzschrift > 2008 > Oberwolfach
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016966595&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016966595&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	VIII, 171 S. graph. Darst.
ISBN:	9783764389048 9783764389055

Internformat

MARC


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Datensatz im Suchindex

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adam_text	How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semi-algebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models. CONTENTS PREFACE VII 1 MARKOV BASES 1 1.1 HYPOTHESIS TESTS FOR CONTINGENCY TABLES . . . . . . . . . . . . . . . 1 1.2 MARKOV BASES OF HIERARCHICAL MODELS . . . . . . . . . . . . . . . . . 11 1.3 THE MANY BASES OF AN INTEGER LATTICE . . . . . . . . . . . . . . . . 19 2 LIKELIHOOD INFERENCE 29 2.1 DISCRETE AND GAUSSIAN MODELS . . . . . . . . . . . . . . . . . . . . . 29 2.2 LIKELIHOOD EQUATIONS FOR IMPLICIT MODELS . . . . . . . . . . . . . . 40 2.3 LIKELIHOOD RATIO TESTS . . . . . . . . . . . . . . . . . . . . . . . . . 48 3 CONDITIONAL INDEPENDENCE 61 3.1 CONDITIONAL INDEPENDENCE MODELS . . . . . . . . . . . . . . . . . . . 61 3.2 GRAPHICAL MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.3 PARAMETRIZATIONS OF GRAPHICAL MODELS . . . . . . . . . . . . . . . . 79 4 HIDDEN VARIABLES 89 4.1 SECANT VARIETIES IN STATISTICS . . . . . . . . . . . . . . . . . . . . . . 89 4.2 FACTOR ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5 BAYESIAN INTEGRALS 105 5.1 INFORMATION CRITERIA AND ASYMPTOTICS . . . . . . . . . . . . . . . . 105 5.2 EXACT INTEGRATION FOR DISCRETE MODELS . . . . . . . . . . . . . . . . 114 6 EXERCISES 123 6.1 MARKOV BASES FIXING SUBTABLE SUMS . . . . . . . . . . . . . . . . . 123 6.2 QUASI-SYMMETRY AND CYCLES . . . . . . . . . . . . . . . . . . . . . . 128 6.3 A COLORED GAUSSIAN GRAPHICAL MODEL . . . . . . . . . . . . . . . . 131 6.4 INSTRUMENTAL VARIABLES AND TANGENT CONES . . . . . . . . . . . . . . 135 6.5 FISHER INFORMATION FOR MULTIVARIATE NORMALS . . . . . . . . . . . . . 142 6.6 THE INTERSECTION AXIOM AND ITS FAILURE . . . . . . . . . . . . . . . . 144 6.7 PRIMARY DECOMPOSITION FOR CI INFERENCE . . . . . . . . . . . . . . . 147 6.8 AN INDEPENDENCE MODEL AND ITS MIXTURE . . . . . . . . . . . . . . . 150 7 OPEN PROBLEMS 157 BIBLIOGRAPHY 165
any_adam_object	1
author	Drton, Mathias 1975- Sturmfels, Bernd 1962- Sullivant, Seth
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discipline	Mathematik Wirtschaftswissenschaften
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series	Oberwolfach seminars
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spellingShingle	Drton, Mathias 1975- Sturmfels, Bernd 1962- Sullivant, Seth Lectures on algebraic statistics Oberwolfach seminars Algebra Mathematical statistics Algebraische Methode (DE-588)4141841-4 gnd Statistik (DE-588)4056995-0 gnd
subject_GND	(DE-588)4141841-4 (DE-588)4056995-0 (DE-588)4101961-1 (DE-588)1071861417
title	Lectures on algebraic statistics
title_auth	Lectures on algebraic statistics
title_exact_search	Lectures on algebraic statistics
title_full	Lectures on algebraic statistics Mathias Drton ; Bernd Sturmfels ; Seth Sullivant
title_fullStr	Lectures on algebraic statistics Mathias Drton ; Bernd Sturmfels ; Seth Sullivant
title_full_unstemmed	Lectures on algebraic statistics Mathias Drton ; Bernd Sturmfels ; Seth Sullivant
title_short	Lectures on algebraic statistics
title_sort	lectures on algebraic statistics
topic	Algebra Mathematical statistics Algebraische Methode (DE-588)4141841-4 gnd Statistik (DE-588)4056995-0 gnd
topic_facet	Algebra Mathematical statistics Algebraische Methode Statistik Oberwolfach Konferenzschrift 2008 Oberwolfach
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016966595&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016966595&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV019806550
work_keys_str_mv	AT drtonmathias lecturesonalgebraicstatistics AT sturmfelsbernd lecturesonalgebraicstatistics AT sullivantseth lecturesonalgebraicstatistics

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