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Lectures on algebraic statistics

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 s...

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Detalles Bibliográficos
Autores principales: Drton, Mathias, Sturmfels, Bernd, Sullivant, Seth
Lenguaje:eng
Publicado: Springer 2009
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-7643-8905-5
http://cds.cern.ch/record/2027681
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author Drton, Mathias
Sturmfels, Bernd
Sullivant, Seth
author_facet Drton, Mathias
Sturmfels, Bernd
Sullivant, Seth
author_sort Drton, Mathias
collection CERN
description 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.
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spelling cern-20276812021-04-21T20:11:00Zdoi:10.1007/978-3-7643-8905-5http://cds.cern.ch/record/2027681engDrton, MathiasSturmfels, BerndSullivant, SethLectures on algebraic statisticsMathematical Physics and MathematicsHow 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.Springeroai:cds.cern.ch:20276812009
spellingShingle Mathematical Physics and Mathematics
Drton, Mathias
Sturmfels, Bernd
Sullivant, Seth
Lectures on algebraic statistics
title Lectures on algebraic statistics
title_full Lectures on algebraic statistics
title_fullStr Lectures on algebraic statistics
title_full_unstemmed Lectures on algebraic statistics
title_short Lectures on algebraic statistics
title_sort lectures on algebraic statistics
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-7643-8905-5
http://cds.cern.ch/record/2027681
work_keys_str_mv AT drtonmathias lecturesonalgebraicstatistics
AT sturmfelsbernd lecturesonalgebraicstatistics
AT sullivantseth lecturesonalgebraicstatistics