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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...
Autores principales: | , , |
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Lenguaje: | eng |
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Springer
2009
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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. |
id | cern-2027681 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2009 |
publisher | Springer |
record_format | invenio |
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 |