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Lectures on Algebraic Statistics

  • Mathias Drton
  • Bernd Sturmfels
  • Seth Sullivant

Part of the Oberwolfach Seminars book series (OWS, volume 39)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Pages 1-28
  3. Pages 29-59
  4. Pages 89-104
  5. Pages 105-121
  6. Pages 123-156
  7. Pages 157-163
  8. Back Matter
    Pages 165-172

About this book

Introduction

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.

Keywords

Factor analysis Grad Likelihood Parameter algebraic geometry algebraic statistics statistics

Authors and affiliations

  • Mathias Drton
    • 1
  • Bernd Sturmfels
    • 2
  • Seth Sullivant
    • 3
  1. 1.University of ChicagoDepartment StatisticsChicagoUSA
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  3. 3.Department of MathematicsNorth Carolina State UniversityRaleighUSA

Bibliographic information

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