Lectures on Algebraic Statistics

Front Cover
Springer Science & Business Media, Dec 10, 2008 - Mathematics - 172 pages

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

Likelihood Inference
29
Conditional Independence 61
60
Hidden Variables
89
Bayesian Integrals
105
Exercises
123
Open Problems
157
Bibliography 165
164
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information