Softcover ISBN:  9781470475109 
Product Code:  GSM/194.S 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
eBook ISBN:  9781470449803 
Product Code:  GSM/194.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470475109 
eBook: ISBN:  9781470449803 
Product Code:  GSM/194.S.B 
List Price:  $174.00 $131.50 
MAA Member Price:  $156.60 $118.35 
AMS Member Price:  $139.20 $105.20 
Softcover ISBN:  9781470475109 
Product Code:  GSM/194.S 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
eBook ISBN:  9781470449803 
Product Code:  GSM/194.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470475109 
eBook ISBN:  9781470449803 
Product Code:  GSM/194.S.B 
List Price:  $174.00 $131.50 
MAA Member Price:  $156.60 $118.35 
AMS Member Price:  $139.20 $105.20 

Book DetailsGraduate Studies in MathematicsVolume: 194; 2018; 490 ppMSC: Primary 62; 14; 13; 52; 60
Algebraic statistics uses tools from algebraic geometry, commutative algebra, combinatorics, and their computational sides to address problems in statistics and its applications. The starting point for this connection is the observation that many statistical models are semialgebraic sets. The algebra/statistics connection is now over twenty years old, and this book presents the first broad introductory treatment of the subject. Along with background material in probability, algebra, and statistics, this book covers a range of topics in algebraic statistics including algebraic exponential families, likelihood inference, Fisher's exact test, bounds on entries of contingency tables, design of experiments, identifiability of hidden variable models, phylogenetic models, and model selection. With numerous examples, references, and over 150 exercises, this book is suitable for both classroom use and independent study.
ReadershipGraduate students and researchers interested in algebraic statistics and its applications.

Table of Contents

Chapters

Introduction

Probability Primer

Algebra Primer

Conditional Independence

Statistics Primer

Exponential Families

Likelihood Inference

The Cone of Sufficient Statistics

Fisher’s Exact Test

Bounds on Cell Entries

Exponential Random Graph Models

Design of Experiments

Graphical Models

Hidden Variables

Phylogenetic Models

Identifiability

Model Selection and Bayesian Integrals

MAP Estimation and Parametric Inference

Finite Metric Spaces


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Algebraic statistics uses tools from algebraic geometry, commutative algebra, combinatorics, and their computational sides to address problems in statistics and its applications. The starting point for this connection is the observation that many statistical models are semialgebraic sets. The algebra/statistics connection is now over twenty years old, and this book presents the first broad introductory treatment of the subject. Along with background material in probability, algebra, and statistics, this book covers a range of topics in algebraic statistics including algebraic exponential families, likelihood inference, Fisher's exact test, bounds on entries of contingency tables, design of experiments, identifiability of hidden variable models, phylogenetic models, and model selection. With numerous examples, references, and over 150 exercises, this book is suitable for both classroom use and independent study.
Graduate students and researchers interested in algebraic statistics and its applications.

Chapters

Introduction

Probability Primer

Algebra Primer

Conditional Independence

Statistics Primer

Exponential Families

Likelihood Inference

The Cone of Sufficient Statistics

Fisher’s Exact Test

Bounds on Cell Entries

Exponential Random Graph Models

Design of Experiments

Graphical Models

Hidden Variables

Phylogenetic Models

Identifiability

Model Selection and Bayesian Integrals

MAP Estimation and Parametric Inference

Finite Metric Spaces