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Handbook of Graphical Models

Marloes Maathuis, Mathias Drton, Steffen Lauritzen, and Martin Wainwright
Chapman and Hall/CRC
Publication Date: 
Number of Pages: 
[Reviewed by
Grant Innerst
, on
A graphical model is a statistical model that represents probability distributions as a graph, where the edges represent a conditional independence structure between random variables. Graphical models have been applied in a wide range of disciplines this book reflects that fact. This book is a collection of chapters that attempts to encompass the entire scope of graphical models.
The editors group the book into five parts: (1) Conditional Independence and Markov Properties, (2) Computing with factorizing distributions, (3) Statistical inference, (4) Causal Inference, and (5) Applications. Part 1 is meant to provide an understanding of the foundations of graphical models, while parts 2-4 offer discussions of the major topics in the graphical model literature. Compared to other texts on graphical models, this book contains a large section on causal inference, part 4, an area of research that has received a lot of attention lately. Lastly, part 5 discusses applications of graphical models in applied problems from biology and forensic science.
It is not recommended that the parts of this book, or even the chapters within the parts are read sequentially. Like most handbooks, each chapter is written by separate authors. Consistent with the theme of this book, the authors are from a wide range of disciplines. This leads to chapters that are written with different styles, notation choices, and assumptions about the reader's familiarity with the subject. Rather than an expository text on graphical models, this book is intended for a mathematically mature audience looking for a reference text on the current methods in graphical models. To that end, the coverage of most topics are theoretical in nature, containing few examples or mentions of applications. It is likely that introductory readers may find many of the chapters intimidating.
Overall, this book is an excellent reference text on a wide range of topics in graphical models for those familiar with the area.
Grant Innerst is an Assistant Professor of Mathematics at Shippensburg University. He is a trained statistician interested in statistics education and algebraic statistics.