Preface
A graphical model is a statistical model that is associated to a graph. The nodes of the
graph correspond to the random variables of interest, and the edges encode allowed condi-
tional dependencies among the variables. The factorization properties underlying graphical
models facilitate tractable computation with multivariate distributions, making the models
a valuable tool in a plethora of applications. Furthermore, directed graphical models admit
intuitive causal interpretations and have become a cornerstone for causal inference.
While there exist a number of excellent books on graphical models, the field has grown so
much that individual authors can hardly cover its entire scope. Moreover, the field is inter-
disciplinary by nature, with important contributions from a range of disciplines, including
statistics, computer science, electrical engineering, biology, mathematics and philosophy.
Through chapters by leading researchers from these different areas, this handbook provides
a broad and accessible overview of the state of the art.
The book contains a total of twenty-one chapters, grouped into five parts:
I. Conditional independencies and Markov properties
II. Computing with factorizing distributions
III. Statistical inference
IV. Causal inference
V. Applications
Part I reviews the foundations of graphical models. It discusses how graphs can encode
conditional independencies between random variables, or equivalently, a factorization of the
joint distribution of the variables. The main theme of Part II is how to perform efficient
computations based on the joint distribution of a given graphical model, in particular by
leveraging the associated factorization properties. In Part III, the focus of the book shifts to
problems of statistical inference, such as learning the graph and estimating the associated
parameters from available data. Part IV focuses on the causal interpretation of directed
acyclic graphs. The corresponding chapters review fundamental concepts of graphical ap-
proaches to causal inference, and also treat statistical aspects such as learning a directed
acyclic graph from data. Finally, Part V shows how graphical models are used in selected
applied problems in forensic science and biology.
Part I forms the basis of the book. The remaining Parts II through V can be read inde-
pendently, while cross-references between the chapters highlight connections. The topics of
the chapters range from explanations of basic concepts at a level that is suitable to newcom-
ers to descriptions of recent developments or original research. As such, the book targets a
wide audience, including graduate students in statistics, mathematics and computer science,
users of graphical models in applied research, as well as experts on graphical models. Most
of all, we hope that the book will spark further research in this exciting field.
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