Handbook of Graphical Models

A graphical model is a statistical model that isrepresented bya graph. The factorization properties underlying graphical models facilitate tractable computation with multivariate distributions, making the models a valuable tool with a plethora of applications. Furthermore, directed graphical models allow 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 interdisciplinary by nature. Through chapters by leading researchers from different areas, this handbook provides a broad and accessible overview of the state of the art. Key features: * Contributions by leading researchers from a range of disciplines * Structured in five parts, covering foundations, computational aspects, statistical inference, causal inference, and applications * Balanced coverage of concepts, theory, methods, examples, and applications * Chapters can be read mostly independently, while cross-references highlight connections The handbook is targeted at a wide audience, including graduate students, applied researchers, and experts in graphical models.

Part I Conditional independencies and Markov properties Conditional Independence and Basic Markov Properties - Milan Studený Markov Properties for Mixed Graphical Models - Robin Evans Algebraic Aspects of Conditional Independence and Graphical Models - Thomas Kahle, Johannes Rauh, and Seth Sullivant Part II Computing with factorizing distributions Algorithms and Data Structures for Exact Computation of Marginals - Jeffrey A. Bilmes Approximate methods for calculating marginals and likelihoods - Nicholas Ruozzi MAP Estimation: Linear Programming Relaxation and Message-Passing Algorithms - Ofer Meshi and Alexander G. Schwing Sequential Monte Carlo Methods - Arnaud Doucet and Anthony Lee PartIII Statistical inference Discrete Graphical Models and their Parametrization - Luca La Rocca and Alberto Roverato Gaussian Graphical Models - Caroline Uhler Bayesian inference in Graphical Gaussian Models - Hélène Massam Latent tree models - Piotr Zwiernik Neighborhood selection methods - Po-Ling Loh Nonparametric Graphical Models - Han Liu and John Laerty Inference in high-dimensional graphical models - Jana Janková and Sara van de Geer Part IV Causal inference Causal Concepts and Graphical Models - Vanessa Didelez Identication In Graphical Causal Models - Ilya Shpitser Mediation Analysis - Johan Steen and Stijn Vansteelandt Search for Causal Models - Peter Spirtes and Kun Zhang Part V Applications Graphical Models for Forensic Analysis - A. Philip Dawid and Julia Mortera Graphical models in molecular systems biology - Sach Mukherjee and Chris Oates Graphical Models in Genetics, Genomics and Metagenomics - Hongzhe Li and Jing Ma

Marloes Maathuis is Professor of Statistics at ETH Zurich. Mathias Drton is Professor of Statistics at the University of Copenhagen and the University of Washington. Steffen Lauritzen is Professor of Statistics at the University of Copenhagen. Martin Wainwright is Chancellor's Professor at the University of Berkeley.