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Author: Marloes Maathuis
Publisher: CRC Press
ISBN: 0429874243
Category : Mathematics
Languages : en
Pages : 536
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Book Description
A graphical model is a statistical model that is represented by a 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.
Author: Marloes Maathuis
Publisher: CRC Press
ISBN: 0429874243
Category : Mathematics
Languages : en
Pages : 536
Get Book
Book Description
A graphical model is a statistical model that is represented by a 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.
Author: Mathias Drton
Publisher:
ISBN: 9781498788632
Category : Electronic books
Languages : en
Pages :
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Book Description
"Graphical models are a statistical tool used for a wide range of applications. There has been a huge amount of research in this topic across statistics, mathematics and computer science in the last few decades, and the timing is right for a handbook that presents an overview of the state-of-the-art. This handbook presents a comprehensive overview of the area through a collection of 25-30 chapters from some of the leading researchers. Each chapter has been carefully edited to ensure that the handbook is consistent in style, level and notation, and that it is accessible for graduate students and researchers new to the topic. It is sure to become a landmark reference in the area."--Provided by publisher.
Author: Steffen L. Lauritzen
Publisher: Clarendon Press
ISBN: 019159122X
Category : Mathematics
Languages : en
Pages : 314
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Book Description
The idea of modelling systems using graph theory has its origin in several scientific areas: in statistical physics (the study of large particle systems), in genetics (studying inheritable properties of natural species), and in interactions in contingency tables. The use of graphical models in statistics has increased considerably over recent years and the theory has been greatly developed and extended. This book provides the first comprehensive and authoritative account of the theory of graphical models and is written by a leading expert in the field. It contains the fundamental graph theory required and a thorough study of Markov properties associated with various type of graphs. The statistical theory of log-linear and graphical models for contingency tables, covariance selection models, and graphical models with mixed discrete-continous variables in developed detail. Special topics, such as the application of graphical models to probabilistic expert systems, are described briefly, and appendices give details of the multivarate normal distribution and of the theory of regular exponential families. The author has recently been awarded the RSS Guy Medal in Silver 1996 for his innovative contributions to statistical theory and practice, and especially for his work on graphical models.
Author: Mahlet G. Tadesse
Publisher: CRC Press
ISBN: 1000510255
Category : Mathematics
Languages : en
Pages : 762
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Book Description
Bayesian variable selection has experienced substantial developments over the past 30 years with the proliferation of large data sets. Identifying relevant variables to include in a model allows simpler interpretation, avoids overfitting and multicollinearity, and can provide insights into the mechanisms underlying an observed phenomenon. Variable selection is especially important when the number of potential predictors is substantially larger than the sample size and sparsity can reasonably be assumed. The Handbook of Bayesian Variable Selection provides a comprehensive review of theoretical, methodological and computational aspects of Bayesian methods for variable selection. The topics covered include spike-and-slab priors, continuous shrinkage priors, Bayes factors, Bayesian model averaging, partitioning methods, as well as variable selection in decision trees and edge selection in graphical models. The handbook targets graduate students and established researchers who seek to understand the latest developments in the field. It also provides a valuable reference for all interested in applying existing methods and/or pursuing methodological extensions. Features: Provides a comprehensive review of methods and applications of Bayesian variable selection. Divided into four parts: Spike-and-Slab Priors; Continuous Shrinkage Priors; Extensions to various Modeling; Other Approaches to Bayesian Variable Selection. Covers theoretical and methodological aspects, as well as worked out examples with R code provided in the online supplement. Includes contributions by experts in the field. Supported by a website with code, data, and other supplementary material
Author: William L. William L. Hamilton
Publisher: Springer Nature
ISBN: 3031015886
Category : Computers
Languages : en
Pages : 141
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Book Description
Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.
Author:
Publisher: Elsevier
ISBN: 0080471269
Category : Mathematics
Languages : en
Pages : 458
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Book Description
This Handbook covers latent variable models, which are a flexible class of models for modeling multivariate data to explore relationships among observed and latent variables. - Covers a wide class of important models - Models and statistical methods described provide tools for analyzing a wide spectrum of complicated data - Includes illustrative examples with real data sets from business, education, medicine, public health and sociology. - Demonstrates the use of a wide variety of statistical, computational, and mathematical techniques.
Author: Stephen L. Morgan
Publisher: Springer Science & Business Media
ISBN: 9400760949
Category : Social Science
Languages : en
Pages : 423
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Book Description
What constitutes a causal explanation, and must an explanation be causal? What warrants a causal inference, as opposed to a descriptive regularity? What techniques are available to detect when causal effects are present, and when can these techniques be used to identify the relative importance of these effects? What complications do the interactions of individuals create for these techniques? When can mixed methods of analysis be used to deepen causal accounts? Must causal claims include generative mechanisms, and how effective are empirical methods designed to discover them? The Handbook of Causal Analysis for Social Research tackles these questions with nineteen chapters from leading scholars in sociology, statistics, public health, computer science, and human development.
Author: Judea Pearl
Publisher: John Wiley & Sons
ISBN: 1119186862
Category : Mathematics
Languages : en
Pages : 162
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Book Description
CAUSAL INFERENCE IN STATISTICS A Primer Causality is central to the understanding and use of data. Without an understanding of cause–effect relationships, we cannot use data to answer questions as basic as "Does this treatment harm or help patients?" But though hundreds of introductory texts are available on statistical methods of data analysis, until now, no beginner-level book has been written about the exploding arsenal of methods that can tease causal information from data. Causal Inference in Statistics fills that gap. Using simple examples and plain language, the book lays out how to define causal parameters; the assumptions necessary to estimate causal parameters in a variety of situations; how to express those assumptions mathematically; whether those assumptions have testable implications; how to predict the effects of interventions; and how to reason counterfactually. These are the foundational tools that any student of statistics needs to acquire in order to use statistical methods to answer causal questions of interest. This book is accessible to anyone with an interest in interpreting data, from undergraduates, professors, researchers, or to the interested layperson. Examples are drawn from a wide variety of fields, including medicine, public policy, and law; a brief introduction to probability and statistics is provided for the uninitiated; and each chapter comes with study questions to reinforce the readers understanding.
Author: David Edwards
Publisher: Springer Science & Business Media
ISBN: 1461204933
Category : Mathematics
Languages : en
Pages : 342
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Book Description
A useful introduction to this topic for both students and researchers, with an emphasis on applications and practicalities rather than on a formal development. It is based on the popular software package for graphical modelling, MIM, freely available for downloading from the Internet. Following a description of some of the basic ideas of graphical modelling, subsequent chapters describe particular families of models, including log-linear models, Gaussian models, and models for mixed discrete and continuous variables. Further chapters cover hypothesis testing and model selection. Chapters 7 and 8 are new to this second edition and describe the use of directed, chain, and other graphs, complete with a summary of recent work on causal inference.
Author: Michael D. Lee
Publisher: Cambridge University Press
ISBN: 1107653916
Category : Psychology
Languages : en
Pages : 279
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Book Description
Bayesian inference has become a standard method of analysis in many fields of science. Students and researchers in experimental psychology and cognitive science, however, have failed to take full advantage of the new and exciting possibilities that the Bayesian approach affords. Ideal for teaching and self study, this book demonstrates how to do Bayesian modeling. Short, to-the-point chapters offer examples, exercises, and computer code (using WinBUGS or JAGS, and supported by Matlab and R), with additional support available online. No advance knowledge of statistics is required and, from the very start, readers are encouraged to apply and adjust Bayesian analyses by themselves. The book contains a series of chapters on parameter estimation and model selection, followed by detailed case studies from cognitive science. After working through this book, readers should be able to build their own Bayesian models, apply the models to their own data, and draw their own conclusions.
