Højsgaard S., Edwards D., Lauritzen S. Graphical Models with R

Springer, 2012. — 186 p. — ISBN: 1461422981.Graphical models in their modern form have been around since the late 1970s and appear today in many areas of the sciences. Along with the ongoing developments of graphical models, a number of different graphical modeling software programs have been written over the years. In recent years many of these software developments have taken place within the R community, either in the form of new packages or by providing an R interface to existing software. This book attempts to give the reader a gentle introduction to graphical modeling using R and the main features of some of these packages. In addition, the book provides examples of how more advanced aspects of graphical modeling can be represented and handled within R. Topics covered in the seven chapters include graphical models for contingency tables, Gaussian and mixed graphical models, Bayesian networks and modeling high dimensional data.Graphs and Conditional IndependenceGraphs
Undirected Graphs
Directed Acyclic Graphs
Mixed Graphs
Conditional Independence and Graphs
More About Graphs
Special Properties
Graph Layout in Rgraphviz
The igraph Package
3-D Graphs
AlternativeGraphRepresentations
Operations on Graphs in Different Representations
Log-Linear ModelsPreliminaries
FourDatasets
DataFormats
Log-Linear Models
Preliminaries andNotation
Hierarchical Log-Linear Models
Graphical and Decomposable Log-Linear Models
Estimation, Likelihood, and Model Fitting
Hypothesis Testing
Model Selection
FurtherTopics
Fitting Log-Linear Models with glm()
Working with dModelObjects
Various
Bayesian NetworksTheChestClinicExample
Models Based on Directed Acyclic Graphs
Inference
Building and Using Bayesian Networks
Specification of Conditional Probability Tables
BuildingtheNetwork
Absorbing Evidence and Answering Queries
FurtherTopics
BuildingaNetworkfromData
Bayesian Networks with RHugin
Simulation
Prediction
Working with HUGIN Files
Learning Bayesian Networks
Gaussian Graphical ModelsSomeExamples
CarcassData
BodyFatData
Undirected Gaussian Graphical Models
Preliminaries andNotation
Estimation, Likelihood, and Model Fitting
Hypothesis Testing
Concentration and Regression
Decomposition of UGGMs
Model Selection
Stepwise Methods
ConvexOptimization
Thresholding
Simultaneous p-Values
Summary of Models
Directed Gaussian Graphical Models
Markov Equivalence
Model Selection for DGGMs
ThePCAlgorithm
Alternative Methods for Identifying DGGMs
Gaussian Chain Graph Models
Selecting a Chain Graph Model
Various
Mixed Interaction ModelsExampleDatasets
Mixed Data and CG-densities
Homogeneous Mixed Interaction Models
Model Formulae
Graphical and Decomposable MI-models
Maximum Likelihood Estimation
Likelihood and Deviance
Dimension of MI-models
Inference
Likelihood Equations
Iterative Proportional Scaling
Using gRim
Updating Models
Inference
Stepwise Model Selection
An Example of Chain Graph Modelling
Various
Graphical Models for Complex Stochastic SystemsBayesian Graphical Models
Simple Repeated Sampling
Models Based on Directed Acyclic Graphs
Inference Based on Probability Propagation
Computations Using Monte Carlo Methods
Metropolis–Hastings andtheGibbsSampler
UsingWinBUGSviaRWinBUGS
Various
High Dimensional ModellingTwoDatasets
Computational Efficiency
The Extended Chow–Liu Algorithm
Decomposable Stepwise Search
SelectionbyApproximation
FindingMAPForests