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 ofgraphical 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 describedbriefly, 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.
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.
Thorvald Nicolai Thiele was a brilliant Danish researcher of the 19th century: a Professor of Astronomy at the University of Copenhagen and the founder of Hafnia, the first Danish private insurance company. This book examines his statistical work and translates three of his masterpieces.
The pOint of view behind the present work is that the connection between a statistical model and a statistical analysis-is a dua lity (in a vague sense). In usual textbooks on mathematical statistics it is often so that the statistical model is given in advance and then various in ference principles are applied to deduce the statistical ana lysis to be performed. It is however possible to reverse the above procedure: given that one wants to perform a certain statistical analysis, how can this be expressed in terms of a statistical model? In that sense we think of the statistical analysis and the stati stical model as two ways of expressing the same phenomenon, rather than thinking of the model as representing an idealisation of "truth" and the statistical analysis as a method of revealing that truth to the scientist. It is not the aim of the present work to solve the problem of giving the correct-anq final mathematical description of the quite complicated relation between model and analysis. We have rather restricted ourselves to describe a particular aspect of this, formulate it in mathematical terms, and then tried to make a rigorous and consequent investigation of that mathematical struc ture.
Probabilistic expert systems are graphical networks which support the modeling of uncertainty and decisions in large complex domains, while retaining ease of calculation. Building on original research by the authors, this book gives a thorough and rigorous mathematical treatment of the underlying ideas, structures, and algorithms. The book will be of interest to researchers in both artificial intelligence and statistics, who desire an introduction to this fascinating and rapidly developing field. The book, winner of the DeGroot Prize 2002, the only book prize in the field of statistics, is new in paperback.
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