Probabilistic expert systems are graphical networks which support the modelling of uncertainty and decisions in large complex domains, while retaining ease of calculation. Building on original research by the authors over a number of years, this book gives a thorough and rigorous mathematical treatment of the underlying ideas, structures and algorithms, emphasizing those cases in which exact answers are obtainable. It covers both the updating of probabilistic uncertainty in the light of new evidence, and statistical inference, about unknown probabilities or unknown model structure, in the light of new data. The book will be of interest to researchers and graduate students in artificial intelligence who desire an understanding of the mathematical and statistical basis of probabilistic expert systems, and to students and research workers in statistics wanting an introduction to this fascinating and rapidly developing field. The careful attention to detail will also make this work as an important reference source for all those involved in the theory and applications of probabilistic expert systems. Robert Cowell is Research Fellow and Computer Manager in the Department of Actuarial Science and Statistics of City University, London. He has been working in the field of probabilistic expert systems for over 10 years, and has published a number of research and tutorial articles in the area. A. Philip Dawid is Professor of Statistics at University College London. He has served as Editor of the Journal of the Royal Statistical Society (Series B) and Biometrika, and is currently President-Elect of the International Society for Bayesian Analysis. He holds the Guy Medal in Bronze of the Royal Statistical Society, and the G.W. Snedecor Award for the Best Publication in Biometry. He has published over 100 articles on statistics and related topics.

This book studies the brilliant Danish 19th Century astronomer, T.N. Thiele who made important contributions to statistics, actuarial science, astronomy and mathematics. The most important of these contributions in statistics are translated into English for the first time, and the text includes comments that set his achievements in a modern and historical perspective.

This book is a winner of the 2002 DeGroot Prize. Probabilistic expert systems are graphical networks that support the modelling of uncertainty and decisions in large complex domains, while retaining ease of calculation. book gives a thorough and rigorous mathematical treatment of the underlying ideas, structures, and algorithms, emphasizing those cases in which exact answers are obtainable. It covers both the updating of probabilistic uncertainty in the light of new evidence, and statistical inference, about unknown probabilities or unknown model structure, in the light of new data. The careful attention to detail will make this work an important reference source for all those involved in the theory and applications of probabilistic expert systems. This book was awarded the first DeGroot Prize by the International Society for Bayesian Analysis for a book making an important, timely, thorough, and notably original contribution to the statistics literature.

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."

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.