Steffen L. Lauritzen - Böcker
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6 produkter
6 produkter
2 411 kr
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Thorvald Nicolai Thiele was a brilliant Danish researcher of the 19th Century. He was a professor of Astronomy at the University of Copenhagen and the founder of Hafnia, the first Danish private insurance company. Thiele worked in astronomy, mathematics, actuarial science, and statistics, his most spectacular contributions were in the latter two areas, where his published work was far ahead of his time. This book, written for researchers and graduate students of statistical, science and mathematics history, is concerned with his statistical work. It evolves around his three main statistical masterpieces, which are now translated into English for the first time:1) His article from 1880 where he derives the Kalman filter; 2) His book from 1889, where he lays out the subject of statistics in a highly original way, derives the half-invariants (today known as cumulants), the notion of likelihood in the case of binomial experiments, the canonical form of the linear normal model, and develops model criticism via analysis of residuals. 3) An article from 1899 where he completes the theory of the half-invariants.Thiele - Pioneer in Statistics also contains three papers, written by A. Hald and S.L. Lauritzen which describes Thiele's statistical work in modern terms and puts them into an historical perspective. The texts are supplemented with introductory material on Thiele's life and other interests, as well as with explanatory comments from the translator in the form of footnotes.
1 705 kr
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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.
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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.This new and extended edition of Graphical Models provides the basic mathematical and statistical theory of graphical models, incorporating the many advances that have been made in the field since the publication of the first edition in 1996. Lauritzen discusses basic graph theory and the fundamentals of conditional independence both in abstract form for conditional independence based on graphs and for probabilistic conditional independence. The associated Markov theory, forming the basis of all models in the book, is treated in some detail. The statistical theory based on likelihood methods and conjugate Bayesian analysis is developed for log-linear and Gaussian graphical models, as well as for graphical models involving mixed discrete and continuous data. A new and important chapter is devoted to structure estimation because this has become a dominating part of modern developments. Causal interpretation of models based on directed acyclic graphs and chain graphs are also discussed.The appendices contain some of the general mathematical results needed as background for the main contents of the book, including basic measure theory and the theory of Markov kernels, convex optimization, properties of the multivariate Gaussian distributions and derived distributions, as well as a brief exposition of the theory of exponential families.
Probabilistic Networks and Expert Systems
Exact Computational Methods for Bayesian Networks
Häftad, Engelska, 2007
1 275 kr
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WINNER OF THE 2001 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. 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 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.
Del 49 - Lecture Notes in Statistics
Extremal Families and Systems of Sufficient Statistics
Häftad, Engelska, 1988
1 275 kr
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This book surveys results in the area sometimes denoted as "partial exchangeability" of "de Finetti type theorems". It is to be seen as an attempt to give sense to the general idea that there is a strong coupling between a statistical model and the statistical analysis. So strong that there is a canonical mathematical construction leading from the analysis to the model. Special sections are devoted to the study of sufficiency, of triviality of tails of Markov chains, studied e. g. by coupling methods, Martin boundaries and projective limits of Markov kernels and Polish spaces. In addition, many examples of extreme point models are treated in detail. This book is intended for researchers and graduate students in mathematical statistics and probability.
Probabilistic Networks and Expert Systems
Exact Computational Methods for Bayesian Networks
Inbunden, Engelska, 1999
1 786 kr
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Winner of the 2002 DeGroot Prize. Awarded by the International Society for Bayesian Analysis to a book judged to represent an important, timely, thorough, and notably original contribution to the statistics literature.Probabilistic expert systems are graphical networks that 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 an important reference source for all those involved in the theory and applications of probabilistic expert systems.Robert G. Cowell is a Lecturer in the Faculty of Actuarial Science and Statistics of the Sir John Cass Business School, City of London. He has been working in the field of probabilistic expert systems for over a decade, and has published a number of research and tutorial articles in the area.A. Philip Dawid is Pearson Professor of Statistics at University College London. He has served as Editor of the Journal of the Royal Statistical Society (Series B) and of Biometrika, and as President of the International Society for Bayesian Analysis. He holds the Royal Statistical Society Guy Medal in Bronze and in Silver, and the G. W. Snedecor Award for the Best Publication in Biometry.Steffen L. Lauritzen is Professor of Mathematics and Statistics at the University of Aalborg. He has served as Editor of the Scandinavian Journal of Statistics. He holds the Royal Statistical Guy Medal in Silver and is an Honorary Fellow of the same society. He has, jointly with David J.Spiegelhalter, received the American Statistical Association's award for an "Outstanding Statistical Application."David J. Spiegelhalter is a Senior Scientist at the MRC Biostatistics Unit in the Cambridge University Institute of Public Health. He has published extensively on Bayesian methodology and applications, and holds the Royal Statistical Society Guy Medal in Bronze and in Silver.