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Mathematical statistics --- Distribution (Probability theory) --- Sufficient statistics --- Distribution (Théorie des probabilités) --- Distribution (Théorie des probabilités)

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Fundamentals of Mathematical Statistics is meant for a standard one-semester advanced undergraduate or graduate level course on Mathematical Statistics. It covers all the key topics - statistical models, linear normal models, exponential families, estimation, asymptotics of maximum likelihood, significance testing, and models for tables of counts. It assumes a good background in mathematical analysis, linear algebra, and probability, but includes an appendix with basic results from these areas. Throughout the text, there are numerous examples and graduated exercises that illustrate the topics covered, rendering the book suitable for teaching or self-study. Features a concise, yet rigorous introduction to a one-semester course on mathematical statistics. Thus, this textbook will be a perfect fit for an advanced course on mathematical statistics or statistical theory. The concise and lucid approach means it could also serve as a good alternative, or supplement, to existing texts.

Mathematical statistics

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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. Søren Højsgaard is Associate Professor in Statistics and Head of the Department of Mathematical Sciences at Aalborg University. David Edwards is Associate Professor at the Department of Molecular Biology and Genetics, Aarhus University. Steffen Lauritzen is Professor of Statistics and Head of the Department of Statistics at the University of Oxford.

Graphical modeling (Statistics). --- R (Computer program language). --- Statistics. --- Graphical modeling (Statistics) --- R (Computer program language) --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- 519.2 --- GNU-S (Computer program language) --- Domain-specific programming languages --- Multivariate analysis --- Graphic methods --- Mathematical statistics. --- Statistical Theory and Methods. --- Statistics, general. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistics .

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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. 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. Robert G. Cowell is a Lecturer in the Faculty of Actuarial Science and Insurance of the Sir John Cass Business School, City of London. He has been working on probabilistic expert systems since 1989. A. Philip Dawid is Professor of Statistics at Cambridge University. He has served as Editor of the Journal of the Royal Statistical Society (Series B), Biometrika and Bayesian Analysis, 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 Snedecor Award for the Best Publication in Biometry. Steffen L. Lauritzen is Professor of Statistics at the University of Oxford. He has served as Editor of the Scandinavian Journal of Statistics. He holds the Royal Statistical Society 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 Winton Professor of the Public Understanding of Risk at Cambridge University and Senior Scientist in the MRC Biostatistics Unit, Cambridge. He has published extensively on Bayesian methodology and applications, and holds the Royal Statistical Society Guy Medal in Bronze and in Silver.

519.2 --- Probability. Mathematical statistics --- 519.2 Probability. Mathematical statistics --- Mathematics. --- Artificial intelligence. --- Probabilities. --- Statistics. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Artificial Intelligence (incl. Robotics). --- Expert systems (Computer science) --- Probabilities --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Knowledge-based systems (Computer science) --- Systems, Expert (Computer science) --- Artificial intelligence --- Computer systems --- Soft computing --- Stochastic processes --- Artificial intelligence. Robotics. Simulation. Graphics --- Expert systems (Computer science). --- Systèmes experts (Informatique) --- Probabilités --- EPUB-LIV-FT SPRINGER-B --- Distribution (Probability theory. --- Mathematical statistics. --- Artificial Intelligence. --- Statistics . --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Expert systems (computer science)