Lectures on the Coupling Method - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on the Coupling Method write by Torgny Lindvall. This book was released on 2002-01-01. Lectures on the Coupling Method available in PDF, EPUB and Kindle. An important tool in probability theory and its applications, the coupling method is primarily used in estimates of total variation distances. The method also works well in establishing inequalities, and it has proven highly successful in the study of Markov and renewal process asymptotics. This text represents a detailed, comprehensive examination of the method and its broad variety of applications. Readers progress from simple to advanced topics, with end-of-discussion notes that reinforce the preceding material. Topics include renewal theory, Markov chains, Poisson approximation, ergodicity, and Strassen's theorem. A practical and easy-to-use reference, this volume will accommodate the diverse needs of professionals in the fields of statistics, mathematics, and operational research, as well as those of teachers and students.
Lectures on the Coupling Method
Lectures on the Coupling Method - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on the Coupling Method write by Torgny Lindvall. This book was released on 2012-08-15. Lectures on the Coupling Method available in PDF, EPUB and Kindle. Practical and easy-to-use reference progresses from simple to advanced topics, covering, among other topics, renewal theory, Markov chains, Poisson approximation, ergodicity, and Strassen's theorem. 1992 edition.
An Introduction to Stein's Method
An Introduction to Stein's Method - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Stein's Method write by A. D. Barbour. This book was released on 2005. An Introduction to Stein's Method available in PDF, EPUB and Kindle. A common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical example. Stein's method is a tool which makes this possible in a wide variety of situations. Traditional approaches, for example using Fourier analysis, become awkward to carry through in situations in which dependence plays an important part, whereas Stein's method can often still be applied to great effect. In addition, the method delivers estimates for the error in the approximation, and not just a proof of convergence. Nor is there in principle any restriction on the distribution to be approximated; it can equally well be normal, or Poisson, or that of the whole path of a random process, though the techniques have so far been worked out in much more detail for the classical approximation theorems.This volume of lecture notes provides a detailed introduction to the theory and application of Stein's method, in a form suitable for graduate students who want to acquaint themselves with the method. It includes chapters treating normal, Poisson and compound Poisson approximation, approximation by Poisson processes, and approximation by an arbitrary distribution, written by experts in the different fields. The lectures take the reader from the very basics of Stein's method to the limits of current knowledge.
Probability on Graphs
Probability on Graphs - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Probability on Graphs write by Geoffrey Grimmett. This book was released on 2018-01-25. Probability on Graphs available in PDF, EPUB and Kindle. This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Robust Methods in Biostatistics
Robust Methods in Biostatistics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Robust Methods in Biostatistics write by Stephane Heritier. This book was released on 2009-05-11. Robust Methods in Biostatistics available in PDF, EPUB and Kindle. Robust statistics is an extension of classical statistics that specifically takes into account the concept that the underlying models used to describe data are only approximate. Its basic philosophy is to produce statistical procedures which are stable when the data do not exactly match the postulated models as it is the case for example with outliers. Robust Methods in Biostatistics proposes robust alternatives to common methods used in statistics in general and in biostatistics in particular and illustrates their use on many biomedical datasets. The methods introduced include robust estimation, testing, model selection, model check and diagnostics. They are developed for the following general classes of models: Linear regression Generalized linear models Linear mixed models Marginal longitudinal data models Cox survival analysis model The methods are introduced both at a theoretical and applied level within the framework of each general class of models, with a particular emphasis put on practical data analysis. This book is of particular use for research students,applied statisticians and practitioners in the health field interested in more stable statistical techniques. An accompanying website provides R code for computing all of the methods described, as well as for analyzing all the datasets used in the book.
