ISBN: 978-1-4398361-4-9
Publish Date: 3rd June 2010
Pages: 300 pages
Series: Statistics: A Series of Textbooks and Monographs
Along with many practical applications, Bayesian Model Selection and Statistical Modeling presents an array of Bayesian inference and model selection procedures. It thoroughly explains the concepts, illustrates the derivations of various Bayesian model selection criteria through examples, and provides R code for implementation.
The author shows how to implement a variety of Bayesian inference using R and sampling methods, such as Markov chain Monte Carlo. He covers the different types of simulation-based Bayesian model selection criteria, including the numerical calculation of Bayes factors, the Bayesian predictive information criterion, and the deviance information criterion. He also provides a theoretical basis for the analysis of these criteria. In addition, the author discusses how Bayesian model averaging can simultaneously treat both model and parameter uncertainties.
Selecting and constructing the appropriate statistical model significantly affect the quality of results in decision making, forecasting, stochastic structure explorations, and other problems. Helping you choose the right Bayesian model, this book focuses on the framework for Bayesian model selection and includes practical examples of model selection criteria.
ISBN: 978-1-4398262-7-0
Publish Date: 15th December 2010
Pages: 480 pages
Description
Written for advanced undergraduate and beginning graduate students, the fifth edition of this best-selling book provides a wide range of new examples along with historical discussions of mathematicians, problems, and conjectures. It features new and expanded coverage of such topics as toughness, graph minors, perfect graphs, list colorings, nowhere zero flows, list edge colorings, the road coloring problem, and the rainbow number of a graph. Additional applications, exercises, and examples illustrate the concepts and theorems. A solutions manual is available for qualifying instructors.
ISBN: 978-1-4398400-0-9
Publish Date: 15th February 2011
Pages: 1,024 pages
This handbook provides a complete reference on elliptic and hyperelliptic curve cryptography. Addressing every aspect of the field, the book contains all of the background necessary to understand the theory and security of cryptosystems as well as the algorithms that can be used to implement them. This second edition features the latest developments on pairing-based cryptography, new ideas on index-calculus attacks, improved algorithms for genus-2 arithmetic, and a number of other new additions. It also includes many new applications and provides better explanations on some of the more mathematical presentations
Mathematical Background. Elementary Arithmetic. Arithmetic of Curves. Construction of Curves. Computation of Discrete Logarithms. Applications. Realization of Discrete Logarithm Systems
ISBN: 978-1-4398199-1-3
Publish Date: 15th March 2011
Pages: 352 pages
Series: Discrete Mathematics and Its Applications
The notion of closure pervades mathematics, especially in the fields of topology and projective geometry. Demonstrating this pervasiveness in the field, this graduate-level book provides a complete introduction to closure systems. With an emphasis on finite spaces and algebraic closures, the text covers graph theory, ordered sets, lattices, projective geometry, and formal logic as they apply to the study of closures. Each chapter presents a vignette to illustrate the topic covered. The author also includes numerous exercises as well as concrete examples to support the material discussed.
ISBN: 978-1-4398400-8-5
Publish Date: 15th March 2011
Pages: 352 pages
Series: Chapman & Hall/CRC Applied Mathematics & Nonlinear Science
This book provides complete coverage of Greenfs functions, which have become an important topic of interest in recent years. Along with MathematicaR and MATLABR code, it supplies the necessary background material and presents a large number of examples and exercises from different areas of mathematics, applied science, and engineering. The book includes boundary value problems involving ordinary differential equations, partial differential equations, and stochastic differential equations. The author describes various methods for solving these problems, including classical methods, Bernoullifs separation method, integral transform, conformal mapping, and wavelet transform.