Series: Use R
2009, XII, 300 p., Softcover
ISBN: 978-0-387-92297-3
Due: June 2009
Introduces Bayesian modeling by use of computation using the R language
There has been a dramatic growth in the development and application of Bayesian inferential methods. Some of this growth is due to the availability of powerful simulation-based algorithms to summarize posterior distributions. There has been also a growing interest in the use of the system R for statistical analyses. R's open source nature, free availability, and large number of contributor packages have made R the software of choice for many statisticians in education and industry.
Bayesian Computation with R introduces Bayesian modeling by the use of computation using the R language. The early chapters present the basic tenets of Bayesian thinking by use of familiar one and two-parameter inferential problems. Bayesian computational methods such as Laplace's method, rejection sampling, and the SIR algorithm are illustrated in the context of a random effects model. The construction and implementation of Markov Chain Monte Carlo (MCMC) methods is introduced. These simulation-based algorithms are implemented for a variety of Bayesian applications such as normal and binary response regression, hierarchical modeling, order-restricted inference, and robust modeling. Algorithms written in R are used to develop Bayesian tests and assess Bayesian models by use of the posterior predictive distribution. The use of R to interface with WinBUGS, a popular MCMC computing language, is described with several illustrative examples.
This book is a suitable companion book for an introductory course on Bayesian methods and is valuable to the statistical practitioner who wishes to learn more about the R language and Bayesian methodology. The LearnBayes package, written by the author and available from the CRAN website, contains all of the R functions described in the book.
The second edition contains several new topics such as the use of mixtures of conjugate priors and the use of Zellnerfs g priors to choose between models in linear regression. There are more illustrations of the construction of informative prior distributions, such as the use of conditional means priors and multivariate normal priors in binary regressions. The new edition contains changes in the R code illustrations according to the latest edition of the LearnBayes package.
Jim Albert is Professor of Statistics at Bowling Green State University. He is Fellow of the American Statistical Association and is past editor of The American Statistician. His books include Ordinal Data Modeling (with Val Johnson), Workshop Statistics: Discovery with Data, A Bayesian Approach (with Allan Rossman), and Bayesian Computation using Minitab.
An introduction to R.- Introduction to Bayesian thinking.- Single-parameter models.- Multiparameter models.- Introduction to Bayesian computation.- Markov chain Monte Carlo methods.- Hierarchical modeling.- Model comparison.- Regression models.- Gibbs sampling.- Using R to interface with WinBUGS.
Series: Texts in Applied Mathematics , Vol. 56
2009, Approx. 480 p., Hardcover
ISBN: 978-0-387-87749-5
Due: August 2009
Strong addition to mathematical modeling textbooks
Well known author with previous successful books
The objective of this textbook is the construction, analysis, and interpretation of mathematical models to help us understand the world we live in. Rather than follow a case study approach it develops the mathematical and physical ideas that are fundamental in understanding contemporary problems in science and engineering. Science evolves, and this means that the problems of current interest continually change.
What does not change as quickly is the approach used to derive the relevant mathematical models, and the methods used to analyze the models. Consequently, this book is written in such a way as to establish the mathematical ideas underlying model development independently of a specific application. This does not mean applications are not considered, they are, and connections with experiment are a staple of this book.
The book, as well as the individual chapters, is written in such a way that the material becomes more sophisticated as you progress. This provides some flexibility in how the book is used, allowing consideration for the breadth and depth of the material covered.
Moreover, there are a wide spectrum of exercises and detailed illustrations that significantly enrich the material. Students and researchers interested in mathematical modelling in mathematics, physics, engineering and the applied sciences will find this text useful.
Dimensional Analysis.-Perturbation Methods.- Kinetics.-Diffusion.-Traffic Flow.-Continuum Mechanics: One Spatial Dimension.-Elastic and Viscoelastic Materials.- Continuum Mechanics: Three Spatial Dimensions.- Fluids.- Taylor's Theorem.- Fourier Analysis.- Stochastic Differential Equations.- Identities.- Equations for a Newtonian Fluid.- References.- Index.
Series: Operator Theory: Advances and Applications , Vol. 192
2009, 444 p., Hardcover
ISBN: 978-3-0346-0125-2
Due: June 2009
Applications deal with interpolation, holomorphic families of subspaces and frames, holomorphic equivalence and diagonalization and Plemlj-Muschelishvili factorization
Exposition of the material is made in style and terms which are used in Complex analysis of several variables
This is a book on holomorphic operator functions of a single variable and applications, which is focused on the relations between local and global theories. It is based on methods and technics of complex analysis of several variables.
The first part of the theory starts with a straightforward generalization of some results from the basics of analysis of scalar functions of one complex variable. In the second part, which is the main part of the theory, results are obtained by methods and tools adapted from complex analysis of functions of several variables. We have in mind the theory of holomorphic cocycles (fiber bundles) with values in infinite-dimensional non-commutative groups. As a rule, these results do not appear in traditional complex analysis of one variable, not even for matrix valued cocycles. The third part consists of applications to operator theory. Here applications are presented for holomorphic families of subspaces and Plemelj-Muschelishvili factorization. The fourth part presents a generalization of the theory of cocycles to cocycles with restrictions. This part contains also applications to interpolation problems, to the problem of holomorphic equivalence and diagonalization.
Series: Texts and Monographs in Symbolic Computation
2009, Approx. 260 p., Softcover
ISBN: 978-3-211-99313-2
Due: July 23, 2009
Approximate Commutative Algebra is an emerging field of research which endeavours to bridge the gap between traditional exact Computational Commutative Algebra and approxmate numerical computation. The last 50 years have seen enormous progress in the realm of exact Computational Commutative Algebra, and given the importance of polynomials in scientific modelling, it is very natural to want to extend these ideas to handle approximate, empirical data deriving from physical measurements of phenomena in the real world. In the volume nine contributions from established researchers describe various approaches to tackle a variety of problems arising in Approximate Commutative Algebra.
M. Kreuzer, H. Poulisse, L. Robbiano: From oil fields to Hilbert schemes - D. J. Bates, J. D. Hauenstein, C. Peterson, A. J. Sommese: Numerical decomposition of the rank-deficiency set of a matrix of multivariate polynomials - W. Wu, G. Reid, O. Golubitsky: Towards geometric completion of differential systems by points - R. Scott, G. Reid, W. Wu, L. Zhi: Geometric involutive bases and applications to approximate commutative algebra - Z. Zeng: Regularization and matrix computation in numerical polynomial algebra - B. Shekhtman: Ideal interpolation: translations to and from algebraic geometry - E. Riccomagno, H. P. Wynn: An introduction to regression and errors in variables from an algebraic viewpoint - H. J. Stetter: ApCoA = Embedding commutative algebra into analysis - E. Kaltofen: Exact certification in global polynomial optimization via rationalizing sums-of-squares