Series: Use R
2010, Approx. 300 p., Softcover
ISBN: 978-1-4419-1575-7
Due: January 2010
The first book to present modern Monte Carlo and Markov Chain Monte Carlo (MCMC) methods from a practical perspective through a guided implementation in the R language
All concepts are carefully described with the abtract theoretical background replaced with a corresponding R program that the reader can use and modify at will
The whole entire series of examples from the book is accompanied by a free R package called mcsm that allows for immediate experimentation
Computational techniques based on simulation have now become an essential part of the statistician's toolbox. It is thus crucial to provide statisticians with a practical understanding of those methods, and there is no better way to develop intuition and skills for simulation than to use simulation to solve statistical problems. Introducing Monte Carlo Methods with R covers the main tools used in statistical simulation from a programmer's point of view, explaining the R implementation of each simulation technique and providing the output for better understanding and comparison. While this book constitutes a comprehensive treatment of simulation methods, the theoretical justification of those methods has been considerably reduced, compared with Robert and Casella (2004). Similarly, the more exploratory and less stable solutions are not covered here.
This book does not require a preliminary exposure to the R programming language or to Monte Carlo methods, nor an advanced mathematical background. While many examples are set within a Bayesian framework, advanced expertise in Bayesian statistics is not required. The book covers basic random generation algorithms, Monte Carlo techniques for integration and optimization, convergence diagnoses, Markov chain Monte Carlo methods, including Metropolis {Hastings and Gibbs algorithms, and adaptive algorithms. All chapters include exercises and all R programs are available as an R package called mcsm. The book appeals to anyone with a practical interest in simulation methods but no previous exposure. It is meant to be useful for students and practitioners in areas such as statistics, signal processing, communications engineering, control theory, econometrics, finance and more. The programming parts are introduced progressively to be accessible to any reader.
Basic R programming.- Random variable generation.- Monte Carlo integration.- Controling and accelerating convergence.- Monte Carlo Optimization.- Metropolis-Hastings algorithms.- Gibbs samplers.- Convergence Monitoring for MCMC algorithms
Series: Applied Mathematical Sciences , Vol. 170
2010, Approx. 485 p., Hardcover
ISBN: 978-1-4419-1604-4
Due: February 2010
A wealth of examples from physics, chemistry, biology and engineering
Treads a route between probabilists and physical scientists
Includes many physically relevant results and discussions
This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences. Its aim is to make probability theory readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and in asymptotic methods, rather than in probability and measure theory. It shows how to derive explicit expressions for quantities of interest by solving equations. Emphasis is put on rational modeling and approximation methods.
The book includes many detailed illustrations, applications, examples and exercises. It will appeal to graduate students and researchers in mathematics, physics and engineering.
Beginning graduates in applied mathematics, physics, biologists, engineering, mechanical
Introduction.- The Physical Brownian Motion: Diffusion and Noise.- The Probability Space of Brownian Motion.- Ito Integration and Calculus.- Stochastic Differential Equations.- The Discrete Approach and Boundary Behavior.- The First Passage Time of Diffusions.- Markov Processes and Diffusion Approximations.- Diffusion Approximations to Langevin's Equation.- Large Deviations of Markovian Jump Processes.- Noise-Induced Escape from an Attractor.- Stochastic Stability.- Bibliography.
Series: Understanding Complex Systems
2010, Approx. 330 p. 21 illus. in color., Hardcover
ISBN: 978-3-642-02328-6
Due: February 21, 2010
Time delays in dynamical systems arise as an inevitable consequence of finite speeds of information transmission. Realistic models increasingly demand the inclusion of delays in order to properly understand, analyze, design, and control real-life systems.
The goal of this book is to present the state-of-the-art in research on time-delay dynamics in the framework of complex systems. While the theory of delay equations is quite mature, its application to the particular problems of complex systems and complexity is a newly emerging field, and the present volume aims to play a pioneering role in this perspective.
The chapters in this volume are authored by renowned experts and cover both theory and applications in a wide range of fields, with examples from neurosciences, traffic dynamics and laser physics. Furthermore, all chapters include sufficient introductory material and extensive bibliographies, making the book a self-contained reference for both graduate students and active researchers alike.
Postgraduate students and researchers in natural and physical sciences, engineering and applied mathematics
Amplitude Death, Synchrony, and Chimera States in Delay Coupled Limit Cycle Oscillators.- Delay-Induced Stability: From Oscillators to Networks.- Delay Effects on Output Feedback Control of Dynamical Systems.- Time-Delayed Feedback Control: From Simple Models to Lasers and Neural Systems.- Finite Propagation Speeds in Spatially Extended Systems.- Stochastic Delay-Differential Equations.- Global Convergent Dynamics of Delayed Neural Networks.- Stability and Hopf Bifurcation for a First-Order Delay Differential Equation With Distributed Delay.- Deterministic Time-Delayed Traffic Flow Models: A Survey.- Index.
Series: Springer Undergraduate Mathematics Series
2010, Approx. 125 p. 50 illus., Softcover
ISBN: 978-1-84882-968-8
Due: February 2010
Regression is the branch of Statistics in which a dependent variable of interest is modelled as a linear combination of one or more predictor variables together with a random error. Because the subject is inherently two- or higher- dimensional, and one should first meet Statistics in one dimension, this book presupposes some prior knowledge of Statistics. But these prerequisites are minimal: the contents of any first course in Statistics will suffice.
In addition to a first course in (one-dimensional) Statistics, important pre-requisites are a first course in Probability and some knowledge of standard Linear Algebra. Here the book’s needs are well served within the SUMS series, by John Haigh’s Probability Models and by the two volumes Basic Linear Algebra and Further Linear Algebra by T. S. Blyth and E. F. Robertson.
The book begins with simple linear regression (one predictor variable), and analysis of variance (ANOVA). It goes on to multiple linear regression (several predictor variables), analysis of covariance (ANCOVA), tests of linear hypotheses, departures from standard test conditions, and generalised linear models (GLMs). It concludes with special topics such as non-parametric regression and mixed models, time series, spatial processes and design of experiments. There are many worked examples and exercises with full solutions.
2nd/3rd year undergraduates studying statistics.
Linear Regression.- The Analysis of Variance (ANOVA).- Multiple Regression.- Further Multilinear Regression.- Analysis of Covariance.- Linear Hypotheses.- Model Checking and Transformation of Data.- Generalized linear models.- Solutions
Series: Universitext
2010, Approx. 455 p., Softcover
ISBN: 978-0-387-70913-0
Due: May 2010
Major textbook by a well-known and highly regarded author
The first single-volume textbook to cover related fields of functional analysis and PDEs
This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
Undergraduate and graduate students in mathematics and related fields including physics, engineering and finance
Preface.- 1. The Hahn?Banach Theorems. Introduction to the Theory of Conjugate Convex Functions.- 2. The Uniform Boundedness Principle and the Closed Graph Theorem. Unbounded Operators. Adjoint. Characterization of Surjective Operators.- 3. Weak Topologies. Reflexive Spaces. Separable Spaces. Uniform Convexity.- 4. L^p Spaces.- 5. Hilbert Spaces.- 6. Compact Operators. Spectral Decomposition of Self-Adjoint Compact Operators.- 7. The Hille?Yosida Theorem.- 8. Sobolev Spaces and the Variational Formulation of Boundary Value Problems in One Dimension.- 9. Sobolev Spaces and the Variational Formulation of Elliptic Boundary Value Problems in N Dimensions.- 10. Evolution Problems: The Heat Equation and the Wave Equation.- 11. Some Complements.- Problems.- Solutions of Some Exercises and Problems.- Bibliography.- Index.