Roger Cooke, Dorota Kurowicka

Uncertainty Analysis: Mathematical Foundations and Applications

ISBN: 0-470-86306-4
Hardcover
384 pages
April 2006

Description

There has been an explosion of interest in the area of uncertainty analysis in recent years, and a vast amount of research has been published. It is key to any scientific disciplines that employs the use of statistical models to simulate complex real-world phenomena.. There is a real need for a book that presents the mathematical theory of uncertainty analysis, and provides practical insight into how the theory may be applied to real problems. This book provides both the mathematical foundations and practical application, with software support using UNICORN software. This software has been developed by the authors and can be used to model and analyse uncertainty in complex problems. A version tailored specifically for the book is included on a supplementary Web site, that also features macros and data sets to support the examples in the book. The first-named author is a leading authority in uncertainty analysis, with two highly-regarded books in the area, and his group is at the forefront of research in the area.

Provides a comprehensive overview of the foundations and applications of uncertainty analysis.

Covers a number of key topics, including uncertainty elicitation, dependence modelling, sensitivity analysis and probabilistic inversion.

Illustrated throughout by numerous worked examples and applications.

Includes software support for the examples using UNICORN ? a Windows-based uncertainty modelling package developed by the authors.
Includes a section of workbook problems, enabling use for teaching.

Accompanied by a Website featuring a version of the UNICORN software tailored specifically for the book; as well as computer programs and data sets to support the examples.

Table of contentes

Nitis Mukhopadhyay University of Connecticut, Storrs, USA

Introductory Statistical Inference

Series: Statistics: A Series of Textbooks and Monographs Volume: 187

ISBN: 1574446134
Publication Date: 2/8/2006
Number of Pages: 304

Contains a concise review of probability concepts
Discusses topics such as sufficiency, ancillarity, point estimation, and minimum variance estimation
Includes worked examples of core statistical principles as well as numerous exercises with hints
Introduces techniques of two-stage sampling, tests of hypotheses, and nonparametric methods

Introductory Statistical Inference develops the concepts and intricacies of statistical inference. With a review of probability concepts, this book discusses topics such as sufficiency, ancillarity, point estimation, minimum variance estimation, confidence intervals, multiple comparisons, and large-sample inference. It introduces techniques of two-stage sampling, fitting a straight line to data, tests of hypotheses, nonparametric methods, and the bootstrap method. It also features worked examples of statistical principles as well as exercises with hints. This text is suited for courses in probability and statistical inference at the upper-level undergraduate and graduate levels.

Table of Contents

Review of Probability and Related Concepts. Sufficiency, Completeness, and Ancillarity. Point Estimation. Tests of Hypotheses. Confidence Interval Estimation. Bayesian Methods. Likelihood Ratio and Other Tests. Large-Sample Inference. Sample Size Determination: Two-Stage Procedures. Regression Analysis: Fitting a Straight Line. Nonparametric Methods. Bootstrap Methods. Appendix. References.

Haruzo Hida

Hilbert Modular Forms and Iwasawa Theory

(Hardback)
0-19-857102-X
Publication date: 29 June 2006
Clarendon Press 400 pages, 31 black and white line drawings, 234mm x 156mm
Series: Oxford Mathematical Monographs

Description

Authored by a leading name in the field
Timely and topical coverage of an exciting research area
Includes many exercises and open questions

The 1995 work of Wiles and Taylor-Wiles opened up a whole new technique in algebraic number theory and, a decade on, the waves caused by this incredibly important work are still being felt. This book, authored by a leading researcher, describes the striking applications that have been found for this technique. In the book, the deformation theoretic techniques of Wiles-Taylor are first generalized to Hilbert modular forms (following Fujiwara's treatment), and some applications found by the author are then discussed. With many exercises and open questions given, this text is ideal for researchers and graduate students entering this research area.

Readership: Graduates and researchers in number theory and pure mathematics

Contents

Preface
1 Introduction
2 Automorphic forms on inner forms of GL(2)
3 Hecke algebras as Galois deformation rings
4 Geometric modular forms
5 Modular Iwasawa theory
References
Index

Roman Kossak and James Schmerl

The Structure of Models of Peano Arithmetic

(Hardback)
0-19-856827-4
Publication date: 29 June 2006
Clarendon Press 304 pages, 2 b/w line drawings, 234mm x 156mm
Series: Oxford Logic Guides

Description

A major contribution to the field
An excellent reference by world-renowned experts
Contains graded exercises at the end of each chapter to aid the reader's understanding
Ends with a list of twenty open questions remaining in the field

Aimed at graduate students and research logicians and mathematicians, this much-awaited text covers over forty years of work on relative classification theory for non-standard models of arithmetic. With graded exercises at the end of each chapter, the book covers basic isomorphism invariants: families of types realized in a model, lattices of elementary substructures and automorphism groups. Many results involve applications of the powerful technique of minimal types due to Haim Gaifman, and some of the results are classical but have never been published in a book form before.

Readership: Graduates and researchers in logic and mathematics

Contents

Preface
1 Basics
2 Extensions
3 Minimal and other types
4 Substructure lattices
5 How to control types
6 Generics and forcing
7 Cuts
8 Automorphisms of recursively saturated models
9 Automorphism groups of recursively saturated models
10 Omega 1-like models
11 Order types
12 Twenty questions
References
Index

Hedy Attouch, Giuseppe Buttazzo, Gerard Michaille

Variational Analysis in Sobolev and BV Spaces:
Applications to PDEs and Optimization

“This book is a solid treatise on the (contemporary) calculus of variations. The material presented is quite extensive and slightly nontraditional. For example, the authors include a chapter on convex duality and subdifferential calculus. Often, books on the modern calculus of variations and books devoted to convex optimization have little if any overlap. I believe readers will appreciate the nontrivial overlap in the present text.”
? Rustum Choksi, Associate Professor of Applied and Computational Mathematics, Simon Fraser University.

"The second part has some discussion of more advanced background material (such as BV and SBV functions) needed for work on many modern variational problems, as well as discussions of recent results on a variety of problems, including variational approaches to image segmentation, fracture mechanics, and shape optimization."
? Robert Jerrard, Professor of Mathematics, University of Toronto.

This self-contained book is excellent for graduate-level courses devoted to variational analysis, optimization, and partial differential equations (PDEs). It provides readers with a complete guide to problems in these fields as well as a detailed presentation of the most important tools and methods of variational analysis. New trends in variational analysis are also presented, along with recent developments and applications in this area. Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization is not just for students, however; it is a comprehensive guide for anyone who wants to approach the field of variational analysis in a systematic way, starting from the most classical examples and working up to a research level. This book also contains several applications to problems in geometry, mechanics, elasticity, and computer vision, along with a complete list of references.

Contents

Preface; Chapter 1: Introduction; Part I: First Part: Basic Variational Principles; Chapter 2: Weak solutions methods in variational analysis; Chapter 3: Abstract variational principles; Chapter 4: Complements on measure theory; Chapter 5: Sobolev spaces; Chapter 6: Variational problems: Some classical examples; Chapter 7: The finite element method; Chapter 8: Spectral Analysis of the Laplacian; Chapter 9: Convex duality and optimization; Part II: Second Part: Advanced Variational Analysis. Chapter 10: Spaces BV and SBV; Chapter 11: Relaxation in Sobolev, BV and Young measures spaces; Chapter 12: г-convergence and applications; Chapter 13: Integral functionals of the calculus of variations; Chapter 14: Application in mechanics and computer vision; Chapter 15: Variational problems with a lack of coercivity; Chapter 16: An introduction to shape optimization problems; Bibliography; Index.

Available December 2005 / xii + 634 pages / Softcover / ISBN 0-89871-600-4