ISBN: 978-0-470-06109-1
Hardcover
320 pages
June 2012
In the evaluation of healthcare, rigorous methods of quantitative assessment are necessary to establish interventions that are beneficial, are superior to all alternatives and are cost-effective. Usually one study will not provide answers to these questions and it will be necessary to synthesize evidence from multiple sources. This book aims to outline a coherent approach to such evidence synthesis, for the purpose of decision making. Each chapter contains worked examples, exercises and solutions drawn from a variety of medical disciplines
Evidence Syntesis for Decision Making intends to provide a practical guide to the appropriate methods for synthesizing evidence for use in analytical decision models. More specifically, it proposes a comprehensive evidence synthesis framework, which models all the available data appropriately and efficiently in a format that can be incorporated directly into a decision model.
ISBN: 978-0-470-17896-6
Hardcover
800 pages
July 2012
This new edition, now with a co-author, offers a complete and up-to-date examination of the field. The authors have streamlined previously tedious topics, such as multivariate regression and MANOVA techniques, to add newer, more timely content. Each chapter contains exercises, providing readers with the opportunity to test and extend their understanding. The new edition also presents several expanded topics in Kronecker product; prediction errors; maximum likelihood estimation; and selective key, but accessible proofs. This resource meets the needs of both statistics majors and those of students and professionals in other fields.
ISBN13: 9780199753871
Paperback, 352 pages
Apr 2011,
Our understanding of how the human brain performs mathematical calculations is far from complete, but in recent years there have been many exciting breakthroughs by scientists all over the world. Now, in The Number Sense, Stanislas Dehaene offers a fascinating look at this recent research, in an enlightening exploration of the mathematical mind. Dehaene begins with the eye-opening discovery that animals--including rats, pigeons, raccoons, and chimpanzees--can perform simple mathematical calculations, and that human infants also have a rudimentary number sense. Dehaene suggests that this rudimentary number sense is as basic to the way the brain understands the world as our perception of color or of objects in space, and, like these other abilities, our number sense is wired into the brain. These are but a few of the wealth of fascinating observations contained here. We also discover, for example, that because Chinese names for numbers are so short, Chinese people can remember up to nine or ten digits at a time--English-speaking people can only remember seven. The book also explores the unique abilities of idiot savants and mathematical geniuses, and we meet people whose minute brain lesions render their mathematical ability useless. This new and completely updated edition includes all of the most recent scientific data on how numbers are encoded by single neurons, and which brain areas activate when we perform calculations. Perhaps most important, The Number Sense reaches many provocative conclusions that will intrigue anyone interested in learning, mathematics, or the mind.
Features
A brilliant exploration of how the brain performs mathematical calculations
Traces the history of numbers from ancient to modern times
Offers an intriguing tour of how the structure of the brain shapes our mathematical abilities
Stanislas Dehaene teaches at the College de France and is Director of the Cognitive Neuroimaging Research Unit at INSERM.
Preface to the Revised and Expanded Edition
Preface to the First Edition
Introduction
Part I: Our Numerical Heritage
Chapter 1: Talented and Gifted Animals
Chapter 2: Babies Who Count
Chapter 3: The Adult Number Line
Part II: Beyond Approximation
Chapter 4: The Language of Numbers
Chapter 5: Small Heads for Big Calculations
Chapter 6: Geniuses and Prodigies
Part III: Of Neurons and Numbers
Chapter 7: Losing Number Sense
Chapter 8: The Computing Brain
Chapter 9: What Is a Number?
Epilogue. The Contemporary Science of Number and Brain
Appendix
Notes and References
Bibliography
Main books consulted
Useful web resources
Detailed bibliography
Index
Oxford Lecture Series in Mathematics and Its Applications 11
164 pages | 66 b/w line drawings | 234x156mm
978-0-19-966055-1 | Paperback | May 2012 (estimated)
Written by one of the founders of modern graph theory
Includes details of the historical development of the subject
An unusual and accessible introduction to the field
Graph Theory as I Have Known It provides a unique introduction to graph theory by one of the founding fathers, and will appeal to anyone interested in the subject. It is not intended as a comprehensive treatise, but rather as an account of those parts of the theory that have been of special interest to the author. Professor Tutte details his experience in the area, and provides a fascinating insight into how he was led to his theorems and the proofs he used. As well as being of historical interest it provides a useful starting point for research, with references to further suggested books as well as the original papers.
The book starts by detailing the first problems worked on by Professor Tutte and his colleagues during his days as an undergraduate member of the Trinity Mathematical Society in Cambridge. It covers subjects such as combinatorial problems in chess, the algebraicization of graph theory, reconstruction of graphs, and the chromatic eigenvalues. In each case fascinating historical and biographical information about the author's research is provided.
William Tutte (1917-2002) studied at Cambridge where his fascination for mathematical puzzles brought him into contact with like-minded undergraduates, together becoming known as the 'Trinity four', the founders of modern graph theory. His notable problem-solving skills meant he was brought to Bletchley Park during World War Two. Key in the enemy codebreaking efforts, he cracked the Lorenz cipher for which the Colossus machine was built, making his contribution comparable to Alan Turing's codebreaking for Enigma. Following his incredible war effort Tutte returned to academia and became a fellow of the Royal Society in Britain and Canada, finishing his career as Distinguished Professor Emeritus at the University of Waterloo, Ontario.
Readership: Undergraduate, graduate and research-level graph theorists, as well as mathematical historians of the twentieth century.
1: Squaring the square
2: Knights errant
3: Graphs within graphs
4: Unsymmetrical electricity
5: Algebra in graph theory
6: Symmetry in graphs
7: Graphs on spheres
8: The Cats of Cheshire
9: Reconstruction
10: Planar enumeration
11: The chromatic eigenvalues
12: In conclusion
Bibliography
Index
Oxford Statistical Science Series 38
368 pages | 34 b/w illustrations | 234x156mm
978-0-19-964117-8 | Hardback | May 2012 (estimated)
Clear, comprehensive introudction to the state space approach to time series analysis
Written by leaders in the field
Complete treatment of linear Gaussian models
New material including the filtering of nonlinear and non-Gaussian series and exercise sections
New to this edition
Extensive foundation of filtering and smoothing
Updated discussions on simulation smoothing methods
New sections on dynamic factor analysis, state smoothing analysis and more detail on Markov chain Monte Carlo methods
Analysis of nonlinear and non-Gaussian state space methods
Now includes exercise sections
This new edition updates Durbin & Koopman's important text on the state space approach to time series analysis. The distinguishing feature of state space time series models is that observations are regarded as made up of distinct components such as trend, seasonal, regression elements and disturbance terms, each of which is modelled separately. The techniques that emerge from this approach are very flexible and are capable of handling a much wider range of problems than the main analytical system currently in use for time series analysis, the Box-Jenkins ARIMA system. Additions to this second edition include the filtering of nonlinear and non-Gaussian series.
Part I of the book obtains the mean and variance of the state, of a variable intended to measure the effect of an interaction and of regression coefficients, in terms of the observations.
Part II extends the treatment to nonlinear and non-normal models. For these, analytical solutions are not available so methods are based on simulation.
Readership: Researchers in statistics, econometrics, biometrics, environmetrics, engineering, system theory and physics. Financial analysts in banking and other financial institutions.
1: Introduction
Part I: The linear state space model
2: Local level model
3: Linear Gaussian state space models
4: Filtering, smoothing and forecasting
5: Initialisation of Filter and smoother
6: Further computational aspects
7: Maximum likelihood estimation of parameters
8: Illustrations of the use of the linear Gaussian model
Part II: Non-Gaussian and nonlinear state space models
9: Special cases of nonlinear and non-Gaussian models
10: Approximate filtering and smoothing
11: Importance sampling for smoothing
12: Particle filtering
13: Bayesian estimation of parameters
14: Non-Gaussian and nonlinear illustrations
Subject Index
448 pages | 306 b/w line drawings, 31 b/w halftones | 246x189mm
978-0-19-956644-0 | Paperback | August 2012 (estimated)
978-0-19-956643-3 | Hardback | August 2012 (estimated)
The only textbook on chaos and fractals for non-science and mathematics majors.
Covers central phenomena and ideas of chaos and fractals in a careful, intellectually honest, but accessible way.
Covers current areas of physics and mathematics that are of wide interest
Richly illustrated.
Over 200 end-of-chapter exercises make it easy for instructors to assign homework problems.
A range of additional topics are covered from which instructors can chose as they put together their own courses.
This book provides the reader with an elementary introduction to chaos and fractals, suitable for students with a background in elementary algebra, without assuming prior coursework in calculus or physics. It introduces the key phenomena of chaos - aperiodicity, sensitive dependence on initial conditions, bifurcations - via simple iterated functions. Fractals are introduced as self-similar geometric objects and analyzed with the self-similarity and box-counting dimensions. After a brief discussion of power laws, subsequent chapters explore Julia Sets and the Mandelbrot Set. The last part of the book examines two-dimensional dynamical systems, strange attractors, cellular automata, and chaotic differential equations.
The book is richly illustrated and includes over 200 end-of-chapter exercises. A flexible format and a clear and succinct writing style make it a good choice for introductory courses in chaos and fractals.
Readership: Undergraduate students and lecturers on specialist and non-specialist courses in physics and mathematics.
I. Introducing Discrete Dynamical Systems
0: Opening Remarks
1: Functions
2: Iterating Functions
3: Qualitative Dynamics
4: Time Series Plots
5: Graphical Iteration
6: Iterating Linear Functions
7: Population Models
8: Newton, Laplace, and Determinism
II. Chaos
9: Chaos and the Logistic Equation
10: The Buttery Effect
11: The Bifurcation Diagram
12: Universality
13: Statistical Stability of Chaos
14: Determinism, Randomness, and Nonlinearity
III. Fractals
15: Introducing Fractals
16: Dimensions
17: Random Fractals
18: The Box-Counting Dimension
19: When do Averages exist?
20: Power Laws and Long Tails
20: Introducing Julia Sets
21: Infinities, Big and Small
IV. Julia Sets and The Mandelbrot Set
22: Introducing Julia Sets
23: Complex Numbers
24: Julia Sets for f(z) = z2 + c
25: The Mandelbrot Set
V. Higher-Dimensional Systems
26: Two-Dimensional Discrete Dynamical Systems
27: Cellular Automata
28: Introduction to Differential Equations
29: One-Dimensional Differential Equations
30: Two-Dimensional Differential Equations
31: Chaotic Differential Equations and Strange Attractors
VI. Conclusion
32: Conclusion
VII. Appendices
A: Review of Selected Topics from Algebra
B: Histograms and Distributions
C: Suggestions for Further Reading