ISBN: 978-0-470-50945-6
Hardcover
408 pages
October 2011
A vivid, hands-on discussion of the statistical methods in imaging, optics, and photonics applications
In the field of imaging science, there is a growing need for students and practitioners to be equipped with the necessary knowledge and tools to carry out quantitative analysis of data. Providing a self-contained approach that is not too heavily statistical in nature, Statistics for Imaging, Optics, and Photonics presents necessary analytical techniques in the context of real examples from various areas within the field, including remote sensing, color science, printing, and astronomy.
Bridging the gap between imaging, optics, photonics, and statistical data analysis, the author uniquely concentrates on statistical inference, providing a wide range of relevant methods. Brief introductions to key probabilistic terms are provided at the beginning of the book in order to present the notation used, followed by discussions on multivariate techniques such as:
* Linear regression models, vector and matrix algebra, and random vectors and matrices
* Multivariate statistical inference, including inferences about both mean vectors and covariance matrices
* Principal components analysis
* Canonical correlation analysis
* Discrimination and classification analysis for two or more populations and spatial smoothing
* Cluster analysis, including similarity and dissimilarity measures and hierarchical and nonhierarchical clustering methods
Intuitive and geometric understanding of concepts is emphasized, and all examples are relatively simple and include background explanations. Computational results and graphs are presented using the freely available R software, and can be replicated by using a variety of software packages. Throughout the book, problem sets and solutions contain partial numerical results, allowing readers to confirm the accuracy of their approach; and a related website features additional resources including the book's datasets and figures.
Statistics for Imaging, Optics, and Photonics is an excellent book for courses on multivariate statistics for imaging science, optics, and photonics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for professionals working in imaging, optics, and photonics who carry out data analyses in their everyday work.
ISBN: 978-0-470-74002-6
Hardcover
224 pages
November 2011
This book is based upon an EPSRC funded project aimed at sharing understanding of modelling complex phenomena. The aim of the book is to ease communication between modellers in different disciplines. The book is useful to physicists wishing to find out about statistical approaches to modelling and to statisticians wishing to learn about modelling in the physical sciences. It is also a useful source of modelling case histories. The book provides a much-needed reference guide for approaching statistical modeling and a useful source for modeling case histories.
The book consists of four sections
1.An introductory section covering important concepts in modeling and outlining different traditions as regards the relative utility of simple and complex modeling in statistics.
2.Subject specific chapters illustrating modeling approaches in various disciplines
3.A summary chapter explaining what issues have been resolved and which remain unresolved
4.A glossary giving terms commonly used in different modeling traditions.
This book covers a number of case studies of complex modeling, including climate change, flood risk, deterministic computer modeling and how well the model can predict reality, water distribution systems and looks at how this has evolved, new drug development models and its usage and the petroleum industry and uncertainty of accurate forecasts.
1st Edition., 2011, IX, 284 p. 97 illus., 47 in color.
Hardcover, ISBN 978-0-85729-928-4
The first biography to be written about Sofya Kovalevskaya by a renowned mathematician Offers a well-rounded narrative that incorporates literature, mathematics and personal biography May also appeal to those doing general feminist studies
Sofia Kovalevskaya was a brilliant and determined young Russian woman of the 19th century who wanted to become a mathematician and who succeeded, in often difficult circumstances, in becoming arguably the first woman to have a professional university career in the way we understand it today. This memoir, written by a mathematician who specialises in symplectic geometry and integrable systems, is a personal exploration of the life, the writings and the mathematical achievements of a remarkable woman. It emphasises the originality of Kovalevskayafs work and assesses her legacy and reputation as a mathematician and scientist. Her ideas are explained in a way that is accessible to a general audience, with diagrams, marginal notes and commentary to help explain the mathematical concepts and provide context. This fascinating book, which also examines Kovalevskayafs love of literature, will be of interest to historians looking for a treatment of the mathematics, and those doing feminist or gender studies.
Sofyafs chronology.- Sofyafs names.- Stories.- The thesis of Sofya, the Cauchy?Kovalevskaya theorem.- The Solid.- A letter to Mittag-Leffler.- Stockholm.- A letter to Vollmar.- The Bordin prize and Sofyafs reputation.- The women of Men of mathematics.- I remember Sofya, by George, Gosta, Julia and all the rest.- I too remember Sofya.- Bibliography.
Series: Publications of the Scuola Normale Superiore, Vol. 10
1st Edition., 2011, 198 p.
Softcover, ISBN 978-88-7642-385-7
This textbook collects the notes for an introductory course in measure theory and integration. The course was taught by the authors to undergraduate students of the Scuola Normale Superiore, in the years 2000-2011. The goal of the course was to present, in a quick but rigorous way, the modern point of view on measure theory and integration, putting Lebesgue's Euclidean space theory into a more general context and presenting the basic applications to Fourier series, calculus and real analysis. The text can also pave the way to more advanced courses in probability, stochastic processes or geometric measure theory. Prerequisites for the book are a basic knowledge of calculus in one and several variables, metric spaces and linear algebra. All results presented here, as well as their proofs, are classical. The authors claim some originality only in the presentation and in the choice of the exercises. Detailed solutions to the exercises are provided in the final part of the book.
Measure spaces.- Integration.- Spaces of measurable functions.- Hilbert spaces.- Fourier series.- Operations on measures.- The fundamental theorem of integral calculus.- Operations on measures.- Appendix: Riesz representation theorem of the dual of C(K) and integrals depending on a parameter.- Solutions to the exercises.
2011, 2011, Approx. 650 p. 2-volume-set.
ISBN 978-94-007-0920-1
Due: September 2011
Proof, Computation and Agency Proof, Computation and Agency: Logic at the Cross Roads provides an overview of Logic and its relationship with other disciplines, and some of the emerging areas in terms. The volume brings out an inspiring paradigm, called 'Social Software', the study of patterns of social interaction by means of techniques from logic and computer science. Besides, it demonstrates how an extended view of logic can join forces with the social sciences, game theory or social choice theory, in studying patterns and procedures in social agency, and systematizing this field. Moreover, the study of Logic-Language- Cognition connection forms an important component of the fresh approach the volume. Finally, the volume explores the nature of the contributions made in Indian tradition in logic by demonstrating that the validity of inference is not a purely formal notion and logic could be placed in the context of epistemology and the Indian scientific tradition. The book takes up Indian logic in its connections with philosophical epistemology and the philosophy of science and exhibits how topics ran naturally into each other. Games, Norms and Reasons The explanation as to why logic is perceived as standing at the crossroads has to do with fact that in the recent past logic, in relationship with several academic disciplines closely related to it, has been a catalyst in giving rise to new research programmes or even innovative academic fields. Games, Norms, and Reasons: Logic at the Crossroads provides an overview of Logic and its relationship with other disciplines, and some of the emerging areas in terms of leading articles by pioneers in the field. The first part of this is devoted to exploring aspects of norms, reasons, preferences and beliefs in human agency, human interaction or structured groups, sometimes using the logic of games or by developing novel frameworks, concepts and ideas appropriate for such exploration. The papers in the second part of the volume are dedicated to Rohit Parikh who embodies some of the new trends in the explorations mentioned above that are not only seminal, but shaped the direction of a field, sometimes even creating it.
Series: SpringerBriefs in Statistics
1st Edition., 2012, Approx. 125 p.
Softcover, ISBN 978-3-642-23479-8
Due: September 13, 2011
This book is intended for those interested in the history of mathematics or statistics; though it assumes a strong background in mathematics, it will also be useful for statisticians. My exposition is based chiefly on my own investigations, published in the last 35 years, and a 2009 monograph. I conclude my observations with the axiomatization of probability and the birth of real mathematical statistics, i.e., at Kolmogorov and Fisher.
Introduction.- Prehistory.- Early History.- Jakob Bernoulli and the Law of Large Numbers.- De Moivre and the De Moivre ? Laplace Limit Theorem.- Bayes.- Other Investigations Before Laplace.- Laplace.- Poisson.- Gauss, Helmert, Bessel.- The Second Half of the Nineteenth Century.- Bertrand and Poincare.- Chebyshev.- Markov, Liapunov, Nekrasov.- The Birth of Mathematical Statistics.- Bibliography.- Index of Names.