Hardback (ISBN-13: 9780521195003)
Paperback (ISBN-13: 9780521123907)
David A. Freedman presents here a definitive synthesis of his approach to causal inference in the social sciences. He explores the foundations and limitations of statistical modeling, illustrating basic arguments with examples from political science, public policy, law, and epidemiology. Freedman maintains that many new technical approaches to statistical modeling constitute not progress, but regress. Instead, he advocates a ‘shoe leather’ methodology, which exploits natural variation to mitigate confounding and relies on intimate knowledge of the subject matter to develop meticulous research designs and eliminate rival explanations. When Freedman first enunciated this position, he was met with scepticism, in part because it was hard to believe that a mathematical statistician of his stature would favor ‘low-tech’ approaches. But the tide is turning. Many social scientists now agree that statistical technique cannot substitute for good research design and subject matter knowledge. This book offers an integrated presentation of Freedman’s views.
* Collects in one place many of Freedman’s most important works * Freedman’s
work challenges the assumptions of statistical research in social science,
public policy, law, and epidemiology * Addresses issues of current concern,
including swine flu vaccine, earthquake prediction, and statistical adjustments
to the U.S. census
Editor's introduction: inference and shoe leather; Part I. Statistical Modeling: Foundations and Limitations: 1. Some issues in the foundations of statistics: probability and model validation; 2. Statistical assumptions as empirical commitments; 3. Statistical models and shoe leather; Part II. Studies in Political Science, Public Policy, and Epidemiology: 4. Methods for Census 2000 and statistical adjustments; 5. On 'solutions' to the ecological inference problem; 6. Rejoinder to King; 7. Black ravens, white shoes, and case selection: inference with categorical variables; 8. What is the chance of an earthquake*; 9. Salt and blood pressure: conventional wisdom reconsidered; 10. The Swine Flu vaccine and Guillain-Barre Syndrome: relative risk and specific causation; 11. Survival analysis: an epidemiological hazard*; Part III. New Developments: Progress or Regress*: 12. On regression adjustments in experiments with several treatments; 13. Randomization does not justify logistic regression; 14. The grand leap; 15. On specifying graphical models for causation, and the identification problem; 16. Weighting regressions by propensity scores; 17. On the so-called 'Huber sandwich estimator' and 'robust standard errors'; 18. Endogeneity in probit response models; 19. Diagnostics cannot have much power against general alternatives; Part IV. Shoe Leather, Revisited: 20. On types of scientific inquiry: the role of quantitative reasoning.
Series: Encyclopedia of Mathematics and its Applications (No. 61)
Paperback (ISBN-13: 9780521119658)
This book provides a comprehensive presentation of geometric results, primarily from the theory of convex sets, that have been proved by the use of Fourier series or spherical harmonics. An important feature of the book is that all necessary tools from the classical theory of spherical harmonics are presented with full proofs. These tools are used to prove geometric inequalities, stability results, uniqueness results for projections and intersections by hyperplanes or half-spaces and characterisations of rotors in convex polytopes. Again, full proofs are given. To make the treatment as self-contained as possible the book begins with background material in analysis and the geometry of convex sets. This treatise will be welcomed both as an introduction to the subject and as a reference book for pure and applied mathematics.
* Offers a detailed and self-contained presentation of the theory of spherical
harmonics * Important supplement to books by Schneider and Gardner in the
same series
Preface; 1. Analytic preparations; 2. Geometric preparations; 3. Fourier series and spherical harmonics; 4. Geometric applications of Fourier series; 5. Geometric applications of spherical harmonics; References; List of symbols; Author index; Subject index.
Review of the hardback: ‘… these geometric results appear here in book form for the first time … developed as concretely as possible, with full proofs.’ L’Enseignement Mathematique
Review of the hardback: ‘Of the two main approaches to convex sets, the analytic is comprehensively covered by this welcome book.’ Mathematika
Hardback (ISBN-13: 9780521888608)
This complete introduction to two-dimensional (2-D) information theory and coding provides the key techniques for modeling data and estimating their information content. Throughout, special emphasis is placed on applications to transmission, storage, compression, and error protection of graphic information. The book begins with a self-contained introduction to information theory, including concepts of entropy and channel capacity, which requires minimal mathematical background knowledge. It then introduces error-correcting codes, particularly Reed-Solomon codes, the basic methods for error-correction, and codes applicable to data organized in 2-D arrays. Common techniques for data compression, including compression of 2-D data based on application of the basic source coding, are also covered, together with an advanced chapter dedicated to 2-D constrained coding for storage applications. Numerous worked examples illustrate the theory, whilst end-of-chapter exercises test the reader’s understanding, making this an ideal book for graduate students and also for practitioners in the telecommunications and data storage industries.
* Begins with a self-contained introduction to information theory which
requires minimal mathematical background knowledge * Provides the key techniques
for modeling data and estimating their information content * Includes numerous
worked examples to illustrate the theory and end-of-chapter exercises to
test understanding
Preface; 1. Introduction to information theory; 2. Finite state sources; 3. Channels and linear codes; 4. Reed-Solomon codes and their decoding; 5. Source coding; 6. Information in two-dimensional media; 7. Constrained two-dimensional fields for storage; 8. Reed-Solomon codes in applications; Appendix A: Fast arithmetic coding; Appendix B: Maximizing entropy; Appendix C: Decoding of RS code in F(16); Index.
Hardback (ISBN-13: 9780521874151)
The dream of automatic language translation is now closer thanks to recent advances in the techniques that underpin statistical machine translation. This class-tested textbook from an active researcher in the field, provides a clear and careful introduction to the latest methods and explains how to build machine translation systems for any two languages. It introduces the subject’s building blocks from linguistics and probability, then covers the major models for machine translation: word-based, phrase-based, and tree-based, as well as machine translation evaluation, language modeling, discriminative training and advanced methods to integrate linguistic annotation. The book also reports the latest research, presents the major outstanding challenges, and enables novices as well as experienced researchers to make novel contributions to this exciting area. Ideal for students at undergraduate and graduate level, or for anyone interested in the latest developments in machine translation.
* The first introductory guide to this burgeoning field - takes readers
step by step through theory and methods * Class tested by the author at
universities and conference tutorials * Accompanying website provides additional
exercises and links to further resources
Preface; Part I. Foundations: 1. Introduction; 2. Words, sentences, corpora; 3. Probability theory; Part II. Core Methods: 4. Word-based models; 5. Phrase-based models; 6. Decoding; 7. Language models; 8. Evaluation; Part III. Advanced Topics: 9. Discriminative training; 10. Integrating linguistic information; 11. Tree-based models; Bibliography; Author index; Index.
Series: Cambridge Monographs on Mathematical Physics
Paperback (ISBN-13: 9780521467025)
A paperback edition of a classic text, this book gives a unique survey of the known solutions of Einstein’s field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It introduces the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find or construct solutions. The solutions are then considered, ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties. Includes all the developments in the field since the first edition and contains six completely new chapters, covering topics including generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics. It can also be used as an introductory text on some mathematical aspects of general relativity.
* An updated and expanded edition of a classic text, containing important
new methods and solutions * Includes generation methods and their application,
colliding waves, classification of metrics by invariants and treatments
of homothetic motions * A unique survey of the known solutions of Einstein’s
field equations for vacuum, Einstein-Maxwell, pure radiation and perfect
fluid sources
Preface; List of tables; Notation; 1. Introduction; Part I. General Methods: 2. Differential geometry without a metric; 3. Some topics in Riemannian geometry; 4. The Petrov classification; 5. Classification of the Ricci tensor and the energy-movement tensor; 6. Vector fields; 7. The Newman-Penrose and related formalisms; 8. Continuous groups of transformations; isometry and homothety groups; 9. Invariants and the characterization of geometrics; 10. Generation techniques; Part II. Solutions with Groups of Motions: 11. Classification of solutions with isometries or homotheties; 12. Homogeneous space-times; 13. Hypersurface-homogeneous space-times; 14. Spatially-homogeneous perfect fluid cosmologies; 15. Groups G3 on non-null orbits V2. Spherical and plane symmetry; 16. Spherically-symmetric perfect fluid solutions; 17. Groups G2 and G1 on non-null orbits; 18. Stationary gravitational fields; 19. Stationary axisymmetric fields: basic concepts and field equations; 20. Stationary axisymmetiric vacuum solutions; 21. Non-empty stationary axisymmetric solutions; 22. Groups G2I on spacelike orbits: cylindrical symmetry; 23. Inhomogeneous perfect fluid solutions with symmetry; 24. Groups on null orbits. Plane waves; 25. Collision of plane waves; Part III. Algebraically Special Solutions: 26. The various classes of algebraically special solutions. Some algebraically general solutions; 27. The line element for metrics with κ=σ=0=R11=R14=R44, Θ+iω≠0; 28. Robinson-Trautman solutions; 29. Twisting vacuum solutions; 30. Twisting Einstein-Maxwell and pure radiation fields; 31. Non-diverging solutions (Kundt's class); 32. Kerr-Schild metrics; 33. Algebraically special perfect fluid solutions; Part IV. Special Methods: 34. Applications of generation techniques to general relativity; 35. Special vector and tensor fields; 36. Solutions with special subspaces; 37. Local isometric embedding of four-dimensional Riemannian manifolds; Part V. Tables: 38. The interconnections between the main classification schemes; References; Index.