Analysis
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| Author | : Andrew Gelman |
| Publisher | : CRC Press |
| Total Pages | : 677 |
| Release | : 2013-11-01 |
| Genre | : Mathematics |
| ISBN | : 1439840954 |
Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.
| Author | : Terence Tao |
| Publisher | : Springer |
| Total Pages | : 366 |
| Release | : 2016-08-29 |
| Genre | : Mathematics |
| ISBN | : 9811017891 |
This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
| Author | : Xavier Rival |
| Publisher | : MIT Press |
| Total Pages | : 315 |
| Release | : 2020-02-11 |
| Genre | : Computers |
| ISBN | : 0262043416 |
A self-contained introduction to abstract interpretation–based static analysis, an essential resource for students, developers, and users. Static program analysis, or static analysis, aims to discover semantic properties of programs without running them. It plays an important role in all phases of development, including verification of specifications and programs, the synthesis of optimized code, and the refactoring and maintenance of software applications. This book offers a self-contained introduction to static analysis, covering the basics of both theoretical foundations and practical considerations in the use of static analysis tools. By offering a quick and comprehensive introduction for nonspecialists, the book fills a notable gap in the literature, which until now has consisted largely of scientific articles on advanced topics. The text covers the mathematical foundations of static analysis, including semantics, semantic abstraction, and computation of program invariants; more advanced notions and techniques, including techniques for enhancing the cost-accuracy balance of analysis and abstractions for advanced programming features and answering a wide range of semantic questions; and techniques for implementing and using static analysis tools. It begins with background information and an intuitive and informal introduction to the main static analysis principles and techniques. It then formalizes the scientific foundations of program analysis techniques, considers practical aspects of implementation, and presents more advanced applications. The book can be used as a textbook in advanced undergraduate and graduate courses in static analysis and program verification, and as a reference for users, developers, and experts.
| Author | : Stephen Abbott |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 269 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 0387215069 |
This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.
| Author | : Bernard R. Gelbaum |
| Publisher | : Courier Corporation |
| Total Pages | : 226 |
| Release | : 2012-07-12 |
| Genre | : Mathematics |
| ISBN | : 0486134911 |
These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.
| Author | : Maxwell Rosenlicht |
| Publisher | : Courier Corporation |
| Total Pages | : 270 |
| Release | : 2012-05-04 |
| Genre | : Mathematics |
| ISBN | : 0486134687 |
Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.
| Author | : Abraham Robinson |
| Publisher | : Princeton University Press |
| Total Pages | : 315 |
| Release | : 2016-08-11 |
| Genre | : Mathematics |
| ISBN | : 1400884225 |
Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.
| Author | : Andrew Gelman |
| Publisher | : CRC Press |
| Total Pages | : 717 |
| Release | : 2003-07-29 |
| Genre | : Mathematics |
| ISBN | : 1420057294 |
Incorporating new and updated information, this second edition of THE bestselling text in Bayesian data analysis continues to emphasize practice over theory, describing how to conceptualize, perform, and critique statistical analyses from a Bayesian perspective. Its world-class authors provide guidance on all aspects of Bayesian data analysis and include examples of real statistical analyses, based on their own research, that demonstrate how to solve complicated problems. Changes in the new edition include: Stronger focus on MCMC Revision of the computational advice in Part III New chapters on nonlinear models and decision analysis Several additional applied examples from the authors' recent research Additional chapters on current models for Bayesian data analysis such as nonlinear models, generalized linear mixed models, and more Reorganization of chapters 6 and 7 on model checking and data collection Bayesian computation is currently at a stage where there are many reasonable ways to compute any given posterior distribution. However, the best approach is not always clear ahead of time. Reflecting this, the new edition offers a more pluralistic presentation, giving advice on performing computations from many perspectives while making clear the importance of being aware that there are different ways to implement any given iterative simulation computation. The new approach, additional examples, and updated information make Bayesian Data Analysis an excellent introductory text and a reference that working scientists will use throughout their professional life.
| Author | : Andrew F. Hayes |
| Publisher | : Guilford Publications |
| Total Pages | : 714 |
| Release | : 2017-10-30 |
| Genre | : Social Science |
| ISBN | : 146253466X |
This book has been replaced by Introduction to Mediation, Moderation, and Conditional Process Analysis, Third Edition, ISBN 978-1-4625-4903-0.
| Author | : Patrick Hanks |
| Publisher | : MIT Press |
| Total Pages | : 479 |
| Release | : 2013-01-25 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 0262312867 |
A lexically based, corpus-driven theoretical approach to meaning in language that distinguishes between patterns of normal use and creative exploitations of norms. In Lexical Analysis, Patrick Hanks offers a wide-ranging empirical investigation of word use and meaning in language. The book fills the need for a lexically based, corpus-driven theoretical approach that will help people understand how words go together in collocational patterns and constructions to make meanings. Such an approach is now possible, Hanks writes, because of the availability of new forms of evidence (corpora, the Internet) and the development of new methods of statistical analysis and inferencing. Hanks offers a new theory of language, the Theory of Norms and Exploitations (TNE), which makes a systematic distinction between normal and abnormal usage—between rules for using words normally and rules for exploiting such norms in metaphor and other creative use of language. Using hundreds of carefully chosen citations from corpora and other texts, he shows how matching each use of a word against established contextual patterns plays a large part in determining the meaning of an utterance. His goal is to develop a coherent and practical lexically driven theory of language that takes into account the immense variability of everyday usage and that shows that this variability is rule governed rather than random. Such a theory will complement other theoretical approaches to language, including cognitive linguistics, construction grammar, generative lexicon theory, priming theory, and pattern grammar.
