From Statistical Physics To Statistical Inference And Back

Author : P. Grassberger,J.P. Nadal
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401110686

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From Statistical Physics to Statistical Inference and Back by P. Grassberger,J.P. Nadal Pdf

Physicists, when modelling physical systems with a large number of degrees of freedom, and statisticians, when performing data analysis, have developed their own concepts and methods for making the `best' inference. But are these methods equivalent, or not? What is the state of the art in making inferences? The physicists want answers. More: neural computation demands a clearer understanding of how neural systems make inferences; the theory of chaotic nonlinear systems as applied to time series analysis could profit from the experience already booked by the statisticians; and finally, there is a long-standing conjecture that some of the puzzles of quantum mechanics are due to our incomplete understanding of how we make inferences. Matter enough to stimulate the writing of such a book as the present one. But other considerations also arise, such as the maximum entropy method and Bayesian inference, information theory and the minimum description length. Finally, it is pointed out that an understanding of human inference may require input from psychologists. This lively debate, which is of acute current interest, is well summarized in the present work.

Author : Nitis Mukhopadhyay
Publisher : CRC Press
Page : 289 pages
File Size : 43,7 Mb
Release : 2006-02-07
Category : Mathematics
ISBN : 9781420017403

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Introductory Statistical Inference by Nitis Mukhopadhyay Pdf

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.

Author : George Casella,Roger Berger
Publisher : CRC Press
Page : 1746 pages
File Size : 52,8 Mb
Release : 2024-05-23
Category : Mathematics
ISBN : 9781040024027

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Statistical Inference by George Casella,Roger Berger Pdf

This classic textbook builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and natural extensions, and consequences, of previous concepts. It covers all topics from a standard inference course including: distributions, random variables, data reduction, point estimation, hypothesis testing, and interval estimation. Features The classic graduate-level textbook on statistical inference Develops elements of statistical theory from first principles of probability Written in a lucid style accessible to anyone with some background in calculus Covers all key topics of a standard course in inference Hundreds of examples throughout to aid understanding Each chapter includes an extensive set of graduated exercises Statistical Inference, Second Edition is primarily aimed at graduate students of statistics, but can be used by advanced undergraduate students majoring in statistics who have a solid mathematics background. It also stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures, while less focused on formal optimality considerations. This is a reprint of the second edition originally published by Cengage Learning, Inc. in 2001.

Author : Y. M. Guttmann
Publisher : Cambridge University Press
Page : 283 pages
File Size : 42,5 Mb
Release : 1999-07-13
Category : Mathematics
ISBN : 9780521621281

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The Concept of Probability in Statistical Physics by Y. M. Guttmann Pdf

A most systematic study of how to interpret probabilistic assertions in the context of statistical mechanics.

Author : Edwin T. Jaynes
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 43,9 Mb
Release : 1989-04-30
Category : Mathematics
ISBN : 0792302133

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E.T. Jaynes by Edwin T. Jaynes Pdf

The first six chapters of this volume present the author's 'predictive' or information theoretic' approach to statistical mechanics, in which the basic probability distributions over microstates are obtained as distributions of maximum entropy (Le. , as distributions that are most non-committal with regard to missing information among all those satisfying the macroscopically given constraints). There is then no need to make additional assumptions of ergodicity or metric transitivity; the theory proceeds entirely by inference from macroscopic measurements and the underlying dynamical assumptions. Moreover, the method of maximizing the entropy is completely general and applies, in particular, to irreversible processes as well as to reversible ones. The next three chapters provide a broader framework - at once Bayesian and objective - for maximum entropy inference. The basic principles of inference, including the usual axioms of probability, are seen to rest on nothing more than requirements of consistency, above all, the requirement that in two problems where we have the same information we must assign the same probabilities. Thus, statistical mechanics is viewed as a branch of a general theory of inference, and the latter as an extension of the ordinary logic of consistency. Those who are familiar with the literature of statistics and statistical mechanics will recognize in both of these steps a genuine 'scientific revolution' - a complete reversal of earlier conceptions - and one of no small significance.

Author : R.D. Rosenkrantz
Publisher : Springer Science & Business Media
Page : 457 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400965812

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E. T. Jaynes: Papers on Probability, Statistics and Statistical Physics by R.D. Rosenkrantz Pdf

The first six chapters of this volume present the author's 'predictive' or information theoretic' approach to statistical mechanics, in which the basic probability distributions over microstates are obtained as distributions of maximum entropy (Le. , as distributions that are most non-committal with regard to missing information among all those satisfying the macroscopically given constraints). There is then no need to make additional assumptions of ergodicity or metric transitivity; the theory proceeds entirely by inference from macroscopic measurements and the underlying dynamical assumptions. Moreover, the method of maximizing the entropy is completely general and applies, in particular, to irreversible processes as well as to reversible ones. The next three chapters provide a broader framework - at once Bayesian and objective - for maximum entropy inference. The basic principles of inference, including the usual axioms of probability, are seen to rest on nothing more than requirements of consistency, above all, the requirement that in two problems where we have the same information we must assign the same probabilities. Thus, statistical mechanics is viewed as a branch of a general theory of inference, and the latter as an extension of the ordinary logic of consistency. Those who are familiar with the literature of statistics and statistical mechanics will recognize in both of these steps a genuine 'scientific revolution' - a complete reversal of earlier conceptions - and one of no small significance.

Author : Masahito Hayashi
Publisher : World Scientific
Page : 560 pages
File Size : 49,6 Mb
Release : 2005-02-21
Category : Science
ISBN : 9789814481984

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Asymptotic Theory of Quantum Statistical Inference by Masahito Hayashi Pdf

' Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990; the famous textbooks by Holevo and Helstrom deal only with research results in the earlier stage (1960s-1970s). This book presents the important and recent results of quantum statistical inference. It focuses on the asymptotic theory, which is one of the central issues of mathematical statistics and had not been investigated in quantum statistical inference until the early 1980s. It contains outstanding papers after Holevo's textbook, some of which are of great importance but are not available now. The reader is expected to have only elementary mathematical knowledge, and therefore much of the content will be accessible to graduate students as well as research workers in related fields. Introductions to quantum statistical inference have been specially written for the book. Asymptotic Theory of Quantum Statistical Inference: Selected Papers will give the reader a new insight into physics and statistical inference. Contents:Hypothesis TestingQuantum Cramér-Rao Bound in Mixed States ModelQuantum Cramér-Rao Bound in Pure States ModelGroup Symmetric Approach to Pure States ModelLarge Deviation Theory in Quantum EstimationFuther Topics on Quantum Statistical Inference Readership: Graduate students in quantum physics, mathematical physics, and probability and statistics. Keywords:Quantum Information;Estimation Theory;Statistics;Statistical Inference;Mathematical Physics;Asymptotic Theory;Hypothesis TestingReviews:“This book will give the scholars new insight into physics and statistical inference.”Zentralblatt MATH '

Author : Michael J. Panik
Publisher : John Wiley & Sons
Page : 294 pages
File Size : 49,7 Mb
Release : 2012-06-06
Category : Mathematics
ISBN : 9781118309803

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Statistical Inference by Michael J. Panik Pdf

A concise, easily accessible introduction to descriptive and inferential techniques Statistical Inference: A Short Course offers a concise presentation of the essentials of basic statistics for readers seeking to acquire a working knowledge of statistical concepts, measures, and procedures. The author conducts tests on the assumption of randomness and normality, provides nonparametric methods when parametric approaches might not work. The book also explores how to determine a confidence interval for a population median while also providing coverage of ratio estimation, randomness, and causality. To ensure a thorough understanding of all key concepts, Statistical Inference provides numerous examples and solutions along with complete and precise answers to many fundamental questions, including: How do we determine that a given dataset is actually a random sample? With what level of precision and reliability can a population sample be estimated? How are probabilities determined and are they the same thing as odds? How can we predict the level of one variable from that of another? What is the strength of the relationship between two variables? The book is organized to present fundamental statistical concepts first, with later chapters exploring more advanced topics and additional statistical tests such as Distributional Hypotheses, Multinomial Chi-Square Statistics, and the Chi-Square Distribution. Each chapter includes appendices and exercises, allowing readers to test their comprehension of the presented material. Statistical Inference: A Short Course is an excellent book for courses on probability, mathematical statistics, and statistical inference at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for researchers and practitioners who would like to develop further insights into essential statistical tools.

Author : E.J.G. Pitman
Publisher : CRC Press
Page : 61 pages
File Size : 41,6 Mb
Release : 2018-01-18
Category : Mathematics
ISBN : 9781351093675

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Some Basic Theory for Statistical Inference by E.J.G. Pitman Pdf

In this book the author presents with elegance and precision some of the basic mathematical theory required for statistical inference at a level which will make it readable by most students of statistics.

Author : Harold Adolph Freeman
Publisher : Unknown
Page : 488 pages
File Size : 51,8 Mb
Release : 1963
Category : Mathematics
ISBN : UCAL:B3785917

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Introduction to Statistical Inference by Harold Adolph Freeman Pdf

Author : Deborah G. Mayo
Publisher : Cambridge University Press
Page : 503 pages
File Size : 43,9 Mb
Release : 2018-09-20
Category : Mathematics
ISBN : 9781107054134

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Statistical Inference as Severe Testing by Deborah G. Mayo Pdf

Unlock today's statistical controversies and irreproducible results by viewing statistics as probing and controlling errors.

Author : Michael W. Trosset
Publisher : CRC Press
Page : 496 pages
File Size : 42,6 Mb
Release : 2009-06-23
Category : Mathematics
ISBN : 9781584889489

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An Introduction to Statistical Inference and Its Applications with R by Michael W. Trosset Pdf

Emphasizing concepts rather than recipes, An Introduction to Statistical Inference and Its Applications with R provides a clear exposition of the methods of statistical inference for students who are comfortable with mathematical notation. Numerous examples, case studies, and exercises are included. R is used to simplify computation, create figures

Author : Yury A. Kutoyants
Publisher : Springer Science & Business Media
Page : 493 pages
File Size : 44,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781447138662

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Statistical Inference for Ergodic Diffusion Processes by Yury A. Kutoyants Pdf

The first book in inference for stochastic processes from a statistical, rather than a probabilistic, perspective. It provides a systematic exposition of theoretical results from over ten years of mathematical literature and presents, for the first time in book form, many new techniques and approaches.

Author : D.A. Sprott
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 50,5 Mb
Release : 2008-01-28
Category : Mathematics
ISBN : 9780387227665

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Statistical Inference in Science by D.A. Sprott Pdf

A treatment of the problems of inference associated with experiments in science, with the emphasis on techniques for dividing the sample information into various parts, such that the diverse problems of inference that arise from repeatable experiments may be addressed. A particularly valuable feature is the large number of practical examples, many of which use data taken from experiments published in various scientific journals. This book evolved from the authors own courses on statistical inference, and assumes an introductory course in probability, including the calculation and manipulation of probability functions and density functions, transformation of variables and the use of Jacobians. While this is a suitable text book for advanced undergraduate, Masters, and Ph.D. statistics students, it may also be used as a reference book.

Author : Anonim
Publisher : Elsevier
Page : 849 pages
File Size : 54,7 Mb
Release : 2006-06-27
Category : Science
ISBN : 9780080479231

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Mathematical Statistical Physics by Anonim Pdf

The proceedings of the 2005 les Houches summer school on Mathematical Statistical Physics give and broad and clear overview on this fast developing area of interest to both physicists and mathematicians. Introduction to a field of math with many interdisciplinary connections in physics, biology, and computer science Roadmap to the next decade of mathematical statistical mechanics Volume for reference years to come