Statistical Complexity
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Statistical Complexity
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Author : K.D. Sen
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-27
Statistical Complexity written by K.D. Sen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-27 with Science categories.
The understanding of electron density as the carrier of all the information of a multielectronic system is implicit in the theorems of density functional theory. Information theoretical based measures giving a quantitative understanding of statistical complexity of such systems is shaping up as a new area of research in chemical physics. This book is the first monograph of its kind covering the aspects of complexity measure in atoms and molecules.
Stochastic Complexity In Statistical Inquiry
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Author : Jorma Rissanen
language : en
Publisher: World Scientific
Release Date : 1998-10-07
Stochastic Complexity In Statistical Inquiry written by Jorma Rissanen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-07 with Technology & Engineering categories.
This book describes how model selection and statistical inference can be founded on the shortest code length for the observed data, called the stochastic complexity. This generalization of the algorithmic complexity not only offers an objective view of statistics, where no prejudiced assumptions of 'true' data generating distributions are needed, but it also in one stroke leads to calculable expressions in a range of situations of practical interest and links very closely with mainstream statistical theory. The search for the smallest stochastic complexity extends the classical maximum likelihood technique to a new global one, in which models can be compared regardless of their numbers of parameters. The result is a natural and far reaching extension of the traditional theory of estimation, where the Fisher information is replaced by the stochastic complexity and the Cramer-Rao inequality by an extension of the Shannon-Kullback inequality. Ideas are illustrated with applications from parametric and non-parametric regression, density and spectrum estimation, time series, hypothesis testing, contingency tables, and data compression.
Computational Complexity And Statistical Physics
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Author : Allon Percus
language : en
Publisher: OUP USA
Release Date : 2006-02-23
Computational Complexity And Statistical Physics written by Allon Percus and has been published by OUP USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-23 with Computers categories.
Computer science and physics have been closely linked since the birth of modern computing. In recent years, an interdisciplinary area has blossomed at the junction of these fields, connecting insights from statistical physics with basic computational challenges. Researchers have successfully applied techniques from the study of phase transitions to analyze NP-complete problems such as satisfiability and graph coloring. This is leading to a new understanding of the structure of these problems, and of how algorithms perform on them. Computational Complexity and Statistical Physics will serve as a standard reference and pedagogical aid to statistical physics methods in computer science, with a particular focus on phase transitions in combinatorial problems. Addressed to a broad range of readers, the book includes substantial background material along with current research by leading computer scientists, mathematicians, and physicists. It will prepare students and researchers from all of these fields to contribute to this exciting area.
Information And Complexity In Statistical Modeling
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Author : Jorma Rissanen
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-15
Information And Complexity In Statistical Modeling written by Jorma Rissanen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-15 with Mathematics categories.
No statistical model is "true" or "false," "right" or "wrong"; the models just have varying performance, which can be assessed. The main theme in this book is to teach modeling based on the principle that the objective is to extract the information from data that can be learned with suggested classes of probability models. The intuitive and fundamental concepts of complexity, learnable information, and noise are formalized, which provides a firm information theoretic foundation for statistical modeling. Although the prerequisites include only basic probability calculus and statistics, a moderate level of mathematical proficiency would be beneficial.
Statistical Mechanics
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Author : James Sethna
language : en
Publisher: Oxford University Press
Release Date : 2006-04-06
Statistical Mechanics written by James Sethna and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-06 with Computers categories.
Sethna distills the core ideas of statistical mechanics to make room for new advances important to information theory, complexity, and modern biology. He explores everything from chaos through to life at the end of the universe.
Stochastic Complexity In Statistical Inquiry
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Author : Jorma Rissanen
language : en
Publisher:
Release Date : 1989
Stochastic Complexity In Statistical Inquiry written by Jorma Rissanen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Computational complexity categories.
An Introduction To Kolmogorov Complexity And Its Applications
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Author : Ming Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
An Introduction To Kolmogorov Complexity And Its Applications written by Ming Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).
Stochastic Complexity In Statistical Inquiry Theory
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Author : Jorma Rissanen
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 1989-08-01
Stochastic Complexity In Statistical Inquiry Theory written by Jorma Rissanen and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-08-01 with Business & Economics categories.
Statistical Mechanics Entropy Order Parameters And Complexity
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Author : James P. Sethna
language : en
Publisher: Oxford University Press
Release Date : 2021-01-26
Statistical Mechanics Entropy Order Parameters And Complexity written by James P. Sethna and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-26 with Science categories.
Statistical mechanics is our tool for deriving the laws that emerge from complex systems. Sethna's text distills the subject to be accessible to those in all realms of science and engineering — avoiding extensive use of quantum mechanics, thermodynamics, and molecular physics. Statistical mechanics explains how bacteria search for food, and how DNA replication is proof-read in biology; optimizes data compression, and explains transitions in complexity in computer science; explains the onset of chaos, and launched random matrix theory in mathematics; addresses extreme events in engineering; and models pandemics and language usage in the social sciences. Sethna's exercises introduce physicists to these triumphs and a hundred others — broadening the horizons of scholars both practicing and nascent. Flipped classrooms and remote learning can now rely on 33 pre-class exercises that test reading comprehension (Emergent vs. fundamental; Weirdness in high dimensions; Aging, entropy and DNA), and 70 in-class activities that illuminate and broaden knowledge (Card shuffling; Human correlations; Crackling noises). Science is awash in information, providing ready access to definitions, explanations, and pedagogy. Sethna's text focuses on the tools we use to create new laws, and on the fascinating simple behavior in complex systems that statistical mechanics explains.
Introductory Statistics And Random Phenomena
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Author : Manfred Denker
language : en
Publisher: Birkhäuser
Release Date : 2017-09-16
Introductory Statistics And Random Phenomena written by Manfred Denker and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-16 with Computers categories.
This textbook integrates traditional statistical data analysis with new computational experimentation capabilities and concepts of algorithmic complexity and chaotic behavior in nonlinear dynamic systems. This was the first advanced text/reference to bring together such a comprehensive variety of tools for the study of random phenomena occurring in engineering and the natural, life, and social sciences. The crucial computer experiments are conducted using the readily available computer program Mathematica® Uncertain Virtual WorldsTM software packages which optimize and facilitate the simulation environment. Brief tutorials are included that explain how to use the Mathematica® programs for effective simulation and computer experiments. Large and original real-life data sets are introduced and analyzed as a model for independent study. This is an excellent classroom tool and self-study guide. The material is presented in a clear and accessible style providing numerous exercises and bibliographical notes suggesting further reading. Topics and Features Comprehensive and integrated treatment of uncertainty arising in engineering and scientific phenomena – algorithmic complexity, statistical independence, and nonlinear chaotic behavior Extensive exercise sets, examples, and Mathematica® computer experiments that reinforce concepts and algorithmic methods Thorough presentation of methods of data compression and representation Algorithmic approach to model selection and design of experiments Large data sets and 13 Mathematica®-based Uncertain Virtual WorldsTM programs and code This text is an excellent resource for all applied statisticians, engineers, and scientists who need to use modern statistical analysis methods to investigate and model their data. The present, softcover reprint is designed to make this classic textbook available to a wider audience.