Stochastic Complexity In Statistical Inquiry
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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.
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.
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.
Maximum Entropy And Bayesian Methods In Science And Engineering
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Author : G. Erickson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Maximum Entropy And Bayesian Methods In Science And Engineering written by G. Erickson 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 2012-12-06 with Mathematics categories.
This volume has its origin in the Fifth, Sixth and Seventh Workshops on and Bayesian Methods in Applied Statistics", held at "Maximum-Entropy the University of Wyoming, August 5-8, 1985, and at Seattle University, August 5-8, 1986, and August 4-7, 1987. It was anticipated that the proceedings of these workshops would be combined, so most of the papers were not collected until after the seventh workshop. Because all of the papers in this volume are on foundations, it is believed that the con tents of this volume will be of lasting interest to the Bayesian community. The workshop was organized to bring together researchers from different fields to critically examine maximum-entropy and Bayesian methods in science and engineering as well as other disciplines. Some of the papers were chosen specifically to kindle interest in new areas that may offer new tools or insight to the reader or to stimulate work on pressing problems that appear to be ideally suited to the maximum-entropy or Bayesian method. A few papers presented at the workshops are not included in these proceedings, but a number of additional papers not presented at the workshop are included. In particular, we are delighted to make available Professor E. T. Jaynes' unpublished Stanford University Microwave Laboratory Report No. 421 "How Does the Brain Do Plausible Reasoning?" (dated August 1957). This is a beautiful, detailed tutorial on the Cox-Polya-Jaynes approach to Bayesian probability theory and the maximum-entropy principle.
An Introduction To Kolmogorov Complexity And Its Applications
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Author : Ming Li
language : en
Publisher: Springer
Release Date : 2019-06-11
An Introduction To Kolmogorov Complexity And Its Applications written by Ming Li and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-11 with Mathematics categories.
This must-read textbook presents an essential introduction to Kolmogorov complexity (KC), a central theory and powerful tool in information science that deals with the quantity of information in individual objects. The text covers both the fundamental concepts and the most important practical applications, supported by a wealth of didactic features. This thoroughly revised and enhanced fourth edition includes new and updated material on, amongst other topics, the Miller-Yu theorem, the Gács-Kučera theorem, the Day-Gács theorem, increasing randomness, short lists computable from an input string containing the incomputable Kolmogorov complexity of the input, the Lovász local lemma, sorting, the algorithmic full Slepian-Wolf theorem for individual strings, multiset normalized information distance and normalized web distance, and conditional universal distribution. Topics and features: describes the mathematical theory of KC, including the theories of algorithmic complexity and algorithmic probability; presents a general theory of inductive reasoning and its applications, and reviews the utility of the incompressibility method; covers the practical application of KC in great detail, including the normalized information distance (the similarity metric) and information diameter of multisets in phylogeny, language trees, music, heterogeneous files, and clustering; discusses the many applications of resource-bounded KC, and examines different physical theories from a KC point of view; includes numerous examples that elaborate the theory, and a range of exercises of varying difficulty (with solutions); offers explanatory asides on technical issues, and extensive historical sections; suggests structures for several one-semester courses in the preface. As the definitive textbook on Kolmogorov complexity, this comprehensive and self-contained work is an invaluable resource for advanced undergraduate students, graduate students, and researchers in all fields of science.
Complexity Entropy And The Physics Of Information
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Author : Wojciech H. Zurek
language : en
Publisher: CRC Press
Release Date : 2018-03-08
Complexity Entropy And The Physics Of Information written by Wojciech H. Zurek and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-08 with Science categories.
This book has emerged from a meeting held during the week of May 29 to June 2, 1989, at St. John’s College in Santa Fe under the auspices of the Santa Fe Institute. The (approximately 40) official participants as well as equally numerous “groupies” were enticed to Santa Fe by the above “manifesto.” The book—like the “Complexity, Entropy and the Physics of Information” meeting explores not only the connections between quantum and classical physics, information and its transfer, computation, and their significance for the formulation of physical theories, but it also considers the origins and evolution of the information-processing entities, their complexity, and the manner in which they analyze their perceptions to form models of the Universe. As a result, the contributions can be divided into distinct sections only with some difficulty. Indeed, I regard this degree of overlapping as a measure of the success of the meeting. It signifies consensus about the important questions and on the anticipated answers: they presumably lie somewhere in the “border territory,” where information, physics, complexity, quantum, and computation all meet.
From Statistical Physics To Statistical Inference And Back
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Author : P. Grassberger
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
From Statistical Physics To Statistical Inference And Back written by P. Grassberger 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 2012-12-06 with Science categories.
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.
New Directions In Time Series Analysis
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Author : David Brillinger
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
New Directions In Time Series Analysis written by David Brillinger 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 2012-12-06 with Mathematics categories.
This IMA Volume in Mathematics and its Applications NEW DIRECTIONS IN TIME SERIES ANALYSIS, PART II is based on the proceedings of the IMA summer program "New Directions in Time Series Analysis. " We are grateful to David Brillinger, Peter Caines, John Geweke, Emanuel Parzen, Murray Rosenblatt, and Murad Taqqu for organizing the program and we hope that the remarkable excitement and enthusiasm of the participants in this interdisciplinary effort are communicated to the reader. A vner Friedman Willard Miller, Jr. PREFACE Time Series Analysis is truly an interdisciplinary field because development of its theory and methods requires interaction between the diverse disciplines in which it is applied. To harness its great potential, strong interaction must be encouraged among the diverse community of statisticians and other scientists whose research involves the analysis of time series data. This was the goal of the IMA Workshop on "New Directions in Time Series Analysis. " The workshop was held July 2-July 27, 1990 and was organized by a committee consisting of Emanuel Parzen (chair), David Brillinger, Murray Rosenblatt, Murad S. Taqqu, John Geweke, and Peter Caines. Constant guidance and encouragement was provided by Avner Friedman, Director of the IMA, and his very helpful and efficient staff. The workshops were organized by weeks. It may be of interest to record the themes that were announced in the IMA newsletter describing the workshop: l.
Statistical Data Mining And Knowledge Discovery
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Author : Hamparsum Bozdogan
language : en
Publisher: CRC Press
Release Date : 2003-07-29
Statistical Data Mining And Knowledge Discovery written by Hamparsum Bozdogan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-29 with Business & Economics categories.
Massive data sets pose a great challenge to many cross-disciplinary fields, including statistics. The high dimensionality and different data types and structures have now outstripped the capabilities of traditional statistical, graphical, and data visualization tools. Extracting useful information from such large data sets calls for novel approache
Advances In Minimum Description Length
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Author : Peter D. Grünwald
language : en
Publisher: MIT Press
Release Date : 2005
Advances In Minimum Description Length written by Peter D. Grünwald and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Computers categories.
A source book for state-of-the-art MDL, including an extensive tutorial and recent theoretical advances and practical applications in fields ranging from bioinformatics to psychology.