Stochastic Complexity In Statistical Inquiry

Author : Jorma Rissanen
Publisher : World Scientific
Page : 191 pages
File Size : 41,5 Mb
Release : 1998-10-07
Category : Technology & Engineering
ISBN : 9789814507400

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Stochastic Complexity In Statistical Inquiry by Jorma Rissanen Pdf

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.

Author : Jorma Rissanen
Publisher : World Scientific Publishing Company Incorporated
Page : 188 pages
File Size : 41,7 Mb
Release : 1989-08-01
Category : Business & Economics
ISBN : 981020311X

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Stochastic Complexity in Statistical Inquiry Theory by Jorma Rissanen Pdf

Author : Jorma Rissanen
Publisher : World Scientific Publishing Company Incorporated
Page : 177 pages
File Size : 50,5 Mb
Release : 1989-01-01
Category : Business & Economics
ISBN : 9971508591

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Stochastic Complexity in Statistical Inquiry by Jorma Rissanen Pdf

Author : G. Erickson,C.R. Smith
Publisher : Springer Science & Business Media
Page : 321 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400930490

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Maximum-Entropy and Bayesian Methods in Science and Engineering by G. Erickson,C.R. Smith Pdf

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.

Author : Ming Li,Paul Vitányi
Publisher : Springer
Page : 834 pages
File Size : 40,8 Mb
Release : 2019-06-11
Category : Mathematics
ISBN : 9783030112981

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An Introduction to Kolmogorov Complexity and Its Applications by Ming Li,Paul Vitányi Pdf

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.

Author : Wojciech H. Zurek
Publisher : CRC Press
Page : 545 pages
File Size : 41,7 Mb
Release : 2018-03-08
Category : Science
ISBN : 9780429971433

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Complexity, Entropy And The Physics Of Information by Wojciech H. Zurek Pdf

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.

Author : P. Grassberger,J.P. Nadal
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 49,9 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 : David Brillinger,Peter Caines,John Geweke,Emanuel Parzen,Murray Rosenblatt,Murad S. Taqqu
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461392965

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New Directions in Time Series Analysis by David Brillinger,Peter Caines,John Geweke,Emanuel Parzen,Murray Rosenblatt,Murad S. Taqqu Pdf

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.

Author : Hamparsum Bozdogan
Publisher : CRC Press
Page : 624 pages
File Size : 52,6 Mb
Release : 2003-07-29
Category : Business & Economics
ISBN : 9780203497159

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Statistical Data Mining and Knowledge Discovery by Hamparsum Bozdogan Pdf

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

Author : Peter D. Grünwald,In Jae Myung,Mark A. Pitt
Publisher : MIT Press
Page : 464 pages
File Size : 48,8 Mb
Release : 2005
Category : Computers
ISBN : 0262072629

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Advances in Minimum Description Length by Peter D. Grünwald,In Jae Myung,Mark A. Pitt Pdf

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.

Author : Peter D. Grünwald
Publisher : MIT Press
Page : 736 pages
File Size : 46,8 Mb
Release : 2007
Category : Minimum description length (Information theory).
ISBN : 9780262072816

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The Minimum Description Length Principle by Peter D. Grünwald Pdf

This introduction to the MDL Principle provides a reference accessible to graduate students and researchers in statistics, pattern classification, machine learning, and data mining, to philosophers interested in the foundations of statistics, and to researchers in other applied sciences that involve model selection.

Author : H. Bozdogan
Publisher : Springer Science & Business Media
Page : 421 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401108003

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Proceedings of the First US/Japan Conference on the Frontiers of Statistical Modeling: An Informational Approach by H. Bozdogan Pdf

Often a statistical analysis involves use of a set of alternative models for the data. A "model-selection criterion" is a formula which provides a figure-of merit for the alternative models. Generally the alternative models will involve different numhers of parameters. Model-selection criteria take into account hoth the goodness-or-fit of a model and the numher of parameters used to achieve that fit. 1.1. SETS OF ALTERNATIVE MODELS Thus the focus in this paper is on data-analytic situations ill which there is consideration of a set of alternative models. Choice of a suhset of explanatory variahles in regression, the degree of a polynomial regression, the number of factors in factor analysis, or the numher of dusters in duster analysis are examples of such situations. 1.2. MODEL SELECTION VERSUS HYPOTHESIS TESTING In exploratory data analysis or in a preliminary phase of inference an approach hased on model-selection criteria can offer advantages over tests of hypotheses. The model-selection approach avoids the prohlem of specifying error rates for the tests. With model selection the focus can he on simultaneous competition between a hroad dass of competing models rather than on consideration of a sequence of simpler and simpler models.

Author : Setsuo Arikawa,Akira Maruoka,T. Sato
Publisher : IOS Press
Page : 324 pages
File Size : 46,5 Mb
Release : 1992
Category : Algorithms
ISBN : 4274076997

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Algorithmic Learning Theory II by Setsuo Arikawa,Akira Maruoka,T. Sato Pdf

Author : Alex Gammerman
Publisher : Springer Science & Business Media
Page : 193 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642586484

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Causal Models and Intelligent Data Management by Alex Gammerman Pdf

The need to electronically store, manipulate and analyze large-scale, high-dimensional data sets requires new computational methods. This book presents new intelligent data management methods and tools, including new results from the field of inference. Leading experts also map out future directions of intelligent data analysis. This book will be a valuable reference for researchers exploring the interdisciplinary area between statistics and computer science as well as for professionals applying advanced data analysis methods in industry.

Author : David J. Hand
Publisher : CRC Press
Page : 431 pages
File Size : 41,7 Mb
Release : 2020-11-26
Category : Business & Economics
ISBN : 9781000152913

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Artificial Intelligence Frontiers in Statistics by David J. Hand Pdf

This book presents a summary of recent work on the interface between artificial intelligence and statistics. It does this through a series of papers by different authors working in different areas of this interface. These papers are a selected and referenced subset of papers presented at the 3rd Interntional Workshop on Artificial Intelligence and Statistics, Florida, January 1991.