Conditional Independence In Applied Probability
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Conditional Independence In Applied Probability
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Author : P.E. Pfeiffer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-07
Conditional Independence In Applied Probability written by P.E. Pfeiffer 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 2013-03-07 with Science categories.
It would be difficult to overestimate the importance of stochastic independence in both the theoretical development and the practical appli cations of mathematical probability. The concept is grounded in the idea that one event does not "condition" another, in the sense that occurrence of one does not affect the likelihood of the occurrence of the other. This leads to a formulation of the independence condition in terms of a simple "product rule," which is amazingly successful in capturing the essential ideas of independence. However, there are many patterns of "conditioning" encountered in practice which give rise to quasi independence conditions. Explicit and precise incorporation of these into the theory is needed in order to make the most effective use of probability as a model for behavioral and physical systems. We examine two concepts of conditional independence. The first concept is quite simple, utilizing very elementary aspects of probability theory. Only algebraic operations are required to obtain quite important and useful new results, and to clear up many ambiguities and obscurities in the literature.
Conditional Independence In Applied Probability
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Author : Paul E. Pfeiffer
language : en
Publisher:
Release Date : 1983
Conditional Independence In Applied Probability written by Paul E. Pfeiffer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Probabilities categories.
Introduction To Applied Probability
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Author : Paul E. Pfeiffer
language : en
Publisher: Elsevier
Release Date : 2014-05-10
Introduction To Applied Probability written by Paul E. Pfeiffer and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Introduction to Applied Probability provides a basis for an intelligent application of probability ideas to a wide variety of phenomena for which it is suitable. It is intended as a tool for learning and seeks to point out and emphasize significant facts and interpretations which are frequently overlooked or confused by the beginner. The book covers more than enough material for a one semester course, enhancing the value of the book as a reference for the student. Notable features of the book are: the systematic handling of combinations of events (Section 3-5); extensive use of the mass concept as an aid to visualization; an unusually careful treatment of conditional probability, independence, and conditional independence (Section 6-4); the resulting clarification facilitates the formulation of many applied problems; the emphasis on events determined by random variables, which gives unity and clarity to many topics important for interpretation; and the utilization of the indicator function, both as a tool for dealing with events and as a notational device in the handling of random variables. Students of mathematics, engineering, biological and physical sciences will find the text highly useful.
Probabilistic Conditional Independence Structures
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Author : Milan Studeny
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-22
Probabilistic Conditional Independence Structures written by Milan Studeny 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 2006-06-22 with Computers categories.
Probabilistic Conditional Independence Structures provides the mathematical description of probabilistic conditional independence structures; the author uses non-graphical methods of their description, and takes an algebraic approach. The monograph presents the methods of structural imsets and supermodular functions, and deals with independence implication and equivalence of structural imsets. Motivation, mathematical foundations and areas of application are included, and a rough overview of graphical methods is also given. In particular, the author has been careful to use suitable terminology, and presents the work so that it will be understood by both statisticians, and by researchers in artificial intelligence. The necessary elementary mathematical notions are recalled in an appendix.
Probability And Conditional Expectation
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Author : Rolf Steyer
language : en
Publisher: John Wiley & Sons
Release Date : 2017-05-08
Probability And Conditional Expectation written by Rolf Steyer and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-08 with Mathematics categories.
Probability and Conditional Expectations bridges the gap between books on probability theory and statistics by providing the probabilistic concepts estimated and tested in analysis of variance, regression analysis, factor analysis, structural equation modeling, hierarchical linear models and analysis of qualitative data. The authors emphasize the theory of conditional expectations that is also fundamental to conditional independence and conditional distributions. Probability and Conditional Expectations Presents a rigorous and detailed mathematical treatment of probability theory focusing on concepts that are fundamental to understand what we are estimating in applied statistics. Explores the basics of random variables along with extensive coverage of measurable functions and integration. Extensively treats conditional expectations also with respect to a conditional probability measure and the concept of conditional effect functions, which are crucial in the analysis of causal effects. Is illustrated throughout with simple examples, numerous exercises and detailed solutions. Provides website links to further resources including videos of courses delivered by the authors as well as R code exercises to help illustrate the theory presented throughout the book.
Contributions To The Theory And Application Of Statistics
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Author : Alan E. Gelfand
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Contributions To The Theory And Application Of Statistics written by Alan E. Gelfand and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Contributions to the Theory and Application of Statistics: A Volume in Honor of Herbert Solomon is a collection of 20 papers that cover the significant contributions of Herbert Solomon in the field of statistics. This text is organized into four sections encompassing 20 chapters. Each section defines an area in which Herb has made a contribution and the papers are ordered alphabetically. The first section consists of four papers in the area of operations research and applied probability, while the second section gathers six papers looking into problems in distribution theory and geometric probability. The third section contains five applied articles in the areas of law and justice, medicine, and psychology. The fourth section covers five papers that explore several inference issues. This book will be of value to statisticians and advance students.
An Introduction To Applied Probability
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Author : Richard A. Roberts
language : en
Publisher: Addison Wesley Publishing Company
Release Date : 1992
An Introduction To Applied Probability written by Richard A. Roberts and has been published by Addison Wesley Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
Sparse Graphical Modeling For High Dimensional Data
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Author : Faming Liang
language : en
Publisher: CRC Press
Release Date : 2023-08-02
Sparse Graphical Modeling For High Dimensional Data written by Faming Liang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-02 with Mathematics categories.
This book provides a general framework for learning sparse graphical models with conditional independence tests. It includes complete treatments for Gaussian, Poisson, multinomial, and mixed data; unified treatments for covariate adjustments, data integration, and network comparison; unified treatments for missing data and heterogeneous data; efficient methods for joint estimation of multiple graphical models; effective methods of high-dimensional variable selection; and effective methods of high-dimensional inference. The methods possess an embarrassingly parallel structure in performing conditional independence tests, and the computation can be significantly accelerated by running in parallel on a multi-core computer or a parallel architecture. This book is intended to serve researchers and scientists interested in high-dimensional statistics, and graduate students in broad data science disciplines. Key Features: A general framework for learning sparse graphical models with conditional independence tests Complete treatments for different types of data, Gaussian, Poisson, multinomial, and mixed data Unified treatments for data integration, network comparison, and covariate adjustment Unified treatments for missing data and heterogeneous data Efficient methods for joint estimation of multiple graphical models Effective methods of high-dimensional variable selection Effective methods of high-dimensional inference
Probabilistic Reasoning In Intelligent Systems
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Author : Judea Pearl
language : en
Publisher: Morgan Kaufmann
Release Date : 1988
Probabilistic Reasoning In Intelligent Systems written by Judea Pearl and has been published by Morgan Kaufmann this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Computers categories.
Textbook offers an accessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty. For graduate-level courses in AI, operations research, and applied probability. Annotation copyright Book News, Inc. Portland, Or.
An Introduction To Applied Probability And Random Processes
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Author : John Bowman Thomas
language : en
Publisher:
Release Date : 1981
An Introduction To Applied Probability And Random Processes written by John Bowman Thomas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.