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Conditional Independence In Applied Probability
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Book Synopsis Conditional Independence in Applied Probability by : P.E. Pfeiffer
Download or read book Conditional Independence in Applied Probability written by P.E. Pfeiffer and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Conditional Independence in Applied Probability by : Paul E. Pfeiffer
Download or read book Conditional Independence in Applied Probability written by Paul E. Pfeiffer and published by . This book was released on 1979 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Applied Probability by : Paul E. Pfeiffer
Download or read book Introduction to Applied Probability written by Paul E. Pfeiffer and published by Elsevier. This book was released on 2014-05-10 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Probabilistic Conditional Independence Structures by : Milan Studeny
Download or read book Probabilistic Conditional Independence Structures written by Milan Studeny and published by Springer Science & Business Media. This book was released on 2006-06-22 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Applied Probability by : Paul Pfeiffer
Download or read book Applied Probability written by Paul Pfeiffer and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a "first course" in the sense that it presumes no previous course in probability. The mathematical prerequisites are ordinary calculus and the elements of matrix algebra. A few standard series and integrals are used, and double integrals are evaluated as iterated integrals. The reader who can evaluate simple integrals can learn quickly from the examples how to deal with the iterated integrals used in the theory of expectation and conditional expectation. Appendix B provides a convenient compendium of mathematical facts used frequently in this work. And the symbolic toolbox, implementing MAPLE, may be used to evaluate integrals, if desired. In addition to an introduction to the essential features of basic probability in terms of a precise mathematical model, the work describes and employs user defined MATLAB procedures and functions (which we refer to as m-programs, or simply programs) to solve many important problems in basic probability. This should make the work useful as a stand-alone exposition as well as a supplement to any of several current textbooks. Most of the programs developed here were written in earlier versions of MATLAB, but have been revised slightly to make them quite compatible with MATLAB 7. In a few cases, alternate implementations are available in the Statistics Toolbox, but are implemented here directly from the basic MATLAB program, so that students need only that program (and the symbolic mathematics toolbox, if they desire its aid in evaluating integrals). Since machine methods require precise formulation of problems in appropriate mathematical form, it is necessary to provide some supplementary analytical material, principally the so-called minterm analysis. This material is not only important for computational purposes, but is also useful in displaying some of the structure of the relationships among events.
Book Synopsis Introductory Statistics by : Douglas S. Shafer
Download or read book Introductory Statistics written by Douglas S. Shafer and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Foundations of Probability with Applications by : Patrick Suppes
Download or read book Foundations of Probability with Applications written by Patrick Suppes and published by Cambridge University Press. This book was released on 1996-11-13 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an important collection of essays by a leading philosopher, dealing with the foundations of probability.
Book Synopsis Probability and Conditional Expectation by : Rolf Steyer
Download or read book Probability and Conditional Expectation written by Rolf Steyer and published by John Wiley & Sons. This book was released on 2017-05-08 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fundamentals of Applied Probability and Random Processes by : Oliver Ibe
Download or read book Fundamentals of Applied Probability and Random Processes written by Oliver Ibe and published by Academic Press. This book was released on 2014-06-13 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The long-awaited revision of Fundamentals of Applied Probability and Random Processes expands on the central components that made the first edition a classic. The title is based on the premise that engineers use probability as a modeling tool, and that probability can be applied to the solution of engineering problems. Engineers and students studying probability and random processes also need to analyze data, and thus need some knowledge of statistics. This book is designed to provide students with a thorough grounding in probability and stochastic processes, demonstrate their applicability to real-world problems, and introduce the basics of statistics. The book's clear writing style and homework problems make it ideal for the classroom or for self-study. Demonstrates concepts with more than 100 illustrations, including 2 dozen new drawings Expands readers’ understanding of disruptive statistics in a new chapter (chapter 8) Provides new chapter on Introduction to Random Processes with 14 new illustrations and tables explaining key concepts. Includes two chapters devoted to the two branches of statistics, namely descriptive statistics (chapter 8) and inferential (or inductive) statistics (chapter 9).
Book Synopsis An Introduction to Applied Probability by : Richard A. Roberts
Download or read book An Introduction to Applied Probability written by Richard A. Roberts and published by Addison Wesley Publishing Company. This book was released on 1992 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Contributions to the Theory and Application of Statistics by : Alan E. Gelfand
Download or read book Contributions to the Theory and Application of Statistics written by Alan E. Gelfand and published by Academic Press. This book was released on 2014-05-10 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Handbook of Mathematical Geosciences by : B.S. Daya Sagar
Download or read book Handbook of Mathematical Geosciences written by B.S. Daya Sagar and published by Springer. This book was released on 2018-06-25 with total page 914 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Open Access handbook published at the IAMG's 50th anniversary, presents a compilation of invited path-breaking research contributions by award-winning geoscientists who have been instrumental in shaping the IAMG. It contains 45 chapters that are categorized broadly into five parts (i) theory, (ii) general applications, (iii) exploration and resource estimation, (iv) reviews, and (v) reminiscences covering related topics like mathematical geosciences, mathematical morphology, geostatistics, fractals and multifractals, spatial statistics, multipoint geostatistics, compositional data analysis, informatics, geocomputation, numerical methods, and chaos theory in the geosciences.
Book Synopsis Probability with Applications by : Michael Woodroofe
Download or read book Probability with Applications written by Michael Woodroofe and published by McGraw-Hill Companies. This book was released on 1974 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical model; Axiomatic probability; Conditional probability and independence; The binomial and related probabilities; Random variables; Random vectors; Distribution theory; Expectation; Limit theorems; Conditional distributions and expectation; Random walks; Martingales.
Book Synopsis Sparse Graphical Modeling for High Dimensional Data by : Faming Liang
Download or read book Sparse Graphical Modeling for High Dimensional Data written by Faming Liang and published by CRC Press. This book was released on 2023-08-02 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Probability Theory by : Yuan Shih Chow
Download or read book Probability Theory written by Yuan Shih Chow and published by Springer. This book was released on 2012-02 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1 Classes of Sets, Measures, and Probability Spaces.- 1.1 Sets and set operations.- 1.2 Spaces and indicators.- 1.3 Sigma-algebras, measurable spaces, and product spaces.- 1.4 Measurable transformations.- 1.5 Additive set functions, measures and probability spaces.- 1.6 Induced measures and distribution functions.- 2 Binomial Random Variables.- 2.1 Poisson theorem, interchangeable events, and their limiting probabilities.- 2.2 Bernoulli, Borel theorems.- 2.3 Central limit theorem for binomial random variables, large deviations.- 3 Independence.- 3.1 Independence, random allocation of balls into cells.- 3.2 Borel-Cantelli theorem, characterization of independence, Kolmogorov zero-one law.- 3.3 Convergence in probability, almost certain convergence, and their equivalence for sums of independent random variables.- 3.4 Bernoulli trials.- 4 Integration in a Probability Space.- 4.1 Definition, properties of the integral, monotone convergence theorem.- 4.2 Indefinite integrals, uniform integrability, mean convergence.- 4.3 Jensen, Hölder, Schwarz inequalities.- 5 Sums of Independent Random Variables.- 5.1 Three series theorem.- 5.2 Laws of large numbers.- 5.3 Stopping times, copies of stopping times, Wald's equation.- 5.4 Chung-Fuchs theorem, elementary renewal theorem, optimal stopping.- 6 Measure Extensions, Lebesgue-Stieltjes Measure, Kolmogorov Consistency Theorem.- 6.1 Measure extensions, Lebesgue-Stieltjes measure.- 6.2 Integration in a measure space.- 6.3 Product measure, Fubini's theorem, n-dimensional Lebesgue-Stieltjes measure.- 6.4 Infinite-dimensional product measure space, Kolmogorov consistency theorem.- 6.5 Absolute continuity of measures, distribution functions; Radon-Nikodym theorem.- 7 Conditional Expectation, Conditional Independence, Introduction to Martingales.- 7.1 Conditional expectation.- 7.2 Conditional probabilities, conditional probability measures.- 7.3 Conditional independence, interchangeable random variables.- 7.4 Introduction to martingales.- 8 Distribution Functions and Characteristic Functions.- 8.1 Convergence of distribution functions, uniform integrability, Helly-Bray theorem.- 8.2 Weak compactness, Frêchet-Shohat, Glivenko-Cantelli theorems.- 8.3 Characteristic functions, inversion formula, Lévy continuity theorem.- 8.4 The nature of characteristic functions, analytic characteristic functions, Cramér-Lévy theorem.- 8.5 Remarks on k-dimensional distribution functions and characteristic functions.- 9 Central Limit Theorems.- 9.1 Independent components.- 9.2 Interchangeable components.- 9.3 The martingale case.- 9.4 Miscellaneous central limit theorems.- 10 Limit Theorems for Independent Random Variables.- 10.1 Laws of large numbers.- 10.2 Law of the iterated logarithm.- 10.3 Marcinkiewicz-Zygmund inequality, dominated ergodic theorems.- 10.4 Maxima of random walks.- 11 Martingales.- 11.1 Upcrossing inequality and convergence.- 11.2 Martingale extension of Marcinkiewicz-Zygmund inequalities.- 11.3 Convex function inequalities for martingales.- 11.4 Stochastic inequalities.- 12 Infinitely Divisible Laws.- 12.1 Infinitely divisible characteristic functions.- 12.2 Infinitely divisible laws as limits.- 12.3 Stable laws.
Book Synopsis Probability for Applications by : Paul E. Pfeiffer
Download or read book Probability for Applications written by Paul E. Pfeiffer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: Objecti'ves. As the title suggests, this book provides an introduction to probability designed to prepare the reader for intelligent and resourceful applications in a variety of fields. Its goal is to provide a careful exposition of those concepts, interpretations, and analytical techniques needed for the study of such topics as statistics, introductory random processes, statis tical communications and control, operations research, or various topics in the behavioral and social sciences. Also, the treatment should provide a background for more advanced study of mathematical probability or math ematical statistics. The level of preparation assumed is indicated by the fact that the book grew out of a first course in probability, taken at the junior or senior level by students in a variety of fields-mathematical sciences, engineer ing, physics, statistics, operations research, computer science, economics, and various other areas of the social and behavioral sciences. Students are expected to have a working knowledge of single-variable calculus, including some acquaintance with power series. Generally, they are expected to have the experience and mathematical maturity to enable them to learn new concepts and to follow and to carry out sound mathematical arguments. While some experience with multiple integrals is helpful, the essential ideas can be introduced or reviewed rather quickly at points where needed.
Book Synopsis Probabilistic Reasoning in Intelligent Systems by : Judea Pearl
Download or read book Probabilistic Reasoning in Intelligent Systems written by Judea Pearl and published by Morgan Kaufmann. This book was released on 1988 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
