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Author: P.E. Pfeiffer Publisher: Springer Science & Business Media ISBN: 1461263352 Category : Science Languages : en Pages : 160
Book Description
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.
Author: P.E. Pfeiffer Publisher: Springer Science & Business Media ISBN: 1461263352 Category : Science Languages : en Pages : 160
Book Description
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.
Author: Paul E. Pfeiffer Publisher: Elsevier ISBN: 1483277208 Category : Mathematics Languages : en Pages : 420
Book Description
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.
Author: Milan Studeny Publisher: Springer Science & Business Media ISBN: 1846280834 Category : Computers Languages : en Pages : 285
Book Description
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.
Author: Paul Pfeiffer Publisher: ISBN: Category : Applied mathematics Languages : en Pages : 0
Book Description
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.
Author: Oliver Ibe Publisher: Academic Press ISBN: 0128010355 Category : Mathematics Languages : en Pages : 456
Book Description
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).
Author: Rolf Steyer Publisher: John Wiley & Sons ISBN: 1119243483 Category : Mathematics Languages : en Pages : 600
Book Description
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.
Author: B.S. Daya Sagar Publisher: Springer ISBN: 3319789996 Category : Science Languages : en Pages : 914
Book Description
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.
Author: P.E. Pfeiffer
Author: P.E. Pfeiffer
Author: Paul E. Pfeiffer
Author: Paul E. Pfeiffer
Author: Milan Studeny
Author: Paul Pfeiffer
Author: Oliver Ibe
Author: Douglas S. Shafer
Author: Rolf Steyer
Author: Patrick Suppes
Author: B.S. Daya Sagar