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Author: J. L. Doob
Publisher: Springer Science & Business Media
ISBN: 1461252083
Category : Mathematics
Languages : en
Pages : 865
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Book Description
Potential theory and certain aspects of probability theory are intimately related, perhaps most obviously in that the transition function determining a Markov process can be used to define the Green function of a potential theory. Thus it is possible to define and develop many potential theoretic concepts probabilistically, a procedure potential theorists observe withjaun diced eyes in view of the fact that now as in the past their subject provides the motivation for much of Markov process theory. However that may be it is clear that certain concepts in potential theory correspond closely to concepts in probability theory, specifically to concepts in martingale theory. For example, superharmonic functions correspond to supermartingales. More specifically: the Fatou type boundary limit theorems in potential theory correspond to supermartingale convergence theorems; the limit properties of monotone sequences of superharmonic functions correspond surprisingly closely to limit properties of monotone sequences of super martingales; certain positive superharmonic functions [supermartingales] are called "potentials," have associated measures in their respective theories and are subject to domination principles (inequalities) involving the supports of those measures; in each theory there is a reduction operation whose properties are the same in the two theories and these reductions induce sweeping (balayage) of the measures associated with potentials, and so on.
Author: J. L. Doob
Publisher: Springer Science & Business Media
ISBN: 1461252083
Category : Mathematics
Languages : en
Pages : 865
Get Book Here
Book Description
Potential theory and certain aspects of probability theory are intimately related, perhaps most obviously in that the transition function determining a Markov process can be used to define the Green function of a potential theory. Thus it is possible to define and develop many potential theoretic concepts probabilistically, a procedure potential theorists observe withjaun diced eyes in view of the fact that now as in the past their subject provides the motivation for much of Markov process theory. However that may be it is clear that certain concepts in potential theory correspond closely to concepts in probability theory, specifically to concepts in martingale theory. For example, superharmonic functions correspond to supermartingales. More specifically: the Fatou type boundary limit theorems in potential theory correspond to supermartingale convergence theorems; the limit properties of monotone sequences of superharmonic functions correspond surprisingly closely to limit properties of monotone sequences of super martingales; certain positive superharmonic functions [supermartingales] are called "potentials," have associated measures in their respective theories and are subject to domination principles (inequalities) involving the supports of those measures; in each theory there is a reduction operation whose properties are the same in the two theories and these reductions induce sweeping (balayage) of the measures associated with potentials, and so on.
Author: Claude Dellacherie
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Toby Handfield
Publisher: Cambridge University Press
ISBN: 1107080010
Category : Science
Languages : en
Pages : 265
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Book Description
It is a commonplace that scientific inquiry makes extensive use of probabilities, many of which seem to be objective chances, describing features of reality that are independent of our minds. Such chances appear to have a number of paradoxical or puzzling features: they appear to be mind-independent facts, but they are intimately connected with rational psychology; they display a temporal asymmetry, but they are supposed to be grounded in physical laws that are time-symmetric; and chances are used to explain and predict frequencies of events, although they cannot be reduced to those frequencies. This book offers an accessible and non-technical introduction to these and other puzzles. Toby Handfield engages with traditional metaphysics and philosophy of science, drawing upon recent work in the foundations of quantum mechanics and thermodynamics to provide a novel account of objective probability that is empirically informed without requiring specialist scientific knowledge.
Author: Roman Vershynin
Publisher: Cambridge University Press
ISBN: 1108415199
Category : Business & Economics
Languages : en
Pages : 299
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Book Description
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Author: Rolf Haenni
Publisher: Springer Science & Business Media
ISBN: 9400700083
Category : Science
Languages : en
Pages : 154
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Book Description
While probabilistic logics in principle might be applied to solve a range of problems, in practice they are rarely applied - perhaps because they seem disparate, complicated, and computationally intractable. This programmatic book argues that several approaches to probabilistic logic fit into a simple unifying framework in which logically complex evidence is used to associate probability intervals or probabilities with sentences. Specifically, Part I shows that there is a natural way to present a question posed in probabilistic logic, and that various inferential procedures provide semantics for that question, while Part II shows that there is the potential to develop computationally feasible methods to mesh with this framework. The book is intended for researchers in philosophy, logic, computer science and statistics. A familiarity with mathematical concepts and notation is presumed, but no advanced knowledge of logic or probability theory is required.
Author: Richard E. Fairley
Publisher: John Wiley & Sons
ISBN: 1118210999
Category : Computers
Languages : en
Pages : 515
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Book Description
The book is organized around basic principles of software project management: planning and estimating, measuring and controlling, leading and communicating, and managing risk. Introduces software development methods, from traditional (hacking, requirements to code, and waterfall) to iterative (incremental build, evolutionary, agile, and spiral). Illustrates and emphasizes tailoring the development process to each project, with a foundation in the fundamentals that are true for all development methods. Topics such as the WBS, estimation, schedule networks, organizing the project team, and performance reporting are integrated, rather than being relegating to appendices. Each chapter in the book includes an appendix that covers the relevant topics from CMMI-DEV-v1.2, IEEE/ISO Standards 12207, IEEE Standard 1058, and the PMI® Body of Knowledge. (PMI is a registered mark of Project Management Institute, Inc.)
Author: Avi Pfeffer
Publisher: Simon and Schuster
ISBN: 1638352372
Category : Computers
Languages : en
Pages : 650
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Book Description
Summary Practical Probabilistic Programming introduces the working programmer to probabilistic programming. In it, you'll learn how to use the PP paradigm to model application domains and then express those probabilistic models in code. Although PP can seem abstract, in this book you'll immediately work on practical examples, like using the Figaro language to build a spam filter and applying Bayesian and Markov networks, to diagnose computer system data problems and recover digital images. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the Technology The data you accumulate about your customers, products, and website users can help you not only to interpret your past, it can also help you predict your future! Probabilistic programming uses code to draw probabilistic inferences from data. By applying specialized algorithms, your programs assign degrees of probability to conclusions. This means you can forecast future events like sales trends, computer system failures, experimental outcomes, and many other critical concerns. About the Book Practical Probabilistic Programming introduces the working programmer to probabilistic programming. In this book, you’ll immediately work on practical examples like building a spam filter, diagnosing computer system data problems, and recovering digital images. You’ll discover probabilistic inference, where algorithms help make extended predictions about issues like social media usage. Along the way, you’ll learn to use functional-style programming for text analysis, object-oriented models to predict social phenomena like the spread of tweets, and open universe models to gauge real-life social media usage. The book also has chapters on how probabilistic models can help in decision making and modeling of dynamic systems. What's Inside Introduction to probabilistic modeling Writing probabilistic programs in Figaro Building Bayesian networks Predicting product lifecycles Decision-making algorithms About the Reader This book assumes no prior exposure to probabilistic programming. Knowledge of Scala is helpful. About the Author Avi Pfeffer is the principal developer of the Figaro language for probabilistic programming. Table of Contents PART 1 INTRODUCING PROBABILISTIC PROGRAMMING AND FIGARO Probabilistic programming in a nutshell A quick Figaro tutorial Creating a probabilistic programming application PART 2 WRITING PROBABILISTIC PROGRAMS Probabilistic models and probabilistic programs Modeling dependencies with Bayesian and Markov networks Using Scala and Figaro collections to build up models Object-oriented probabilistic modeling Modeling dynamic systems PART 3 INFERENCE The three rules of probabilistic inference Factored inference algorithms Sampling algorithms Solving other inference tasks Dynamic reasoning and parameter learning
Author: Rick Durrett
Publisher: Cambridge University Press
ISBN: 113949113X
Category : Mathematics
Languages : en
Pages :
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Book Description
This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.
Author: Russel .G Almond
Publisher: Routledge
ISBN: 1351444476
Category : Mathematics
Languages : en
Pages : 455
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Book Description
This innovative volume explores graphical models using belief functions as a representation of uncertainty, offering an alternative approach to problems where probability proves inadequate. Graphical Belief Modeling makes it easy to compare the two approaches while evaluating their relative strengths and limitations. The author examines both theory and computation, incorporating practical notes from the author's own experience with the BELIEF software package. As one of the first volumes to apply the Dempster-Shafer belief functions to a practical model, a substantial portion of the book is devoted to a single example--calculating the reliability of a complex system. This special feature enables readers to gain a thorough understanding of the application of this methodology. The first section provides a description of graphical belief models and probablistic graphical models that form an important subset: the second section discusses the algorithm used in the manipulation of graphical models: the final segment of the book offers a complete description of the risk assessment example, as well as the methodology used to describe it. Graphical Belief Modeling offers researchers and graduate students in artificial intelligence and statistics more than just a new approach to an old reliability task: it provides them with an invaluable illustration of the process of graphical belief modeling.
Author: Michael Todinov
Publisher: John Wiley & Sons
ISBN: 1118873254
Category : Technology & Engineering
Languages : en
Pages : 441
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Book Description
A comprehensively updated and reorganized new edition. The updates include comparative methods for improving reliability; methods for optimal allocation of limited resources to achieve a maximum risk reduction; methods for improving reliability at no extra cost and building reliability networks for engineering systems. Includes: A unique set of 46 generic principles for reducing technical risk Monte Carlo simulation algorithms for improving reliability and reducing risk Methods for setting reliability requirements based on the cost of failure New reliability measures based on a minimal separation of random events on a time interval Overstress reliability integral for determining the time to failure caused by overstress failure modes A powerful equation for determining the probability of failure controlled by defects in loaded components with complex shape Comparative methods for improving reliability which do not require reliability data Optimal allocation of limited resources to achieve a maximum risk reduction Improving system reliability based solely on a permutation of interchangeable components
