Computational Probability
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Computational Probability
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Author : Winfried K. Grassmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Computational Probability written by Winfried K. Grassmann 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 2013-03-14 with Business & Economics categories.
Great advances have been made in recent years in the field of computational probability. In particular, the state of the art - as it relates to queuing systems, stochastic Petri-nets and systems dealing with reliability - has benefited significantly from these advances. The objective of this book is to make these topics accessible to researchers, graduate students, and practitioners. Great care was taken to make the exposition as clear as possible. Every line in the book has been evaluated, and changes have been made whenever it was felt that the initial exposition was not clear enough for the intended readership. The work of major research scholars in this field comprises the individual chapters of Computational Probability. The first chapter describes, in nonmathematical terms, the challenges in computational probability. Chapter 2 describes the methodologies available for obtaining the transition matrices for Markov chains, with particular emphasis on stochastic Petri-nets. Chapter 3 discusses how to find transient probabilities and transient rewards for these Markov chains. The next two chapters indicate how to find steady-state probabilities for Markov chains with a finite number of states. Both direct and iterative methods are described in Chapter 4. Details of these methods are given in Chapter 5. Chapters 6 and 7 deal with infinite-state Markov chains, which occur frequently in queueing, because there are times one does not want to set a bound for all queues. Chapter 8 deals with transforms, in particular Laplace transforms. The work of Ward Whitt and his collaborators, who have recently developed a number of numerical methods for Laplace transform inversions, is emphasized in this chapter. Finally, if one wants to optimize a system, one way to do the optimization is through Markov decision making, described in Chapter 9. Markov modeling has found applications in many areas, three of which are described in detail:Chapter 10 analyzes discrete-time queues, Chapter 11 describes networks of queues, and Chapter 12 deals with reliability theory.
Computational Probability
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Author : John H. Drew
language : en
Publisher: Springer
Release Date : 2016-12-15
Computational Probability written by John H. Drew and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-15 with Business & Economics categories.
This new edition includes the latest advances and developments in computational probability involving A Probability Programming Language (APPL). The book examines and presents, in a systematic manner, computational probability methods that encompass data structures and algorithms. The developed techniques address problems that require exact probability calculations, many of which have been considered intractable in the past. The book addresses the plight of the probabilist by providing algorithms to perform calculations associated with random variables. Computational Probability: Algorithms and Applications in the Mathematical Sciences, 2nd Edition begins with an introductory chapter that contains short examples involving the elementary use of APPL. Chapter 2 reviews the Maple data structures and functions necessary to implement APPL. This is followed by a discussion of the development of the data structures and algorithms (Chapters 3–6 for continuous random variables and Chapters 7–9 for discrete random variables) used in APPL. The book concludes with Chapters 10–15 introducing a sampling of various applications in the mathematical sciences. This book should appeal to researchers in the mathematical sciences with an interest in applied probability and instructors using the book for a special topics course in computational probability taught in a mathematics, statistics, operations research, management science, or industrial engineering department.
Computational Probability
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Author : P. M. Kahn
language : en
Publisher: Elsevier
Release Date : 2014-05-10
Computational Probability written by P. M. Kahn 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 Business & Economics categories.
Computational Probability is a collection of papers presented at the Actuarial Research Conference on Computational Probability and related topics, held at Brown University on August 28-30, 1975. This 19-chapter book explores the development of computational techniques in probability and statistics and their application to problems in insurance. It covers six general topics, including computational probability, computational statistics, computational risk theory, analysis of algorithms, numerical methods, and notation and computation. Applications covered both life and nonlife insurance. This book will prove useful to applied mathematicians, statisticians, and computer scientists.
Computational Probability Applications
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Author : Andrew G. Glen
language : en
Publisher: Springer
Release Date : 2016-12-01
Computational Probability Applications written by Andrew G. Glen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-01 with Business & Economics categories.
This focuses on the developing field of building probability models with the power of symbolic algebra systems. The book combines the uses of symbolic algebra with probabilistic/stochastic application and highlights the applications in a variety of contexts. The research explored in each chapter is unified by the use of A Probability Programming Language (APPL) to achieve the modeling objectives. APPL, as a research tool, enables a probabilist or statistician the ability to explore new ideas, methods, and models. Furthermore, as an open-source language, it sets the foundation for future algorithms to augment the original code. Computational Probability Applications is comprised of fifteen chapters, each presenting a specific application of computational probability using the APPL modeling and computer language. The chapter topics include using inverse gamma as a survival distribution, linear approximations of probability density functions, and also moment-ratio diagrams for univariate distributions. These works highlight interesting examples, often done by undergraduate students and graduate students that can serve as templates for future work. In addition, this book should appeal to researchers and practitioners in a range of fields including probability, statistics, engineering, finance, neuroscience, and economics.
Computational Probability And Mathematical Modeling
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Author : José Roberto Cantú-González
language : en
Publisher: Frontiers Media SA
Release Date : 2019-12-24
Computational Probability And Mathematical Modeling written by José Roberto Cantú-González and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-24 with categories.
In the present time, two of the most important approaches to tackle complex systems are probability and stochastic processes theory. Still from an analytic perspective, modeling and solving a problem using a stochastic approach is not a trivial issue, hence, a combination of the logic of probabilistic reasoning with computational science is needed to obtain qualitatively good solutions in a reasonable time. This eBook presents an interesting view of applications associated to fields of probability, statistics, and mathematic modeling, all of them supported by a computational context though the approach of stochasticity and simulation used in most of them. This collection contains three chapters, which bring applications in fields of biology, finance and physics, each chapter contains work(s) with specific applications. An editorial is also contained with a summarized version of each work, and each of them are widely explained in a specific section, which include a state of art to support the nature of the individual research, a methodology to solve the defined problem and the results and conclusions. We hope the present eBook can represent a potential source of knowledge for the academic community of implicated disciplines, and an inspirational starting point of starting for scientists in the amazing world of applied mathematics and the search to solve complex problems
Computational Probability
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Author : John H. Drew
language : en
Publisher: Springer
Release Date : 2007-11-15
Computational Probability written by John H. Drew and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-15 with Business & Economics categories.
This title organizes computational probability methods into a systematic treatment. The book examines two categories of problems. "Algorithms for Continuous Random Variables" covers data structures and algorithms, transformations of random variables, and products of independent random variables. "Algorithms for Discrete Random Variables" discusses data structures and algorithms, sums of independent random variables, and order statistics.
A Course In Computational Probability And Statistics
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Author : Walter Freiberger
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Course In Computational Probability And Statistics written by Walter Freiberger 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 2012-12-06 with Mathematics categories.
This book arose out of a number of different contexts, and numerous persons have contributed to its conception and development. It had its origin in a project initiated jointly with the IBM Cambridge Scien tific Center, particularly with Dr. Rhett Tsao, then of that Center. We are grateful to Mr. Norman Rasmussen, Manager of the IBM Scientific Center Complex, for his initial support. The work is being carried on at Brown University with generous support from the Office of Computing Activities of the National Science Foundation (grants GJ-174 and GJ-7l0); we are grateful to Dr. John Lehmann of this Office for his interest and encouragement. Professors Donald McClure and Richard Vitale of the Division of Applied Mathematics at Brown University contributed greatly to the project and taught courses in its spirit. We are indebted to them and to Dr. Tore Dalenius of the University of Stockholm for helpful criticisms of the manuscript. The final stimulus to the book's completion came from an invLtation to teach a course at the IBM European Systems Research Institute at Geneva. We are grateful to Dr. J.F. Blackburn, Director of the Institute, for his invitation, and to him and his wife Beverley for their hospitality. We are greatly indebted to Mrs. Katrina Avery for her splendid secretarial and editorial work on the manuscript.
Computation Of Multivariate Normal And T Probabilities
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Author : Alan Genz
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-09
Computation Of Multivariate Normal And T Probabilities written by Alan Genz 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 2009-07-09 with Computers categories.
Multivariate normal and t probabilities are needed for statistical inference in many applications. Modern statistical computation packages provide functions for the computation of these probabilities for problems with one or two variables. This book describes recently developed methods for accurate and efficient computation of the required probability values for problems with two or more variables. The book discusses methods for specialized problems as well as methods for general problems. The book includes examples that illustrate the probability computations for a variety of applications.
Digital Dice
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Author : Paul J. Nahin
language : en
Publisher: Princeton University Press
Release Date : 2008
Digital Dice written by Paul J. Nahin and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Computers categories.
A collection of twenty-one real-life probability puzzles and shows how to get numerical answers without having to solve complicated mathematical equations.
Intermediate Probability
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Author : Marc S. Paolella
language : en
Publisher: John Wiley & Sons
Release Date : 2007-09-27
Intermediate Probability written by Marc S. Paolella 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 2007-09-27 with Mathematics categories.
Intermediate Probability is the natural extension of the author's Fundamental Probability. It details several highly important topics, from standard ones such as order statistics, multivariate normal, and convergence concepts, to more advanced ones which are usually not addressed at this mathematical level, or have never previously appeared in textbook form. The author adopts a computational approach throughout, allowing the reader to directly implement the methods, thus greatly enhancing the learning experience and clearly illustrating the applicability, strengths, and weaknesses of the theory. The book: Places great emphasis on the numeric computation of convolutions of random variables, via numeric integration, inversion theorems, fast Fourier transforms, saddlepoint approximations, and simulation. Provides introductory material to required mathematical topics such as complex numbers, Laplace and Fourier transforms, matrix algebra, confluent hypergeometric functions, digamma functions, and Bessel functions. Presents full derivation and numerous computational methods of the stable Paretian and the singly and doubly non-central distributions. A whole chapter is dedicated to mean-variance mixtures, NIG, GIG, generalized hyperbolic and numerous related distributions. A whole chapter is dedicated to nesting, generalizing, and asymmetric extensions of popular distributions, as have become popular in empirical finance and other applications. Provides all essential programming code in Matlab and R. The user-friendly style of writing and attention to detail means that self-study is easily possible, making the book ideal for senior undergraduate and graduate students of mathematics, statistics, econometrics, finance, insurance, and computer science, as well as researchers and professional statisticians working in these fields.