Computational Probability
Algorithms and Applications in the Mathematical Sciences
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Beschreibung
Computational probability encompasses data structures and algorithms that have emerged over the past decade that allow researchers and students to focus on a new class of stochastic problems. COMPUTATIONAL PROBABILITY is the first book that examines and presents these computational methods in a systematic manner. The techniques described here address problems that require exact probability calculations, many of which have been considered intractable in the past. The first chapter introduces computational probability analysis, followed by a chapter on the Maple computer algebra system. The third chapter begins the description of APPL, the probability modeling language created by the authors. The book ends with three applications-based chapters that emphasize applications in survival analysis and stochastic simulation.
The algorithmic material associated with continuous random variables is presented separately from the material for discrete random variables. Four sample algorithms, which are implemented in APPL, are presented in detail: transformations of continuous random variables, products of independent continuous random variables, sums of independent discrete random variables, and order statistics drawn from discrete populations.
The APPL computational modeling language gives the field of probability a strong software resource to use for non-trivial problems and is available at no cost from the authors. APPL is currently being used in applications as wide-ranging as electric power revenue forecasting, analyzing cortical spike trains, and studying the supersonic expansion of hydrogen molecules. Requests for the software have come from fields as diverse as market research, pathology, neurophysiology, statistics, engineering, psychology, physics, medicine, and chemistry.
Computational probability encompasses data structures and algorithms that have emerged over the past decade that allow researchers and students to focus on a new class of stochastic problems. COMPUTATIONAL PROBABILITY is the first book that examines and presents these computational methods in a systematic manner. The techniques described here address problems that require exact probability calculations, many of which have been considered intractable in the past. The first chapter introduces computational probability analysis, followed by a chapter on the Maple computer algebra system. The third chapter begins the description of APPL, the probability modeling language created by the authors. The book ends with three applications-based chapters that emphasize applications in survival analysis and stochastic simulation.
The algorithmic material associated with continuous random variables is presented separately from the material for discrete random variables. Four sample algorithms, which are implemented in APPL, are presented in detail: transformations of continuous random variables, products of independent continuous random variables, sums of independent discrete random variables, and order statistics drawn from discrete populations.
The APPL computational modeling language gives the field of probability a strong software resource to use for non-trivial problems and is available at no cost from the authors. APPL is currently being used in applications as wide-ranging as electric power revenue forecasting, analyzing cortical spike trains, and studying the supersonic expansion of hydrogen molecules. Requests for the software have come from fields as diverse as market research, pathology, neurophysiology, statistics, engineering, psychology, physics, medicine, and chemistry.
This is an expository monograph with a downloadable modeling language, APPL, that will be used across the Applied Sciences domains including OR/MS, Applied Probability, Engineering, Statistics, Economics, and Applied Mathematics. It will be used by practitioners, as well as academic researchers and students
The book package will sell nicely in both the academic and practitioner areas. Moreover, the software will motivate the sales of the book package. The authors, through their APPL software, have some very good practitioner contacts worldwide.
Autor*in
John H. Drew
Themen in »Computational Probability«
APPL Maple Random variable Simulation Survival analysis Transformation algorithm algorithms calculus computational probability computer algebra computer algebra system modeling statistics univariate random variables
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From the reviews:
"The monograph is devoted to the use of a computer algebra system to solve problems in operations research and probability. … The presented monograph will be of interest for all researchers and specialists that are working in the mathematical sciences … . It will be very useful for the lecturers, which could use it for the preparation of special topics courses in computational probability … . The intended audience for the presented monograph includes researchers, MS students, PhD students, and advanced practitioners … ." (Tzvetan Semerdjiev, Zentralblatt MATH, Vol. 1145, 2008)
"The text is … an introduction to a computer language called A Probability Programming Language (APPL), specially created by the authors to make it easy for statisticians and operational researchers to carry out complex manipulations involving probability distributions. … I would recommend this book to anyone working with probability distributions. … the book could certainly be of use to operational research practitioners working in ‘hard’ OR fields where complex probabilistic models are needed." (John Smith, Journal of the Operational Research society, Vol. 60 (7), 2009)
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