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Computational Probability and Mathematical Modeling

Author: José Roberto Cantú-González

Publisher: Frontiers Media SA

Published: 2019-12-24

Total Pages: 71

ISBN-13: 288963244X

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

Author: John H. Drew

Publisher: Springer

Published: 2016-12-15

Total Pages: 336

ISBN-13: 3319433237

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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 and Simulation

Author: Sidney J. Yakowitz

Publisher: Addison Wesley Publishing Company

Published: 1977

Total Pages: 280

ISBN-13:

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Random processes and Random number generators; Simulation of probability experiments; Gaming, Random Walks, and linear equations; Gambler's ruin with extensions to inventory control; Limiting processes for Random Walks and time series simulation; Monte Carlo integration and solution of differential equations.

Computational Mathematical Modeling

Author: Daniela Calvetti

Publisher: SIAM

Published: 2013-03-21

Total Pages: 229

ISBN-13: 1611972477

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Interesting real-world mathematical modelling problems are complex and can usually be studied at different scales. The scale at which the investigation is carried out is one of the factors that determines the type of mathematics most appropriate to describe the problem. The book concentrates on two modelling paradigms: the macroscopic, in which phenomena are described in terms of time evolution via ordinary differential equations; and the microscopic, which requires knowledge of random events and probability. The exposition is based on this unorthodox combination of deterministic and probabilistic methodologies, and emphasizes the development of computational skills to construct predictive models. To elucidate the concepts, a wealth of examples, self-study problems, and portions of MATLAB code used by the authors are included. This book, which has been extensively tested by the authors for classroom use, is intended for students in mathematics and the physical sciences at the advanced undergraduate level and above.

Computational Probability

Author: John H. Drew

Publisher: Springer Science & Business Media

Published: 2008-01-08

Total Pages: 220

ISBN-13: 0387746765

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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.

Statistical Modeling and Computation

Author: Dirk P. Kroese

Publisher: Springer Science & Business Media

Published: 2013-11-18

Total Pages: 412

ISBN-13: 1461487757

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This textbook on statistical modeling and statistical inference will assist advanced undergraduate and graduate students. Statistical Modeling and Computation provides a unique introduction to modern Statistics from both classical and Bayesian perspectives. It also offers an integrated treatment of Mathematical Statistics and modern statistical computation, emphasizing statistical modeling, computational techniques, and applications. Each of the three parts will cover topics essential to university courses. Part I covers the fundamentals of probability theory. In Part II, the authors introduce a wide variety of classical models that include, among others, linear regression and ANOVA models. In Part III, the authors address the statistical analysis and computation of various advanced models, such as generalized linear, state-space and Gaussian models. Particular attention is paid to fast Monte Carlo techniques for Bayesian inference on these models. Throughout the book the authors include a large number of illustrative examples and solved problems. The book also features a section with solutions, an appendix that serves as a MATLAB primer, and a mathematical supplement.

Computational and Mathematical Modeling in the Social Sciences

Author: Scott de Marchi

Publisher: Cambridge University Press

Published: 2005-08-15

Total Pages: 232

ISBN-13: 9780521853620

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Offers an overview of mathematical modeling concentrating on game theory, statistics and computational modeling.

A Course in Computational Probability and Statistics

Author: Walter Freiberger

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 167

ISBN-13: 1461298377

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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.

Probability and Statistics for Engineering and the Sciences with Modeling using R

Author: William P. Fox

Publisher: CRC Press

Published: 2022-12-29

Total Pages: 429

ISBN-13: 1000825574

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Probability and statistics courses are more popular than ever. Regardless of your major or your profession, you will most likely use concepts from probability and statistics often in your career. The primary goal behind this book is offering the flexibility for instructors to build most undergraduate courses upon it. This book is designed for either a one-semester course in either introductory probability and statistics (not calculus-based) and/or a one-semester course in a calculus-based probability and statistics course. The book focuses on engineering examples and applications, while also including social sciences and more examples. Depending on the chapter flows, a course can be tailored for students at all levels and background. Over many years of teaching this course, the authors created problems based on real data, student projects, and labs. Students have suggested these enhance their experience and learning. The authors hope to share projects and labs with other instructors and students to make the course more interesting for both. R is an excellent platform to use. This book uses R with real data sets. The labs can be used for group work, in class, or for self-directed study. These project labs have been class-tested for many years with good results and encourage students to apply the key concepts and use of technology to analyze and present results.

Computational Probability Applications

Author: Andrew G. Glen

Publisher: Springer

Published: 2016-12-01

Total Pages: 256

ISBN-13: 3319433172

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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.