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A fascinating and instructive guide to Markov chains for experienced users and newcomers alike This unique guide to Markov chains approaches the subject along the four convergent lines of… Altro …

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Markov Chains From Theory to Implementation and Experimentation - copertina rigida, flessible

2017, ISBN: 1119387558

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Dettagli del libro
Markov Chains: From Theory to Implementation and Experimentation Paul A. Gagniuc Author

A fascinating and instructive guide to Markov chains for experienced users and newcomers alike 

This unique guide to Markov chains approaches the subject along the four convergent lines of mathematics, implementation, simulation, and experimentation. It introduces readers to the art of stochastic modeling, shows how to design computer implementations, and provides extensive worked examples with case studies.

Markov Chains: From Theory to Implementation and Experimentation begins with a general introduction to the history of probability theory in which the author uses quantifiable examples to illustrate how probability theory arrived at the concept of discrete-time and the Markov model from experiments involving independent variables. An introduction to simple stochastic matrices and transition probabilities is followed by a simulation of a two-state Markov chain. The notion of steady state is explored in connection with the long-run distribution behavior of the Markov chain. Predictions based on Markov chains with more than two states are examined, followed by a discussion of the notion of absorbing Markov chains. Also covered in detail are topics relating to the average time spent in a state, various chain configurations, and n-state Markov chain simulations used for verifying experiments involving various diagram configurations.

Fascinating historical notes shed light on the key ideas that led to the development of the Markov model and its variants Various configurations of Markov Chains and their limitations are explored at length Numerous examples—from basic to complex—are presented in a comparative manner using a variety of color graphics All algorithms presented can be analyzed in either Visual Basic, Java Script, or PHP Designed to be useful to professional statisticians as well as readers without extensive knowledge of probability theory

Covering both the theory underlying the Markov model and an array of Markov chain implementations, within a common conceptual framework, Markov Chains: From Theory to Implementation and Experimentation is a stimulating introduction to and a valuable reference for those wishing to deepen their understanding of this extremely valuable statistical to

Informazioni dettagliate del libro - Markov Chains: From Theory to Implementation and Experimentation Paul A. Gagniuc Author


EAN (ISBN-13): 9781119387558
ISBN (ISBN-10): 1119387558
Copertina rigida
Anno di pubblicazione: 2017
Editore: Wiley Core >2 >T

Libro nella banca dati dal 2017-06-09T14:37:35+02:00 (Rome)
Pagina di dettaglio ultima modifica in 2023-12-10T12:47:40+01:00 (Rome)
ISBN/EAN: 1119387558

ISBN - Stili di scrittura alternativi:
1-119-38755-8, 978-1-119-38755-8
Stili di scrittura alternativi e concetti di ricerca simili:
Autore del libro : markov, john case, gagniuc
Titolo del libro: markov chains, marko


Dati dell'editore

Autore: Paul A. Gagniuc
Titolo: Markov Chains - From Theory to Implementation and Experimentation
Editore: Wiley; John Wiley & Sons
256 Pagine
Anno di pubblicazione: 2017-09-19
Peso: 0,546 kg
Lingua: Inglese
125,00 € (DE)
Not available (reason unspecified)
158mm x 231mm x 18mm

BB; Hardcover, Softcover / Mathematik; Diskrete Mathematik; Discrete Mathematics; Diskrete Mathematik; Markowsche Kette; Materials Science; Materialwissenschaften; Materialwissenschaften / Theorie, Modellierung u. Simulation; Mathematics; Mathematik; Theory, Modeling & Simulation; Diskrete Mathematik; Materialwissenschaften / Theorie, Modellierung u. Simulation

Abstract ix Preface xi Acknowledgments xiii About the CompanionWebsite xv 1 Historical Notes 1 1.1 Introduction 1 1.2 On theWings of Dependent Variables 2 1.3 From Bernoulli to Markov 5 2 FromObservation to Simulation 9 2.1 Introduction 9 2.2 Stochastic Matrices 9 2.3 Transition Probabilities 11 2.4 The Simulation of a Two-State Markov Chain 14 3 Building the Stochastic Matrix 25 3.1 Introduction 25 3.2 Building a Stochastic Matrix from Events 25 3.3 Building a Stochastic Matrix from Percentages 32 4 Predictions Using Two-State Markov Chains 37 4.1 Introduction 37 4.2 Performing the Predictions by Using the Stochastic Matrix 37 4.3 The Steady State of a Markov Chain 46 4.4 The Long-Run Distribution of a Markov Chain 55 5 Predictions Using n-State Markov Chains 61 5.1 Introduction 61 5.2 Predictions by Using the Three-State Markov Chain 61 5.3 Predictions by Using the Four-State Markov Chain 71 5.4 Predictions by Using n-State Markov Chains 80 5.5 Markov Chain Modeling on Measurements 84 6 AbsorbingMarkov Chains 93 6.1 Introduction 93 6.2 The Absorbing State 93 7 The Average Time Spent in Each State 99 7.1 Introduction 99 7.2 The Proportion of Balls in the System 99 7.3 The Average Time Spent in A Particular State 100 7.4 Exemplification of the Average Time and Proportions 101 8 Discussions on Different Configurations of Chains 107 8.1 Introduction 107 8.2 Examples of Two-State Diagrams 113 8.3 Examples of Three-State Diagrams 115 8.4 Examples of Four-State Diagrams 117 8.5 Examples of State Diagrams Divided into Classes 123 8.6 Examples of State Diagrams with Absorbing States 127 8.7 The Gambler's Ruin 128 9 The Simulation of an n-State Markov Chain 131 9.1 Introduction 131 9.2 The Simulation of Behavior 131 9.3 Simulation of Different Chain Configurations 145 A Supporting Algorithms in PHP 165 B Supporting Algorithms in Javascript 193 C Syntax Equivalence between Languages 223 Glossary 225 References 227 Index 231

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