Markov chains : from theory to implementation and experimentation
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 mod...
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| Hlavný autor: | |
|---|---|
| Médium: | E-kniha Kniha |
| Jazyk: | English |
| Vydavateľské údaje: |
Hoboken, N.J
Wiley
2017
John Wiley & Sons, Incorporated Wiley-Blackwell |
| Vydanie: | 1 |
| Predmet: | |
| ISBN: | 9781119387558, 1119387558, 9781119387589, 1119387582 |
| On-line prístup: | Získať plný text |
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- Intro -- Markov Chains -- Contents -- Abstract -- Preface -- Acknowledgments -- About the Companion Website -- 1 Historical Notes -- 1.1 Introduction -- 1.2 On the Wings of Dependent Variables -- 1.3 From Bernoulli to Markov -- 2 From Observation to Simulation -- 2.1 Introduction -- 2.2 Stochastic Matrices -- 2.3 Transition Probabilities -- 2.4 The Simulation of a Two-State Markov Chain -- 2.4.1 The White Jar of the Original Machine -- 2.4.2 The Black Jar of the Original Machine -- 2.4.3 The Representation of New Jars -- 2.4.4 Simulation of the System -- 3 Building the Stochastic Matrix -- 3.1 Introduction -- 3.2 Building a Stochastic Matrix from Events -- 3.3 Building a Stochastic Matrix from Percentages -- 4 Predictions Using Two-State Markov Chains -- 4.1 Introduction -- 4.2 Performing the Predictions by Using the Stochastic Matrix -- 4.3 The Steady State of a Markov Chain -- 4.4 The Long-Run Distribution of a Markov Chain -- 4.4.1 Case A -- 4.4.2 Case B -- 4.4.3 Case C -- 4.4.4 Case D -- 4.4.5 Case E -- 5 Predictions Using n-State Markov Chains -- 5.1 Introduction -- 5.2 Predictions by Using the Three-State Markov Chain -- 5.3 Predictions by Using the Four-State Markov Chain -- Nucleotide Prediction in Step 1 -- Nucleotide Prediction in Step 2 -- Nucleotide Prediction in Step 3 -- 5.4 Predictions by Using n-State Markov Chains -- 5.5 Markov Chain Modeling on Measurements -- 6 Absorbing Markov Chains -- 6.1 Introduction -- 6.2 The Absorbing State -- 7 The Average Time Spent in Each State -- 7.1 Introduction -- 7.2 The Proportion of Balls in the System -- 7.3 The Average Time Spent in A Particular State -- 7.4 Exemplification of the Average Time and Proportions -- 7.4.1 The Proportion of Ball Types -- 7.4.2 The Average Time Spent in a State -- 8 Discussions on Different Configurations of Chains -- 8.1 Introduction
- 8.2 Examples of Two-State Diagrams -- 8.2.1 Case A -- 8.2.2 Case B -- 8.3 Examples of Three-State Diagrams -- 8.3.1 Case C -- 8.3.2 Case D -- 8.4 Examples of Four-State Diagrams -- 8.4.1 Case E -- 8.4.2 Case F -- 8.4.3 Case G -- 8.5 Examples of State Diagrams Divided into Classes -- 8.5.1 Case H -- 8.5.2 Case I -- 8.5.3 Case J -- 8.5.4 Case K -- 8.6 Examples of State Diagrams with Absorbing States -- 8.6.1 Case L -- 8.7 The Gamblers Ruin -- 8.7.1 Case M -- 9 The Simulation of an n-State Markov Chain -- 9.1 Introduction -- 9.2 The Simulation of Behavior -- 9.2.1 The State Diagram Example -- 9.2.2 From Markov Diagrams to Jars and Balls -- 9.2.3 Representation of the Jars -- 9.2.4 Discussion on the Imbalance of Chances -- 9.2.5 Simulation of the System -- 9.3 Simulation of Different Chain Configurations -- 9.3.1 Alternative Parameters and the Framework Expansion -- 9.3.2 The Output Verification -- 9.3.3 Determination of Average Time by Experiment -- 9.3.4 A Window into the Behavior of Random Processes -- Appendix A Supporting Algorithms in PHP -- Supporting algorithm (PHP alternative) 1. -- Supporting algorithm (PHP alternative) 2. -- Supporting algorithm (PHP alternative) 3. -- Supporting algorithm (PHP alternative) 4. -- Supporting algorithm (PHP alternative) 5. -- Supporting algorithm (PHP alternative) 6. -- Supporting algorithm (PHP alternative) 7. -- Supporting algorithm (PHP alternative) 8. -- Supporting algorithm (PHP alternative) 9. -- Supporting algorithm (PHP alternative) 10. -- Supporting algorithm (PHP alternative) 11. -- Supporting algorithm (PHP alternative) 12. -- Supporting algorithm (PHP alternative) 13. -- Supporting algorithm (PHP alternative) 14. -- Supporting algorithm (PHP alternative) 15. -- Supporting algorithm (PHP alternative) 16. -- Supporting algorithm (PHP alternative) 17. -- Appendix B Supporting Algorithms in JavaScript
- Supporting algorithm (JS alternative) 1. -- Supporting algorithm (JS alternative) 2. -- Supporting algorithm (JS alternative) 3. -- Supporting algorithm (JS alternative) 4. -- Supporting algorithm (JS alternative) 5. -- Supporting algorithm (JS alternative) 6. -- Supporting algorithm (JS alternative) 7. -- Supporting algorithm (JS alternative) 8. -- Supporting algorithm (JS alternative) 9. -- Supporting algorithm (JS alternative) 10. -- Supporting algorithm (JS alternative) 11. -- Supporting algorithm (JS alternative) 12. -- Supporting algorithm (JS alternative) 13. -- Supporting algorithm (JS alternative) 14. -- Supporting algorithm (JS alternative) 15. -- Supporting algorithm (JS alternative) 16. -- Supporting algorithm (JS alternative) 17. -- Appendix C Syntax Equivalence between Languages -- Glossary -- References -- Index -- EULA