| Titre : | Monte Carlo simulation for Markov chain |
| Auteurs : | Abd El kader Djaafri, Directeur de thèse ; hadj kaddour Nasrallah, Auteur |
| Type de document : | texte imprimé |
| Editeur : | UNIVERSITY OF SAIDA - Dr. MOULAY TAHAR Faculty of Science and Technology Department of Materials Science, 2024/2025 |
| Format : | 55 p |
| Accompagnement : | CD |
| Langues: | Anglais |
| Langues originales: | Anglais |
| Catégories : | |
| Note de contenu : |
Chapter 1 Generalities about the Markov chain…………....………....….……..16
Introduction………………………………………………………………..…………………..…….….17 1.2 Definition……………………………………………………………..…………………..………….18 1.3 history…………………………………………………………………...…………………..………..18 1.4 Applications of Markov Chains………………………………...……………..…….…….20 1.4.1 Physics……………………………………………………………...……………..………..21 1.4.2 Weather Prediction……………………………………………....…………..……….21 1.4.3 Google PageRank………………………………………………....………..………….22 1.4.4 Text Generation (Markov Chain Text Models)….....………..………….22 1.4.5 Solar irradiance variability………………………………….....…….……………22 1.4.6 Speech recognition……………………………………..………...……….………….22 1.4.7 Information theory……………………………..…………..….…………….…….…22 1.4.8 Queueing theory…………………………………..……….….…………….…………24 1.5 Probability properties………………………………………..……….………………..………24 1.6 Other properties…………………………………………………...………………..……….….25 1.6.1 Stationary Distribution……………………………...…………………..…………25 1.6.2 Irreducibility…………………………………………………..………………..……….26 1.6.3 Ergodicity………………………………………………………………....………………26 1.6.4 Reversibility…………………………………………….………………....…………….26 1.6.5 Absorbing States………………………………..……………………....…………...27 1.6.6 Transience and Recurrence………………………………………..….………..27 1.6.7 Periodic States………………………………………………..…………..…………...28 1.6.8 Mixing Time…………………………………………………………..………………..28 51. 7 References of Markov Chain…………………………………………..…………………28 1.8 Conclusions ……………………………………………………………………..………………..29 Chapter 2 : Monte Carlo simulation……………………………..…...………………..30 2.1 Introduction.......................................................................................... .................32 2.2 Convergence and Statistical Accuracy………………………………...…………….33 2.2.1 Output Analysis…………………………………………………………...……………….33 2.2.2 Sensitivity Analysis…………………………………………………...………………….33 2.2.3 Variance Reduction Techniques………………………………...…………………34 2.2.4 Sampling Methods……………………………………………………...…………………34 2.3 Steps in a Monte Carlo Simulation…………………………………...…………………34 2.3.1 Define the Problem or System…………………………………...…………………34 2.3.2 Identify Input Variables and Define Probability Distributions…..…35 2.3.3 Generate Random Samples……………………………………………………..…..35 2.3.4 Run the Simulation (Perform One Trial)…………………………………...….36 2.4 Repeat the Simulation (Multiple Trials) ………………………………………..…....36 2.4.1 Analyze the Results………………………………………………………………..….….36 2.4.2 Make Decisions Based on Results…………………..………………………..….37 2.4.3 Validate and Refine the Model (Optional)…………………………........……37 2.5 Applications of Monte Carlo Simulations……………………………………………38 2.5.2 estimating π using Monte Carlo……………………………………………………38 2.5.3 General Monte Carlo Estimation Formula…………………………………….39 2.5.4 Finance and Investment…………………………………………..………………….39 2.5.5 Project Management……………………………………………………………………..40 2.5.6 Healthcare and Medicine……………………………………………………………….40 2.5.7 Environmental Science………………………………………………………………….41 2.6 Conclusion…………………………………………………………………………………………….40 2.7 References ………………………………………………………………………………………….41 Chapter 3 : Inverse Markov problem by monte Carlo simulation………….42 3.1 Introduction………………………………………………………………………………………….42 3.2 Ion channel…………………………………………………………………………………………..42 63.3 Markov model………………………………………………………………………………………42 3.3.1 Continuous matrix Q…………………………………………………………………….42 3.3.2 Discrete matrix T………………………………………………………………………….44 3.3.3 Steady-State Probabilities…………………………………………………………...44 3.3.4 Validation by simulation……………………………………………………………….44 3.4 Inverse Estimation of a Markov Transition Matrix…………….. …………….45 3.4.1 Metropolis Algorithm …………………………………………………….……………45 3.4.2 Energy Function ………………………………………….……………………………..45 3.4.3 Methodology …………………………………………………………………………….. 46 3.4.4 Results…………………………………………………………. …………………………… 48 3.4.5 Conclusion …………………………………………………………..………………………49 |
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