Module : Stochastic Modelling and Simulation
| Semestre 5 SC | VHS C/TD/TP |
VHH Total C/TD/TP |
V.H. Hebdomadaire | Coef | Crédits | ||
|---|---|---|---|---|---|---|---|
| C | TD | TP | |||||
| UE Methodologiques 5.1 | 60 | 4 | 2 | 1.5 | 0.5 | 3 | 5 |
Course Description:
This course provides an introduction to the theory and practice of stochastic modelling and simulation. Stochastic modelling is the study of systems subject to random variations, where probability theory provides a powerful tool for modelling the behaviour of such systems.
Prerequisite : Probability and Inference
Evaluation Method : Coursework (40 %) + Final Exam (60%)
Course Content
Part 1: Stochastic Processes and their Classification
- Discrete time Markov chains
- Poisson processes
- Continuous time Markov chains
Part 2: Introduction to Stochastic Simulation
- Pseudo random number generator
- Simulation of random variables
- Simulation of random vectors
- Monte Carlo methods and variance reduction methods
- Simulation of stochastic processes (MCMC, queuing models)
Part 3: Probabilistic Machine Learning
- Bayesian networks
- Hidden Markov Models
References
- S. M. Ross: Introduction to Probability Models. Academic Press; 13th edition, 2023.
- M. A. Pinsky et S. Karlin : An Introduction to Stochastic Modeling. 4th ed. Academic Press, 2011.
- Hossein Pishro-Nik, Introduction to probability, statistics and random processes, Kappa Research, 2014.
- T. Hastie, R. Tibshirani and Friedman, The Elements of Statistical Learning, Springer.
- F. V. Jensen. “Bayesian Networks and Decision Graphs”. Springer. 2001.