This is an undergraduate course (in French!) introducing standard techniques from stochastic modeling. Numerical elements are provided in Python.
Course content
See GitHub website: HAX603X - Modélisation Stochastique for the course content.
- Generating randomness
- Pseudo-random number generators
- Digital illustrations and visualization in Python (law of large numbers, central limit theorem)
- Simulations of random variables (inverse method, rejection method, specific cases, etc.)
- Monte Carlo Method
- Monte Carlo method for the approximate calculation of an integral
- Variance reduction: antithetic variables, control variables, preferential sampling.
- Supplementary topics
- Gaussian vectors and their connection with common laws in inferential statistics (Student's t, chi-square)
- Construction of confidence intervals.
- Simple random walk, etc.
Additional Resources
Beginner Level
- Introduction to Python Python Course 🇫🇷
- HLMA310 - Scientific Software 🇫🇷
- Algorithmic Manual in Pythonf 🇫🇷
- Data Science: Python Data Science Handbook, With Application to Understanding Data by J. Van DerPlas, 2016; 🇬🇧
videos: Reproducible Data Analysis in Jupyter - Math for Journalists by Naël Shiab 🇬🇧
Advanced Level
- Software Dev. for Data Science by J. Salmon and B. Charlier, 🇬🇧
- Markov Chains: Markov Chains by Ethan N. Epperly 🇬🇧
- Advanced Data Analysis from an Elementary Point of View by Cosma Shalizi; 🇬🇧
- Maximum Likelihood by Numerical Optimization 🇬🇧
- Conditioning, Martingales, and Other Proofs of the Law of Large Numbers: 🇬🇧