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 Python [@Courant_deFalco_Gonnord_Filliatre_Conchon_Dowek_Wack13] 🇫🇷
- 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: [@Williams91] 🇬🇧