Module : Statistical Inference
| Semestre 4 CP | VHS C/TD/TP |
VHH Total C/TD/TP |
V.H. Hebdomadaire | Coef | Crédits | ||
|---|---|---|---|---|---|---|---|
| C | TD | TP | |||||
| UE Fondamentales 4.1 | 67.5 | 4.5 | 1.5 | 1.5 | 1.5 | 3 | 5 |
Course Description :
This course covers the classical aspects of probability theory and focuses on the probabilistic model and its basic properties. It also considers random experiments whose characteristic of interest can be modelled by univariate or multivariate random variables (discrete or continuous). It introduces random vectors, sequences of random variables, and different aspects of convergence. Finally, students will be introduced to elements of statistical and Bayesian inference, such as parameter estimation and hypothesis testing.
Prerequisite : Probability and Statistics I, Analysis
Evaluation Method : Coursework (40%) + Final Exam (60%)
Course Content
- Limit Theorems
- Chebyshev’s Inequality and the Weak Law of Large Numbers
- The Central Limit Theorem
- The Strong Law of Large Numbers
- Statistical Inference
- Point Estimation
- Interval Estimation
- Hypothesis Testing
- Bayesian Inference
- The Prior and Posterior Distributions
- Inferences Based on the Posterior
- Bayesian Computations
- Choosing Priors
References
- Sheldon M. Ross, A first course in probability, Pearson, 2018.
- Hossein Pishro-Nik, Introduction to probability, statistics and random processes, Kappa Research, 2014.
- Sheldon M. Ross, Introduction in probability and statistics for scientists and engineers, Academic Press, 2014.
- David Forsyth, Probability and statistics for computer science, Springer, 2018
- Mario Triola, Elementary Statistics, Pearson, 2021.