Probability and Data Analysis (Year 1 - Term 1) Introduction to Statistical Modeling (Year 1 - Term 2) Statistical Learning (Year 2 - Term 1) Predictive Modeling (Year 2 - Term 2)

* R programming and introduction to R Markdown * Probability refresher * Statistics refresher 1. Random numbers (Monte Carlo tecniques) 1.1 Probability and inference refresher 1.2 Statistical validation techniques 1.3 (Pseudo)random number generation 1.4 Approximation of probabilities and volumes 1.5 Monte Carlo integration 2. Simulating random variables and vectors 2.1 Inverse transform 2.2 Aceptance-rejection 2.3 Composition approach 2.4 Multivariate distributions 2.5 Multivariate normal distribution 3. Discrete event simulation 3.1 Poisson processes 3.2 Gaussian processes 3.3 Single- and multi-server Queueing systems 3.4 Inventory model 3.5 Insurance risk model 3.6 Repair problem 3.7 Exercising a stock option 4. Efficiency improvement (variance reduction) techniques 4.1 Antithetic variables 4.2 Control variates 4.3 Stratified sampling 4.4 Importance sampling 5. MCMC 5.1 Markov chains 5.2 Metropolis-Hastings 5.3 Gibbs sampling 6. Introduction to the bootstrap 6.1 The bootstrap principle 6.2 Estimating standard errors 6.3 Bootstrap Inference (Confidence Intervals) 6.4 The two-sample problem 6.5 Bootstrapping regression models

- Lectures and problem sessions with a computer: introducing the theoretical concepts and developments with examples, and solving problems: 25 on-site hours - Homework: 49 non on-site hours - Evaluation sessions (continuous evaluation and final exam): 5 on-site hours - Specific exam preparation: 49 non on-site hours