Probability Statistical Inference

Knowledge acquisition of: 1) random variables, elementary probability and distributions; 2) relevant probabilistic inequalities; 3) random vectors, marginal and joint distributions; 4) sequences of random variables and concepts of convergences; 5) Markov chains; 6) Poisson processes; 7) processes in continuous time; 8) univariate and multivariate simulation methods; 9) non-parametric and parametric resampling methods.

1. Introduction to Monte Carlo techniques 2. Simulating random variables and vectos 3. Discrete event simulation 4. Variance reduction and MCMC 5. Introduction to the bootstrap 6. Bootstrap for two samples and complicated data structures 7. Bootstrap-based inference