Modelling and Simulation
- Random number generation: pseudo random number generators.
- Simulating samples from discrete distributions.
- Simulating samples from continuous distributions: the inverse transform method, rejection sampling,
- Simulating statistical models: multivariate normal distributions, hierarchical models (Bayesian models, mixture distributions), Markov chains.
- Monte Carlo methods: Studying models via simulation, Monte Carlo estimates, variance reduction, and applications to statistical learning.Markov Chain Monte Carlo (MCMC) methods: the Metropolis-Hastings method, Convergence of MCMC methods, applications to Bayesian learning.
- Resampling methods: bootstrap estimates, applications to machine learning.