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.