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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, and transformation of random variables.

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.