Monte Carlo methods

Monte Carlo methods turn randomness into a computational tool. When a problem is too complex to be solved exactly, one can instead simulate many “possible worlds” and use the results to say something about what is expected to happen on average. In this course, you learn the probability-theoretic ideas that make these methods reliable, how to reformulate deterministic problems in probabilistic terms, and the core algorithms underlying simulation. You work with techniques for generating random variables from many types of distributions, simulating more complex stochastic models, and making simulations far more efficient through variance reduction (e.g., control variates, importance sampling, stratification, and Latin hypercube sampling). The course also introduces Metropolis–Hastings and Gibbs sampling in order to draw samples from complicated high-dimensional distributions.