Stochastic simulation: Generation of random variables; Acceptance and rejection methods. Numerical optimization: EM algorithm; Simulated annealing. Approximate inference methods: Laplace approximation; Importance sampling; Monte Carlo Integration, Sequential Monte Carlo Methods. Monte Carlo method via Markov Chains: Gibbs sampler; Metropolis and Metropolis Hastings algorithm; Convergence diagnostics. Calculation of marginal distribution: reversible jump MCMC; Comparison of models.