Overview

Course name: Monte Carlo Methods and Bayesian Computation

Instructor:

Kevin K. Dobbin

Date: Spring, 2021

Course Description:

1. Simulation and the Monte Carlo Method, 3rd Edition, Rubinstein and Kroese, Wiley

2. Bayesian Methods for Data Analysis, 3rd Edition, Carlin and Louis, Chapman & Hall

3. Monte Carlo Statistical Methods, 2nd Edition, Robert and Casella, Springer

Objectives:

1. Bayesian framework of inference

2. Markov Chain Monte Carlo methods (MCMC) to estimate Bayesian posterior distributions (Gibbs sampler, Metropolis-Hastings algorithm, Hamiltonian algorithm)

3. Sensitivity analyses and the splitting method for analyzing difficult estimation problems will also be discussed.

4. Monte Carlo methods, including Monte Carlo integration (classic, importance sampling, Laplacian, saddlepoint approximation)

5. variance reduction techniques (Rao-Blackwellization, Control and antithetic variates)

6. Monte Carlo optimization (EM algorithm).

My notes