Short-courses and Tutorials

Monte Carlo Methods

First Conference on Computational Interdisciplinary Sciences
Instituto Nacional de Pesquisas Espaciais,
August 23rd to 27th 2010
Sao Jose dos Campos, Brazil

Tutorial material (PDF FILE)

Tutorial outline

Part 1: Monte Carlo Methods

Part 2: Markov Chain Monte Carlo Methods

R code

Example 0. Approximating pi.

Example i. Monte Carlo integration.

Example ii. Monte Carlo integration via importance sampling.

Example iii. Rejection method and sampling importance resampling.

Example iv. Rejection method, SIR and Metropolis-Hastings algorithms.

Example v. Rejection method, SIR and Metropolis-Hastings algorithms.

Example vi. Random walk MH and independent MH algorithms.

Example vii. Simulated annealing.

Example viii. Gibbs sampler.


Other useful links

MCMC: Stochastic Simulation for Bayesian Inference

The R project

Markov Chain Monte Carlo Preprint

Classical Monte Carlo papers

Metropolis and Ulam (1949) The Monte Carlo method. JASA, 44, 335-341.

Metropolis, Rosenbluth, Rosenbluth, Teller and Teller (1953) Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21, 2087-1092.

Hastings (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97-109.

Peskun (1973) Optimum Monte Carlo sampling using Markov chains. Biometrika, 60, 607-612.

Besag (1974) Spatial Interaction and the Statistical Analysis of Lattice Systems. JRSS-B, 36, 192-236.

Kirkpatrick, Gelatt and Vecchi (1983) Optimization by Simulated Annealing. Science, 220 (4598), 671-680.

Geman and Geman (1984) Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Analysis and Machine Intelligence, 6, 721-741.

Pearl (1987) Evidential reasoning using stochastic simulation of causal models. Artificial intelligence, 32, 245-257.

Tanner and Wong (1987) The Calculation of Posterior Distributions by Data Augmentation. JASA, 82, 528-540.

Geweke (1989) Bayesian Inference in Econometric Models Using Monte Carlo Integration. Econometrica, 57, 1317-1339.

Gelfand and Smith (1990) Sampling-Based Approaches to Calculating Marginal Densities. JASA, 85, 398-409.

Casella and George (1992) Explaining the Gibbs Sampler. The American Statistician, 46, 167-174.

Gilks and Wild (1992) Adaptive Rejection Sampling for Gibbs Sampling. Applied Statistics, 41, 337-348.

Smith and Gelfand (1992) Bayesian Statistics without Tears: A Sampling-Resampling Perspective. The American Statistician, 46, 84-88.

Chib and Greenberg (1995) Understanding the Metropolis-Hastings algorithm. The American Statistician, 49, 327-335.