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.
- Raoblackwellization.
Other useful links
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.