论文信息 - Markov Chain

Markov Chain

Many problems can not be solved analytically, but can be solved using statistical sampling. This idea is certainly old and was first used in a question by Georges-Louis Leclerc, Comte de Buffon (Buffon’s needle experiment) and William Gosset. Although these early applications were typically used to simulate data on a understood analytical problem. In 1945 and the following years Nicolas Metropolis and others, including Stanislaw (Stan) Ulam developed statistical sampling method to test the ENIAC computer. Metropolis coined the term Monte Carlo methods (the famous casino town in Monaco in Southern France) [influenced by the fondness of poker of Ulam who had an uncle who once borrowed money to go gambling in Monte Carlo]. Enrico Fermi was using statistical sampling for many problems in the 1930 and later, but he never published his way but used it to impress others about the accuracy of results. In 1953 Metropolis et al. described the now famous Metropolis algorithm and so the first Markov chain Monte Carlo method.

Monte Carlo | Monte Carlo

[1] G. Roberts,et al. Updating Schemes, Correlation Structure, Blocking and Parameterization for the Gibbs Sampler , 1997 .

[2] Adrian F. M. Smith,et al. Gibbs Sampling for Marginal Posterior Expectations , 1991 .

[3] Christian P. Robert,et al. Recycling rejected values in accept-reject methods , 1995 .

[4] Adrian F. M. Smith,et al. Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[5] P. Pathak,et al. Introduction to Rao (1945) Information and the Accuracy Attainable in the Estimation of Statistical Parameters , 1992 .

[6] R. Schonmann,et al. Behavior of droplets for a class of Glauber dynamics at very low temperature , 1992 .

[7] W. Wefelmeyer,et al. Outperforming the Gibbs sampler empirical estimator for nearest-neighbor random fields , 1996 .

[8] Gerhard Winkler,et al. Image analysis, random fields and dynamic Monte Carlo methods: a mathematical introduction , 1995, Applications of mathematics.

[9] C. Hwang,et al. Optimal Spectral Structure of Reversible Stochastic Matrices, Monte Carlo Methods and the Simulation of Markov Random Fields , 1992 .

[10] Wang,et al. Nonuniversal critical dynamics in Monte Carlo simulations. , 1987, Physical review letters.

[11] Jun S. Liu,et al. Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes , 1994 .