Metropolis Algorithm and Beyond

  • Jun S. Liu
Part of the Springer Series in Statistics book series (SSS)


We have discussed in the previous chapters the important role of Monte Carlo methods in evaluating integrals and simulating stochastic systems. The most critical step in developing an efficient Monte Carlo algorithm is the simulation (sampling) from an appropriate probability distribution π(x). When directly generating independent samples from π(x) is not possible, we have to either opt for an importance sampling strategy, in which random samples are generated from a trial distribution different from (but close to) the target one and then weighted according to the importance ratio; or produce statistically dependent samples based on the idea of Markov chain Monte Carlo sampling.


Markov Chain Ising Model Transition Rule Detailed Balance Target Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Jun S. Liu
    • 1
  1. 1.Department of StatisticsHarvard UniversityCambridgeUSA

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