Multilevel Sampling and Optimization Methods

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


In this chapter, we describe a few innovative ideas in using auxiliary distributions and multiple Markov chains (in parallel) to improve the efficiency of Monte Carlo simulations. Roughly speaking, in order to improve the mixing property of an underlying Monte Carlo Markov chain, one can build a few “companion chains” whose sole purpose is to help bridging parts of the sample space that are separated by very high energy (or low probability) barriers in the original distribution.


Simulated Tempering Target Distribution Augmented System Dynamic Weighting Umbrella Sampling 
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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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