Three Examples of Monte-Carlo Markov Chains: At the Interface Between Statistical Computing, Computer Science, and Statistical Mechanics

  • Persi Diaconis
  • Susan Holmes
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 72)


The revival of interest in Markov chains is based in part on their recent applicability in solving real world problems and in part on their ability to resolve issues in theoretical computer science. This paper presents three examples which are used to illustrate both parts: a Markov chain algorithm for estimating the tails of the bootstrap also illustrates the Jerrum-Sinclair theory of approximate counting. The Geyer-Thompson work on Monte-Carlo evaluation of maximum likelihood is compared with work on evaluation of the partition function. Finally, work of Diaconis-Sturmfels on conditional inference is complemented by the work of theoretical computer scientists on approximate computation of the volume of convex polyhedra.


Markov Chain Partition Function Ising Model Grade Point Average Convex Polyhedron 
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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Persi Diaconis
    • 1
  • Susan Holmes
    • 2
  1. 1.Dept. of MathematicsHarvard UniversityCambridgeUSA
  2. 2.INRAUnité de BiométrieMontpellierFrance

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