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Metropolis Algorithm and equienergy sampling for two mean field spin systems

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  • Federico Bassetti

    (Department of Mathematics, University of Pavia, Italy)

  • Fabrizio Leisen

    (Department of Economics, University of Insubria, Italy)

Abstract

In this paper we study the Metropolis algorithm in connection with two mean–field spin systems, the so called mean–field Ising model and the Blume–Emery–Griffiths model. In both this examples the naive choice of proposal chain gives rise, for some parameters, to a slowly mixing Metropolis chain, that is a chain whose spectral gap decreases exponentially fast (in the dimension N of the problem). Here we show how a slight variant in the proposal chain can avoid this problem, keeping the mean computational cost similar to the cost of the usual Metropolis.

Suggested Citation

  • Federico Bassetti & Fabrizio Leisen, 2007. "Metropolis Algorithm and equienergy sampling for two mean field spin systems," Economics and Quantitative Methods qf0704, Department of Economics, University of Insubria.
    • Handle: RePEc:ins:quaeco:qf0704
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    File URL: https://www.eco.uninsubria.it/RePEc/pdf/QF2007_4.pdf
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    References listed on IDEAS

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    1. Antonietta Mira & Luke Tierney, 2002. "Efficiency and Convergence Properties of Slice Samplers," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 1-12, March.
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    Cited by:

    1. Rudolf Daniel, 2010. "Error bounds for computing the expectation by Markov chain Monte Carlo," Monte Carlo Methods and Applications, De Gruyter, vol. 16(3-4), pages 323-342, January.

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