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Exact Simulation for Discrete Time Spin Systems and Unilateral Fields

Author

Listed:
  • Emilio De Santis

    (Sapienza Università di Roma)

  • Mauro Piccioni

    (Sapienza Università di Roma)

Abstract

In this paper we generalize the technique presented by Häggström and Steif (Comb. Probab. Comput. 9:425–439, 2000) for the exact simulation of finite sections of infinite-volume Gibbs random fields, to a more general class of discrete time nearest neighbour spin systems. The main role is played by an auxiliary binary field, which indicates the sampling region. Percolation bounds can be used to prove that the algorithm terminates a.s. In the simplest case this field is Bernoulli; however blocking techniques can be used that destroy the independence property but extend the validity of the algorithm. Finally, the connection with stationary unilateral fields in the plane considered by Pickard (Adv. Appl. Probab. 12:655–671, 1980) and Galbraith and Walley (J. Appl. Probab. 19:332–343, 1982) is discussed.

Suggested Citation

  • Emilio De Santis & Mauro Piccioni, 2008. "Exact Simulation for Discrete Time Spin Systems and Unilateral Fields," Methodology and Computing in Applied Probability, Springer, vol. 10(1), pages 105-120, March.
    • Handle: RePEc:spr:metcap:v:10:y:2008:i:1:d:10.1007_s11009-007-9041-7
    DOI: 10.1007/s11009-007-9041-7
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    References listed on IDEAS

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    1. James P. Hobert, 2002. "On the applicability of regenerative simulation in Markov chain Monte Carlo," Biometrika, Biometrika Trust, vol. 89(4), pages 731-743, December.
    2. Noel Cressie & Craig Liu, 2001. "Binary Markov Mesh Models and Symmetric Markov Random Fields: Some Results on their Equivalence," Methodology and Computing in Applied Probability, Springer, vol. 3(1), pages 5-34, March.
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