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A kind of dual form for coupling from the past algorithm, to sample from Markov chain steady-state probability

Author

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  • Nasroallah Abdelaziz

    (Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, B. P. 2390, Marrakesh, Morocco)

  • Bounnite Mohamed Yasser

    (Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, B. P. 2390, Marrakesh, Morocco)

Abstract

The standard coupling from the past (CFTP) algorithm is an interesting tool to sample from exact Markov chain steady-state probability. The CFTP detects, with probability one, the end of the transient phase (called burn-in period) of the chain and consequently the beginning of its stationary phase. For large and/or stiff Markov chains, the burn-in period is expensive in time consumption. In this work, we propose a kind of dual form for CFTP called D-CFTP that, in many situations, reduces the Monte Carlo simulation time and does not need to store the history of the used random numbers from one iteration to another. A performance comparison of CFTP and D-CFTP will be discussed, and some numerical Monte Carlo simulations are carried out to show the smooth running of the proposed D-CFTP.

Suggested Citation

  • Nasroallah Abdelaziz & Bounnite Mohamed Yasser, 2019. "A kind of dual form for coupling from the past algorithm, to sample from Markov chain steady-state probability," Monte Carlo Methods and Applications, De Gruyter, vol. 25(4), pages 317-327, December.
    • Handle: RePEc:bpj:mcmeap:v:25:y:2019:i:4:p:317-327:n:3
    DOI: 10.1515/mcma-2019-2050
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    References listed on IDEAS

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    1. A. Mira & J. Møller & G. O. Roberts, 2001. "Perfect slice samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 593-606.
    2. G. Casella & K. L. Mengersen & C. P. Robert & D. M. Titterington, 2002. "Perfect samplers for mixtures of distributions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 777-790, October.
    3. Fakhouri H. & Nasroallah A., 2009. "On the simulation of Markov chain steady-state distribution using CFTP algorithm," Monte Carlo Methods and Applications, De Gruyter, vol. 15(2), pages 91-105, January.
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