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Fitting sparse Markov models through a collapsed Gibbs sampler

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  • Iris Bennett

    (North Carolina State University)

  • Donald E. K. Martin

    (North Carolina State University)

  • Soumendra Nath Lahiri

    (Washington University in St. Louis)

Abstract

Sparse Markov models (SMMs) provide a parsimonious representation for higher-order Markov models. We present a computationally efficient method for fitting SMMs using a collapsed Gibbs sampler, the GSDPMM. We prove the consistency of the GSDPMM in fitting SMMs. In simulations, the GSDPMM was found to perform as well or better than existing methods for fitting SMMs. We apply the GSDPMM method to fit SMMs to patterns of wind speeds and DNA sequences.

Suggested Citation

  • Iris Bennett & Donald E. K. Martin & Soumendra Nath Lahiri, 2023. "Fitting sparse Markov models through a collapsed Gibbs sampler," Computational Statistics, Springer, vol. 38(4), pages 1977-1994, December.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:4:d:10.1007_s00180-022-01310-8
    DOI: 10.1007/s00180-022-01310-8
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    References listed on IDEAS

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    1. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    2. Abhra Sarkar & David B. Dunson, 2016. "Bayesian Nonparametric Modeling of Higher Order Markov Chains," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1791-1803, October.
    3. John Haslett & Adrian E. Raftery, 1989. "Space‐Time Modelling with Long‐Memory Dependence: Assessing Ireland's Wind Power Resource," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 38(1), pages 1-21, March.
    4. Väinö Jääskinen & Jie Xiong & Jukka Corander & Timo Koski, 2014. "Sparse Markov Chains for Sequence Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 639-655, September.
    5. Adrian Raftery & Simon Tavaré, 1994. "Estimation and Modelling Repeated Patterns in High Order Markov Chains with the Mixture Transition Distribution Model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(1), pages 179-199, March.
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