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Distributions of pattern statistics in sparse Markov models

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  • Donald E. K. Martin

    (North Carolina State University)

Abstract

Markov models provide a good approximation to probabilities associated with many categorical time series, and thus they are applied extensively. However, a major drawback associated with them is that the number of model parameters grows exponentially in the order of the model, and thus only very low-order models are considered in applications. Another drawback is lack of flexibility, in that Markov models give relatively few choices for the number of model parameters. Sparse Markov models are Markov models with conditioning histories that are grouped into classes such that the conditional probability distribution for members of each class is constant. The model gives a better handling of the trade-off between bias associated with having too few model parameters and variance from having too many. In this paper, methodology for efficient computation of pattern distributions through Markov chains with minimal state spaces is extended to the sparse Markov framework.

Suggested Citation

  • Donald E. K. Martin, 2020. "Distributions of pattern statistics in sparse Markov models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 895-913, August.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:4:d:10.1007_s10463-019-00714-6
    DOI: 10.1007/s10463-019-00714-6
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    References listed on IDEAS

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    1. 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.
    2. Gabadinho, Alexis & Ritschard, Gilbert, 2016. "Analyzing State Sequences with Probabilistic Suffix Trees: The PST R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 72(i03).
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