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Faster exact distributions of pattern statistics through sequential elimination of states

Author

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  • Donald E. K. Martin

    (North Carolina State University)

  • Laurent Noé

    (CRIStAL (UMR 9189 Lille University/CNRS), INRIA Lille Nord-Europe)

Abstract

When using an auxiliary Markov chain (AMC) to compute sampling distributions, the computational complexity is directly related to the number of Markov chain states. For certain complex pattern statistics, minimal deterministic finite automata (DFA) have been used to facilitate efficient computation by reducing the number of AMC states. For example, when statistics of overlapping pattern occurrences are counted differently than non-overlapping occurrences, a DFA consisting of prefixes of patterns extended to overlapping occurrences has been generated and then minimized to form an AMC. However, there are situations where forming such a DFA is computationally expensive, e.g., with computing the distribution of spaced seed coverage. In dealing with this problem, we develop a method to obtain a small set of states during the state generation process without forming a DFA, and show that a huge reduction in the size of the AMC can be attained.

Suggested Citation

  • Donald E. K. Martin & Laurent Noé, 2017. "Faster exact distributions of pattern statistics through sequential elimination of states," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 231-248, February.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:1:d:10.1007_s10463-015-0540-y
    DOI: 10.1007/s10463-015-0540-y
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    References listed on IDEAS

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    1. James Fu & W. Lou & Zhi-Dong Bai & Gang Li, 2002. "The Exact and Limiting Distributions for the Number of Successes in Success Runs Within a Sequence of Markov-Dependent Two-State Trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(4), pages 719-730, December.
    2. Morteza Ebneshahrashoob & Tangan Gao & Mengnien Wu, 2005. "An Efficient Algorithm for Exact Distribution of Discrete Scan Statistics," Methodology and Computing in Applied Probability, Springer, vol. 7(4), pages 459-471, December.
    3. Lou, W. Y. Wendy, 2003. "The exact distribution of the k-tuple statistic for sequence homology," Statistics & Probability Letters, Elsevier, vol. 61(1), pages 51-59, January.
    4. Martin, Donald E.K. & Aston, John A.D., 2008. "Waiting time distribution of generalized later patterns," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4879-4890, July.
    5. Martin, Donald E.K., 2008. "Application of auxiliary Markov chains to start-up demonstration tests," European Journal of Operational Research, Elsevier, vol. 184(2), pages 574-583, January.
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