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Moments of the Count of a Regular Expression in a Heterogeneous Random Sequence

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  • G. Nuel

    (Sorbonne University)

Abstract

We focus here on the distribution of the random count N of a regular expression in a multi-state random sequence generated by a heterogenous Markov source. We first briefly recall how classical Markov chain embedding techniques allow reducing the problem to the count of specific transitions in a (heterogenous) order 1 Markov chain over a deterministic finite automaton state space. From this result we derive the expression of both the mgf/pgf of N as well as the factorial and non-factorial moments of N. We then introduce the notion of evidence-based constraints in this context. Following the classical forward/backward algorithm in hidden Markov models, we provide explicit recursions allowing to compute the mgf/pgf of N under the evidence constraint. All the results presented are illustrated with a toy example.

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  • G. Nuel, 2019. "Moments of the Count of a Regular Expression in a Heterogeneous Random Sequence," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 875-887, September.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:3:d:10.1007_s11009-019-09700-0
    DOI: 10.1007/s11009-019-09700-0
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    References listed on IDEAS

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    1. 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.
    2. Vergne Nicolas, 2008. "Drifting Markov Models with Polynomial Drift and Applications to DNA Sequences," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 7(1), pages 1-45, February.
    3. Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
    4. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
    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.
    6. Frosso Makri & Zaharias Psillakis, 2013. "Exact distributions of constrained (k, ℓ) strings of failures between subsequent successes," Statistical Papers, Springer, vol. 54(3), pages 783-806, August.
    7. M. Koutras & V. Alexandrou, 1995. "Runs, scans and URN model distributions: A unified Markov chain approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 743-766, December.
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    Cited by:

    1. He Yi & Lirong Cui & Narayanaswamy Balakrishnan, 2022. "On the Derivative Counting Processes of First- and Second-order Aggregated Semi-Markov Systems," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1849-1875, September.

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