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Martingale Methods for Patterns and Scan Statistics

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Scan Statistics

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

We show how martingale techniques (both old and new) can be used to obtain otherwise hard-to-get information for the moments and distributions of waiting times for patterns in independent or Markov sequences. In particular, we show how these methods provide moments and distribution approximations for certain scan statistics, including variable length scan statistics. Each general problem that is considered is also illustrated with a concrete example confirming the computational tractability of the method.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of Connecticut, Storrs, CT, USA

    Vladimir Pozdnyakov

  2. Department of Statistics, University of Pennsylvania, Philadelphia, PA, USA

    J. Michael Steele

Authors
  1. Vladimir Pozdnyakov
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  2. J. Michael Steele
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Editor information

Editors and Affiliations

  1. Dept. Statistics, University of Connecticut, Glenbrook Rd. 215, Storrs, 06269-3120, U.S.A.

    Joseph Glaz

  2. Dept. Statistics, University of Connecticut, Glenbrook Road 215, Storrs, 06269-4120, U.S.A.

    Vladimir Pozdnyakov

  3. Center for Biomathematical Sciences, Mount Sinai School of Medicine, Gustave L Levy Place 1, New York, 10029, U.S.A.

    Sylvan Wallenstein

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© 2009 Birkhäuser Boston, a part of Springer Science+Business Media, LLC

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Pozdnyakov, V., Steele, J.M. (2009). Martingale Methods for Patterns and Scan Statistics. In: Glaz, J., Pozdnyakov, V., Wallenstein, S. (eds) Scan Statistics. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4749-0_14

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