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Statistics and Computing

, Volume 22, Issue 4, pp 981–993 | Cite as

Implied distributions in multiple change point problems

  • J. A. D. Aston
  • J. Y. Peng
  • D. E. K. Martin
Article

Abstract

A method for efficiently calculating exact marginal, conditional and joint distributions for change points defined by general finite state Hidden Markov Models is proposed. The distributions are not subject to any approximation or sampling error once parameters of the model have been estimated. It is shown that, in contrast to sampling methods, very little computation is needed. The method provides probabilities associated with change points within an interval, as well as at specific points.

Keywords

Finite Markov chain imbedding Hidden Markov models Change point probability Run length distributions Generalised change points Waiting time distributions 

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Supplementary material

11222_2011_9268_MOESM1_ESM.pdf (273 kb)
Implied distributions in multiplechange point problems—supplementary information (PDF 272 KB)

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • J. A. D. Aston
    • 1
  • J. Y. Peng
    • 2
    • 3
  • D. E. K. Martin
    • 4
  1. 1.Centre for Research in Statistical MethodologyUniversity of WarwickCoventryUK
  2. 2.Institute of Information ScienceAcademia SinicaTaipeiTaiwan
  3. 3.Institute of Biomedical InformaticsNational Yang-Ming UniversityTaipeiTaiwan
  4. 4.Dept. of StatisticsNorth Carolina State UniversityRaleighUSA

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