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Optimal Detection of a Change Point in a Poisson Process for Different Observation Schemes

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  • Tina Herberts
  • Uwe Jensen

Abstract

. Change point problems are considered where at some unobservable time the intensity of a point process (Tn), n ∈ ℕ, has a jump. For a given reward functional we detect the change point optimally for different information schemes. These schemes differ in the available information. We consider three information levels, namely sequential observation of (Tn), ex post decision after observing the point process up to a fixed time t* and a combination of both observation schemes. In all of these cases the detection problem is viewed as an optimal stopping problem which can be solved by deriving a semimartingale representation of the gain process and applying tools from filtering theory.

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  • Tina Herberts & Uwe Jensen, 2004. "Optimal Detection of a Change Point in a Poisson Process for Different Observation Schemes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 347-366, September.
    • Handle: RePEc:bla:scjsta:v:31:y:2004:i:3:p:347-366
    DOI: 10.1111/j.1467-9469.2004.02-102.x
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    Cited by:

    1. Brown, Marlo, 2008. "Monitoring a Poisson process in several categories subject to changes in the arrival rates," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2637-2643, November.
    2. Brown, Marlo & Zacks, Shelemyahu, 2006. "A note on optimal stopping for possible change in the intensity of an ordinary Poisson process," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1417-1425, July.

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