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A note on Bayesian detection of change-points with an expected miss criterion

  • Karatzas Ioannis
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    A process X is observed continuously in time; it behaves like Brownian motion with drift, which changes from zero to a known constant ϑ>0 at some time τ that is not directly observable. It is important to detect this change when it happens, and we attempt to do so by selecting a stopping rule T* that minimizes the “expected miss” E|T−τ| over all stopping rules T. Assuming that τ has an exponential distribution with known parameter λ>0 and is independent of the driving Brownian motion, we show that the optimal rule T* is to declare that the change has occurred, at the first time t for which

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    Article provided by De Gruyter in its journal Statistics & Risk Modeling.

    Volume (Year): 21 (2003)
    Issue (Month): 1/2003 (January)
    Pages: 3-14

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    Handle: RePEc:bpj:strimo:v:21:y:2003:i:1/2003:p:3-14:n:5
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