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

Karatzas Ioannis

Statistics & Risk Modeling, 2003, vol. 21, issue 1, 3-14

Abstract: 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.Here, with Λ=2λ/ϑ2, the constant p* is uniquely determined in (1/2,1) by the equation.

Date: 2003
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Citations: View citations in EconPapers (3)

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DOI: 10.1524/stnd.21.1.3.20317

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