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A note on Bayesian detection of change-points with an expected miss criterion
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Ioannis Karatzas
Published/Copyright:
September 25, 2009
Summary
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 (½,1) by the equation
.
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Published Online: 2009-09-25
Published in Print: 2003-01-01
© 2003 Oldenbourg Wissenschaftsverlag GmbH
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Articles in the same Issue
- Editorial Note
- A note on Bayesian detection of change-points with an expected miss criterion
- The estimation problem of minimum mean squared error
- Parameter estimation for some non-recurrent solutions of SDE
- Variational sums and power variation: a unifying approach to model selection and estimation in semimartingale models
- A robust generalized Bayes estimator improving on the James-Stein estimator for spherically symmetric distributions
- Tail behaviour of a general family of control charts
