Tracking Stopping Times Through Noisy Observations - CiteSeerX
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tracks S, in the sense that T minimizes the expected reaction delay E(T â S)+, while keeping ... The tracking stopping time (TST) problem is defined as follows.
Tracking Stopping Times. Through Noisy Observations. Urs Niesen, Student Member, IEEE, and Aslan Tchamkerten. AbstractâA novel quickest detection ...
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Tracking Stopping Times Through Noisy Observations - CiteSeerX
is to find a stopping time T with respect to fYigi 1 that optimally tracks S, in the sense that T minimizes the expected reaction delay. (T 0 S). +. , while keeping the ...
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IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 55, NO. 1, JANUARY 2009
Tracking Stopping Times Through Noisy Observations Urs Niesen, Student Member, IEEE, and Aslan Tchamkerten
Abstract—A novel quickest detection setting is proposed, generalizing the well-known Bayesian change-point detection model. Suppose f( i i )gi1 is a sequence of pairs of random variables, and that is a stopping time with respect to f i gi1 . The problem is to find a stopping time with respect to f i gi1 that optimally tracks , in the sense that minimizes the expected reaction delay + ( 0 ) , while keeping the false-alarm probability ( ) below a given threshold 2 [0 1]. This problem formulation applies in several areas, such as in communication, detection, forecasting, and quality control. Our results relate to the situation where the i ’s and i ’s take values in finite alphabets and where is bounded by some positive integer . By using elementary methods based on the analysis of the tree structure of stopping times, we exhibit an algorithm that computes the optimal average reaction delays for all 2 [0 1], and constructs the associated optimal stopping times . Under certain conditions on f( i i )gi1 and , the algorithm running time is polynomial in .
