Tracking Stopping Times Through Noisy Observations

Details Tracking Stopping Times Through Noisy Observations Tracking Stopping Times Through Noisy Observations

2007-01-09

arxiv.org/abs/math/0701261v4

IEEE Transactions on Information Theory, vol. 55, pp. 422-432, January 2009

Mathematics

Statistics Theory

19 pages, 4 figures, to appear in IEEE Transactions on Information Theory

Scientific paper

A novel quickest detection setting is proposed which is a generalization of the well-known Bayesian change-point detection model. Suppose \{(X_i,Y_i)\}_{i\geq 1} is a sequence of pairs of random variables, and that S is a stopping time with respect to \{X_i\}_{i\geq 1}. The problem is to find a stopping time T with respect to \{Y_i\}_{i\geq 1} that optimally tracks S, in the sense that T minimizes the expected reaction delay E(T-S)^+, while keeping the false-alarm probability P(T

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