Statistics and Its Interface

Volume 1 (2008)

Number 1

Detecting the emergence of a signal in a noisy image

Pages: 3 – 12



David Siegmund (Department of Statistics, Stanford University, Stanford, Calif., U.S.A.)

Benjamin Yakir (The Hebrew University, Jerusalem, Israel)


We study sequential change-point detection when observations form a sequence of independent Gaussian random fields, and the change-point is the time at which a signal of known functional form involving a finite number of unknown parameters appears. Building on Siegmund and Yakir (2008), which identifies in a simpler problem a detection procedure of Shiryayev-Roberts type that is asymptotically minimax up to terms that vanish as the false detection rate converges to zero, we compare easily computed approximations to the Shiryayev-Roberts detection procedure with similar approximations to CUSUM type procedures. Although the CUSUM type procedures are suboptimal, our studies indicate that they compare favorably to the asymptotically optimal procedures.


change-point, sequential detection, image detection

2010 Mathematics Subject Classification

Primary 62L15. Secondary 60G40.

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