Statistics and Its Interface

Volume 1 (2008)

Number 1

Detecting the emergence of a signal in a noisy image

Pages: 3 – 12

DOI: http://dx.doi.org/10.4310/SII.2008.v1.n1.a1

Authors

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

Benjamin Yakir (The Hebrew University, Jerusalem, Israel)

Abstract

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.

Keywords

change-point, sequential detection, image detection

2010 Mathematics Subject Classification

Primary 62L15. Secondary 60G40.

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