Exact optimality of the Shiryaev-Roberts procedure for detecting changes in distributions

• Published in: 2008 International Symposium on Information Theory and its Applications pp. 1 - 6
• Main Authors: Pollak, M., Tartakovsky, A.G.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.12.2008
• Subjects: Delay effects; Filtration; H infinity control; Information theory; Mathematics; Minimax techniques; Motion detection; Statistical distributions; Statistics; Stochastic processes
• ISBN: 9781424420681; 1424420687
• DOI: 10.1109/ISITA.2008.4895424

We consider the simple changepoint problem setting, where observations are independent, iid pre-change and iid post-change, with known pre- and post-change distributions. The Shiryaev-Roberts detection procedure is known to be asymptotically minimax in the sense of minimizing maximal expected detection delay subject to a bound on the average run length to false alarm, as the latter goes to infinity. Here we present other optimality properties of the Shiryaev-Roberts procedure. Specifically, we first prove that the Shiryaev-Roberts procedure is exactly optimal (for any average run length to false alarm) with respect to the integral average detection delay. We then continue to tackle the problem of quickest detection of a change in a stationary regime, considered by Shiryaev in 1961 for a Brownian motion, and show that the repeated Shiryaev-Roberts procedure minimizes the expected delay to detection of a change occurring at a far horizon, which precedes by a stationary flow of false alarms.