Exact Optimality of the Shiryaev-Roberts Procedure for Detecting Changes in Distributions

Host Institution:

University Technology, Sydney

Title of Seminar:

Exact Optimality of the Shiryaev-Roberts Procedure for Detecting Changes in Distributions

Speaker's Name:

Dr Alexander Tartakovsky

Speaker's Institution:

Department of Mathematics, University of Southern California

Time and Date:

3 pm Thursday 27 November 2008

Seminar Abstract:

Changepoint problems deal with detecting abrupt changes in observed processes. In the sequential setting, as long as the behavior of observations is consistent with the normal state, one is content to let the process continue. If the state changes, then one is interested in detecting that a change is in effect as soon as possible.

I will consider the simple changepoint problem setting in discrete time, where observations are 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 (i.e., for low false alarm rate).

I will present other optimality properties of the Shiryaev-Roberts procedure. Specifically, I will first prove that the Shiryaev-Roberts procedure is exactly optimal in the sense of minimizing the integral average delay to detection for an arbitrary average run length to false alarm. This is instrumental for proving optimality in a more practical setting where a change occurs in a distant future and is preceded by a stationary flow of false alarms.

I will prove that the Shiryaev-Roberts procedure is the best that one can do in terms of minimizing the expected detection delay in the latter setting for any false alarm rate. The method of proof relies on optimal stopping theory and on renewal theory.

(Joint work with Moshe Pollak, Department of Statistics, Hebrew University of Jerusalem)

Seminar Convenor:

Mark Craddock

AGR IT support:

Mike Lake