A Numerical Approach to Performance Analysis of Quickest Change-Point Detection Procedures

For the most popular sequential change detection rules such as CUSUM, EWMA and the Shiryaev-Roberts test, we develop integral equations and a concise numerical method to compute a number of performance metrics including average detection delay and average time to false alarm. We pay special attention to the Shiryaev-Roberts procedure and evaluate its performance for various initialization strategies. Regarding the randomized initialization variant proposed by Pollak, which is known to be asymptotically optimal of order-3, we offer, for the first time, a means for numerically computing the quasi-stationary distribution, which is the distribution of the initializing random variable, thus making this test applicable in practice. A significant side-product of our computational technique is the observation that deterministic initializations of the Shiryaev-Roberts procedure can also enjoy the same order-3 optimality property as Pollak's randomized test and, after careful selection, even uniformly outperform it.