2015/10/13 by Alexander G. Tartakovsky, Tartakovsky, Alexander G. · 1 citation
Decision Sciences · Mathematics · #60G40 #60J05 #60J20 (Secondary) #62L10 #62L15 (Primary) #Advanced Statistical Process Monitoring #FOS: Mathematics #Statistical Methods and Inference #Statistical Methods in Clinical Trials #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1510.03827
openalex publication_date 2015/10/13 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We consider a sequential Bayesian changepoint detection problem for a general\nstochastic model, assuming that the observed data may be dependent and\nnon-identically distributed and the prior distribution of the change point is\narbitrary, not necessarily geometric. Tartakovsky and Veeravalli (2004)\ndeveloped a general asymptotic theory of changepoint detection in the non-iid\ncase and discrete time, and Baron and Tartakovsky (2006) in continuous time\nassuming certain stability of the log-likelihood ratio process. This stability\nproperty was formulated in terms of the r-quick convergence of the normalized\nlog-likelihood ratio process to a positive and finite number, which can be\ninterpreted as the limiting Kullback-Leibler information between the "change"\nand "no change" hypotheses. In these papers, it was conjectured that the\nr-quick convergence can be relaxed in the r-complete convergence, which is\ntypically much easier to verify in particular examples. In the present paper,\nwe justify this conjecture by showing that the Shiryaev change detection\nprocedure is nearly optimal, minimizing asymptotically (as the probability of\nfalse alarm vanishes) the moments of the delay to detection up to order r\nwhenever r-complete convergence holds. We also study asymptotic properties of\nthe Shiryaev-Roberts detection procedure in the Bayesian context.\n