On Optimum Methods in Quickest Detection Problems

By Albert N. Shiryaev. 1963

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Citations in the corpus

The duality of optimal exercise and domineering claims: a Doob–Meyer decomposition approach to the Snell envelope (2007, unknown): “There are also interesting concrete instances with explicit solutions available only in the infinite horizon case t [ 1⁄20;1Þ, such as the perpetual American put, the Russian options in [32], or the (radar) detection problem in [33].”
Some Current Directions in the Theory and Application of Statistical Process Monitoring (2014, methodology): “The Shiryaev–Roberts surveillance method (Shiryaev (1963), Roberts (1966)) has a quasi-Bayesian justification.”
Asymptotic Optimality of Change-Point Detection Schemes in General Continuous-Time Models (2006, methodology): “Furthermore, in continuous time the Bayesian solution is only available for the very limited set of models—for detecting a change in the constant drift of a Brownian motion (Shiryaev, 1963, 1978) and in the constant intensity of a Poisson process (Peskir and Shiryaev, 2002).”
Quickest detection of drift change for Brownian motion in generalized Bayesian and minimax settings (2006, background): “The process(πt)t≥0 satisfies the stochastic differential equation dπt = ( λ− μ 2 σ2 π(2) t ) (1− πt) dt + μ σ2 πt(1− πt) dXt with π0 = π; see [17, 18, 19] for details.”
Mathematical modeling of infectious disease dynamics (2013, background): “[44] [45] [46] [47] [48] [49] Hence, denoting by f(θ 0 ) and f(θ 1 ) the probability function of the in-control and out-of-control processes with parameters θ 0 and θ 1 respectively, the reference value reads: ”
Is Average Run Length to False Alarm Always an Informative Criterion? (2008, methodology): “…observations, which were studied by Shewhart (1931) and Page (1954) but not rigorously formulated and solved until between 1963 and 1990 (Shiryayev, 1963; Lorden, 1971; Moustakides, 1986; Pollak, 1985, 1987; Ritov, 1990), it should be anticipated that significant time and effort will be…”
Bayesian Quickest Detection Problems for Some Diffusion Processes (2010, background): “An optimality criterion was proposed in [23] and [24] for the time of alarm to minimize a linear combination of the false alarm probability and the expected time delay in detecting the disorder correctly, for sequences of independent and identically distributed observations.”
A novel approach to detection of intrusions in computer networks via adaptive sequential and batch-sequential change-point detection methods (2006, background): “The second is a Bayesian formulation, proposed by Shiryaev [27], in which the change point is assumed to have a prior distribution and the goal is to minimize the expected delay subject to an upper bound”
Numerical Comparison of CUSUM and Shiryaev–Roberts Procedures for Detecting Changes in Distributions (2009, methodology): “These latter performance measures and their corresponding properties were motivated by similar results obtained for the Shiryaev–Roberts procedure for the continuous-time Brownian motion model; see Shiryaev (1963) and Feinberg and Shiryaev (2006).”
Nonanticipating estimation applied to sequential analysis and changepoint detection (2005, background): “te setting. 1. Introduction. In all but the simplest cases, the problem of detecting a change involves at least one unknown post-change parameter. In the well-known Shiryayev–Roberts detection scheme [11, 12], a change from parameter value θ=θ0 (possibly multidimensional) to θ=θ1, say, in the distri”
A SIMPLE BAYESIAN APPROACH TO MULTIPLE CHANGE-POINTS (2011, methodology): “Zhang and Siegmund (2007) propose to approximate ln(k) by using the circular binary segmentation procedure of Olshen et al.”