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Aleksey S. Polunchenko

  1. State-of-the-Art in Sequential Change-Point Detection.

    Thu, 09/15/2011 - 15:01 — SomNambul
    Authors: Aleksey S. Polunchenko, Alexander G. Tartakovsky
    Subjects: Statistics
    Abstract

    We provide an overview of the state-of-the-art in the area of sequential
    change-point detection assuming discrete time and known pre- and post-change
    distributions. The overview spans over all major formulations of the underlying
    optimization problem, namely, Bayesian, generalized Bayesian, and minimax. We
    pay particular attention to the latest advances in each. Also, we link together
    the generalized Bayesian problem with multi-cyclic disorder detection in a
    stationary regime when the change occurs at a distant time horizon.

  2. Third-order Asymptotic Optimality of the Generalized Shiryaev-Roberts Changepoint Detection Procedures.

    Mon, 05/10/2010 - 15:01 — SomNambul
    Authors: Aleksey S. Polunchenko, Alexander G. Tartakovsky, Moshe Pollak
    Subjects: Statistics
    Abstract

    Several variations of the Shiryaev-Roberts detection procedure in the context
    of the simple changepoint problem are considered: starting the procedure at
    $R_0=0$ (the original Shiryaev-Roberts procedure), at $R_0=r$ for fixed $r>0$,
    and at $R_0$ that has a quasi-stationary distribution. Comparisons of operating
    characteristics are made. The differences fade as the average run length to
    false alarm tends to infinity.

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

    Thu, 12/10/2009 - 16:01 — SomNambul
    Authors: Aleksey S. Polunchenko, Alexander G. Tartakovsky, George V. Moustakides
    Subjects: Computation
    Abstract

    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.

  4. Numerical Comparison of Cusum and Shiryaev-Roberts Procedures for Detecting Changes in Distributions.

    Mon, 08/31/2009 - 17:16 — SomNambul
    Authors: Aleksey S. Polunchenko, Alexander G. Tartakovsky, George V. Moustakides
    Subjects: Computation
    Abstract

    The CUSUM procedure is known to be optimal for detecting a change in
    distribution under a minimax scenario, whereas the Shiryaev-Roberts procedure
    is optimal for detecting a change that occurs at a distant time horizon. As a
    simpler alternative to the conventional Monte Carlo approach, we propose a
    numerical method for the systematic comparison of the two detection schemes in
    both settings, i.e., minimax and for detecting changes that occur in the
    distant future.

  5. On Optimality of the Shiryaev-Roberts Procedure for Detecting Changes in Distributions.

    Wed, 08/26/2009 - 14:59 — SomNambul
    Authors: Aleksey S. Polunchenko, Alexander G. Tartakovsky
    Subjects: gr. Statistics
    Abstract

    In 1985, for detecting changes in distributions Pollak introduced a specific
    minimax performance metric and a randomized version of the Shiryaev-Roberts
    procedure where the zero initial condition is replaced by a random variable
    sampled from the quasi-stationary distribution. Pollak proved that this
    procedure is third-order asymptotically optimal as the mean time to false alarm
    becomes large. The question whether Pollak's procedure is strictly minimax for
    any false alarm rate has been open for more than two decades, and there were
    several attempts to prove this strict optimality.

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