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51st IEEE Annual Conference on Decision and Control (CDC)

作者： Ludkovski, Michael Univ Calif Santa Barbara Dept Stat & Appl Probabil Santa Barbara CA 93106 USA

ISBN: (纸本)9781467320665

We study bayesian quickest detection problems where the observations and the underlying change-point are coupled. This setup supersedes classical models that assume independence of the two. We develop several continuous-time formulations of this problem for the cases of Poissonian and Brownian sensors. Our approach to detection uses methods of nonlinear filtering and optimal stopping and lends itself to an efficient numerical scheme that combines particle filtering with Monte Carlo dynamic programming. The developed models and algorithms are illustrated with numerical examples.

关键词： bayesian quickest detection Hawkes Process Particle Filtering Monte Carlo Dynamic Programming

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bayesian quickest detection in Sensor Arrays

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SEQUENTIAL ANALYSIS-DESIGN METHODS AND APPLICATIONS 2012年第4期31卷 481-504页

作者： Ludkovski, Michael Univ Calif Santa Barbara Dept Stat & Appl Probabil Santa Barbara CA 93106 USA

We study bayesian quickest detection problems with sensor arrays. An underlying signal is assumed to gradually propagate through a network of several sensors, triggering a cascade of interdependent change-points. The aim of the decision maker is to centrally fuse all available information to find an optimal detection rule that minimizes Bayes risk. We develop a tractable continuous-time formulation of this problem focusing on the case of sensors collecting point process observations and monitoring the resulting changes in intensity and type of observed events. Our approach uses methods of nonlinear filtering and optimal stopping and lends itself to an efficient numerical scheme that combines particle filtering with a Monte Carlo-based approach to dynamic programming. The developed models and algorithms are illustrated with plenty of numerical examples.

关键词： bayesian quickest detection Multiple change-point detection Particle filtering Sensor arrays

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Model Misspecification in Discrete Time bayesian Online Change detection

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METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY 2023年第1期25卷 1-27页

作者： Dayanik, Savas Sezer, Semih O. Bilkent Univ Ind Engn Dept TR-06800 Ankara Turkiye Sabanci Univ Fac Engn & Nat Sci TR-34956 Istanbul Turkiye

We revisit the classical formulation of the discrete time bayesian online change detection problem in which the common distribution of an observed sequence of random variables changes at an unknown point in time. The objective is to detect the change with a stopping time of the observations and minimize a given Bayes risk. When the change time has a zero-modified geometric prior distribution, the first crossing time of the odds-ratio process over a threshold is known to be an optimal solution. In the current paper, we consider a modeler who misspecifies some of the elements of this formulation. Because of this misspecification, the modeler computes a wrong stopping threshold and follows an incorrect odds-ratio process in implementation. To find her actual Bayes risk, which is different from the value function evaluated with the wrong choices, one needs to compute the expected costs accumulated by the true odds-ratio process until modeler's odd-ratio process crosses this wrong boundary. In the paper, we carry out these computations in the extended state space of both processes, and we illustrate these computations on examples. In those examples, we construct tolerance regions for the parameters to be estimated by the modeler. For a given choice by the modeler, the tolerance region is the set of true values for which her relative loss is less than or equal to a predetermined level.

关键词： Sequential analysis bayesian quickest detection optimal stopping

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