author={George V. Moustakides},
  journal={Annals of Statistics},
  • G. Moustakides
  • Published 1 April 2008
  • Computer Science
  • Annals of Statistics
In sequential change detection, existing performance measures differ significantly in the way they treat the time of change. By modeling this quantity as a random time, we introduce a general framework capable of capturing and better understanding most well-known criteria and also propose new ones. For a specific new criterion that constitutes an extension to Lorden's performance measure, we offer the optimum structure for detecting a change in the constant drift of a Brownian motion and a… 

Figures from this paper

Optimal Sequential Change Detection for Fractional Diffusion-Type Processes

It is shown that the CUSUM test optimizes Lorden's original criterion when a fractional Brownian motion with Hurst index H adopts a polynomial drift term with exponent H + 1/2 after the change.


The sequential detection of an abrupt and persistent change in the dynamics of an arbitrary continuous-path stochastic process is considered; the optimality of the cumulative sums (cusum) test is es-

Minimax optimality of Shiryaev-Roberts procedure for quickest drift change detection of a Brownian motion

Analytical and numerical justifications are provided toward establishing that the Shiryaev-Roberts procedure with a specially designed starting point is exactly optimal for the proposed mathematical setup.

Sequentially detecting transitory changes

The sequential test that optimizes the proposed criterion is derived, in the exact sense, the well known CUSUM rule with the corresponding test-statistic-update being not only a function of all pre- and post-change pdfs but also of the false-alarm constraint.

Asymptotical Optimality of Change Point Detection With Unknown Discrete Post-Change Distributions

A sequential version of universal hypothesis test across the curved boundary is introduced, and it is proved that this sequential test asymptotically achieves smaller average sample size than any other sequential test.

Detecting Changes in Hidden Markov Models

  • G. Moustakides
  • Computer Science
    2019 IEEE International Symposium on Information Theory (ISIT)
  • 2019
For each formulation of the problem of sequential detection of a change in the statistical behavior of a hidden Markov model, the optimum Shewhart test is derived that maximizes the worst-case detection probability while guaranteeing infrequent false alarms.


By introducing suitable loss random variables of detection, we obtain optimal tests in terms of the stopping time or alarm time for Bayesian change-point detection not only for a general prior

Optimal Sequential Tests for Monitoring Changes in the Distribution of Finite Observation Sequences

This article develops a method to construct the optimal sequential test for monitoring the changes in the distribution of finite observation sequences with a general dependence structure. This method

Bayesian quickest detection with observation-changepoint feedback

  • M. Ludkovski
  • Mathematics
    2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
  • 2012
This work develops several continuous-time formulations of Bayesian quickest detection problems where the observations and the underlying change-point are coupled and lends itself to an efficient numerical scheme that combines particle filtering with Monte Carlo dynamic programming.

Online Change Detection for a Poisson Process with a Phase-Type Change-Time Prior Distribution

Abstract We consider a change detection problem in which the arrival rate of a Poisson process changes suddenly at some unknown and unobservable disorder time. It is assumed that the prior



A note on Bayesian detection of change-points with an expected miss criterion

A process X is observed continuously in time; it behaves like Brownian motion with drift, which changes from zero to a known constant ϑ>0 at some time τ that is not directly observable. It is

Adaptive Poisson disorder problem

The objective is to design an alarm time which is adapted to the history of the arrival process and detects the disorder time as soon as possible, and assumes in this paper that the new arrival rate after the disorder is a random variable.

A note on optimal detection of a change in distribution

Suppose X 1 , X 2 ,..., X v-1 are iid random variables with distribution F 0 , and X ν , X ν+1,... are are iid with distributed F 1 . The change point ν is unknown. The problem is to raise an alarm

Quickest detection with exponential penalty for delay

  • H. Poor
  • Mathematics, Computer Science
  • 1998
Stopping times are derived that optimize the tradeoff between detection delay and false alarms within two criteria within a lower-bound constraint on the mean time between false alarms.

Optimality of the CUSUM procedure in continuous time

It is demonstrated the optimality of the CUSUM test for Ito processes, in a sense similar to Lorden's, but with a criterion that replaces expected delays by the corresponding Kullback-Leibler divergence.

Poisson Disorder Problem with Exponential Penalty for Delay

The Poisson disorder problem when the delay is penalized exponentially is solved and a stopping rule is sought that minimizes the frequency of false alarms and an exponential cost function of the detection delay.

Solving the Poisson Disorder Problem

The Poisson disorder problem seeks to determine a stopping time which is as close as possible to the (unknown) time of ‘disorder’ when the intensity of an observed Poisson process changes from one

Optimal stopping times for detecting changes in distributions

On donne une generalisation d'un resultat prouvant que le temps d'arret de Page est asymptotiquement optimal

Stochastic integration and differential equations

I Preliminaries.- II Semimartingales and Stochastic Integrals.- III Semimartingales and Decomposable Processes.- IV General Stochastic Integration and Local Times.- V Stochastic Differential

A note on Ritov's Bayes approach to the minimax property of the cusum procedure

This work transfers Lorden's approach to a continuous time model and discusses the structure of the Bayes risk, and shows the minimax optimality of the cusum procedures, when the initial and nal distribution are both known.