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This paper considers the quickest detection problem for hidden Markov models (HMMs) in a Bayesian setting. We construct an augmented HMM representation of the problem that allows the application of a dynamic programming approach to prove…
As saturated output observations are ubiquitous in practice, identifying stochastic systems with such nonlinear observations is a fundamental problem across various fields. This paper investigates the asymptotically efficient identification…
In this paper, the problem of quickly detecting an abrupt change on a stochastic process under Bayesian framework is considered. Different from the classic Bayesian quickest change-point detection problem, this paper considers the case…
The problem of joint detection and lossless source coding is considered. We derive asymptotically optimal decision rules for deciding whether or not a sequence of observations has emerged from a desired information source, and to compress…
A new class of stochastic processes called independent and periodically identically distributed (i.p.i.d.) processes is defined to capture periodically varying statistical behavior. A novel Bayesian theory is developed for detecting a…
We consider the detection and localization of change points in the distribution of an offline sequence of observations. Based on a nonparametric framework that uses a similarity graph among observations, we propose new test statistics when…
We are interested in estimating the location of what we call "smooth change-point" from $n$ independent observations of an inhomogeneous Poisson process. The smooth change-point is a transition of the intensity function of the process from…
Change-of-measure is a powerful technique used across statistics, probability and analysis. Particularly known as Wald's likelihood ratio identity, the technique enabled the proof of a number of exact and asymptotic optimality results…
Time-varying random objects have been increasingly encountered in modern data analysis. Moreover, in a substantial number of these applications, periodic behaviour of the random objects has been observed. We develop a novel procedure to…
For the problem of sequential detection of changes, we adopt the probability maximizing approach in place of the classical minimization of the average detection delay, and propose modified versions of the Shiryaev, Lorden and Pollak…
We consider the problem of quickest changepoint detection under the Average Run Length (ARL) constraint where the pre-change and post-change laws lie in composite families $\mathscr{P}$ and $\mathscr{Q}$ respectively. In such a problem, a…
We consider the quickest change-point detection problem where the aim is to detect the onset of a pre-specified drift in "live"-monitored standard Brownian motion; the change-point is assumed unknown (nonrandom). The object of interest is…
We consider a change-point detection problem for a simple class of Piecewise Deterministic Markov Processes (PDMPs). A continuous-time PDMP is observed in discrete time and through noise, and the aim is to propose a numerical method to…
We study change point detection and localization for univariate data in fully nonparametric settings in which, at each time point, we acquire an i.i.d. sample from an unknown distribution. We quantify the magnitude of the distributional…
The problem of detection and possible estimation of a signal generated by a dynamic system when a variable number of noisy measurements can be taken is here considered. Assuming a Markov evolution of the system (in particular, the pair…
An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum…
We consider the problem of quickest change-point detection where the observations form a first-order autoregressive (AR) process driven by temporally independent standard Gaussian noise. Subject to possible change are both the drift of the…
Modern information systems generate large volumes of data with anomalies that occur at unknown points in time and have to be detected quickly and reliably with low false alarm rates. The paper develops a general theory of quickest…
This paper investigates a novel offline change-point detection problem from an information-theoretic perspective. In contrast to most related works, we assume that the knowledge of the underlying pre- and post-change distributions are not…
The problem of quickest change detection is studied, where there is an additional constraint on the cost of observations used before the change point and where the post-change distribution is composite. Minimax formulations are proposed for…