Related papers: Quickest drift change detection in L\'evy-type for…
In 1960s Shiryaev developed Bayesian theory of change detection in independent and identically distributed (i.i.d.) sequences. In Shiryaev's classical setting the goal is to minimize an average detection delay under the constraint imposed…
This paper solves a Bayes sequential impulse control problem for a diffusion, whose drift has an unobservable parameter with a change point. The partially-observed problem is reformulated into one with full observations, via a change of…
We construct a Bayesian sequential test of two simple hypotheses about the value of the unobservable drift coefficient of a Brownian motion, with a possibility to change the initial decision at subsequent moments of time for some penalty.…
In this paper, Bayesian quickest change detection problems with sampling right constraints are considered. Specifically, there is a sequence of random variables whose probability density function will change at an unknown time. The goal is…
The popular criteria of optimality for quickest change detection procedures are the Lorden criterion, the Shiryaev-Roberts-Pollak criterion, and the Bayesian criterion. In this paper a robust version of these quickest change detection…
We consider the problem of efficient estimation of the drift parameter of an Ornstein-Uhlenbeck type process driven by a L\'{e}vy process when high-frequency observations are given. The estimator is constructed from the time-continuous…
We consider the quickest change detection problem where both the parameters of pre- and post- change distributions are unknown, which prevents the use of classical simple hypothesis testing. Without additional assumptions, optimal solutions…
We study a continuous time Bayesian quickest detection problem in which observation times are a scarce resource. The agent, limited to making a finite number of discrete observations, must adaptively decide his observation strategy to…
Given a Wiener process with unknown and unobservable drift, we try to estimate this drift as effectively but also as quickly as possible, in the presence of a quadratic penalty for the estimation error and of a fixed, positive cost per unit…
Optimal control in non-stationary Markov decision processes (MDP) is a challenging problem. The aim in such a control problem is to maximize the long-term discounted reward when the transition dynamics or the reward function can change over…
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 distribution of the disorder time is known. The objective is…
The problem of disorder seeks to determine a stopping time which is as close as possible to the unknown time of ``disorder'' when the observed process changes its probability characteristics. We give a partial answer to this question for…
The problem of quickest detection of a change in the distribution of a sequence of random variables is studied. The objective is to detect the change with the minimum possible delay, subject to constraints on the rate of false alarms and…
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…
Rapid detection of spatial events that propagate across a sensor network is of wide interest in many modern applications. In particular, in communications, radar, IoT, environmental monitoring, and biosurveillance, we may observe…
The problem of detecting changes in the statistical properties of a stochastic system and time series arises in various branches of science and engineering. It has a wide spectrum of important applications ranging from machine monitoring to…
The gist of the quickest change-point detection problem is to detect the presence of a change in the statistical behavior of a series of sequentially made observations, and do so in an optimal detection-speed-vs.-"false-positive"-risk…
We study a classical Bayesian statistics problem of sequentially testing the sign of the drift of an arithmetic Brownian motion with the $0$-$1$ loss function and a constant cost of observation per unit of time for general prior…
Recent attention in quickest change detection in the multi-sensor setting has been on the case where the densities of the observations change at the same instant at all the sensors due to the disruption. In this work, a more general…
This work examines the problem of sequential detection of a change in the drift of a Brownian motion in the case of two-sided alternatives. Applications to real life situations in which two-sided changes can occur are discussed.…