Related papers: On the Wiener disorder problem
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…
The problem of sequential change diagnosis is considered, where observations are obtained on-line, an abrupt change occurs in their distribution, and the goal is to quickly detect the change and accurately identify the post-change…
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.…
A sensor network is considered where at each sensor a sequence of random variables is observed. At each time step, a processed version of the observations is transmitted from the sensors to a common node called the fusion center. At some…
Quickest change point detection is concerned with the detection of statistical change(s) in sequences while minimizing the detection delay subject to false alarm constraints. In this paper, the problem of change point detection is studied…
The claim arrival process to an insurance company is modeled by a compound Poisson process whose intensity and/or jump size distribution changes at an unobservable time with a known distribution. It is in the insurance company's interest to…
We consider the Wiener process with drift $$ dX_t=\mu dt +\sigma d W_t $$ with initial value problem $X_0=x_0$, where $x_0 \in R$, $ \mu \in R$ and $\sigma > 0$ are parameters. By use values $(z_k)_{k \in N}$ of corresponding trajectories…
Multivariate data sources with components of different information value seem to appear frequently in practice. Models in which the components change their homogeneity at different times are of significant importance. The fact whether any…
Aleatoric and Epistemic uncertainty have achieved recent attention in the literature as different sources from which uncertainty can emerge in stochastic modeling. Epistemic being intrinsic or model based notions of uncertainty, and…
Continuous-time event sequences represent discrete events occurring in continuous time. Such sequences arise frequently in real-life. Usually we expect the sequences to follow some regular pattern over time. However, sometimes these…
The problem of detecting a change in the drift of a Brownian motion is considered. The change point is assumed to have a modified exponential prior distribution with unknown parameters. A worst-case analysis with respect to these parameters…
The paper deals with disorders detection in the multivariate stochastic process. We consider the multidimensional Poisson process or the multivariate renewal process. This class of processes can be used as a description of the distributed…
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.…
In the 1960s, Shiryaev developed a Bayesian theory of change-point detection in the i.i.d. case, which was generalized in the beginning of the 2000s by Tartakovsky and Veeravalli for general stochastic models assuming a certain stability of…
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…
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 present a novel Bayesian approach to analysing multiple time-series with the aim of detecting abnormal regions. These are regions where the properties of the data change from some normal or baseline behaviour. We allow for the…
This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the…
In the problem of quickest change detection, a change occurs at some unknown time in the distribution of a sequence of random vectors that are monitored in real time, and the goal is to detect this change as quickly as possible subject to a…
The first passage time density of a diffusion process to a time varying threshold is of primary interest in different fields. Here we consider a Brownian motion in presence of an exponentially decaying threshold to model the neuronal…