This paper addresses the problem of quickest change detection of an unknown mean-shift in multiple Gaussian data streams. We propose a novel extension of the window-limited CuSum (WL-CuSum) test which utilizes the James-Stein estimator to improve detection performance. Compared to traditional maximum likelihood-based approaches, the proposed approach can considerably reduce the detection delay, especially when the number of streams is large. Our theoretical results indicate that the proposed test asymptotically optimal, and non-asymptotically a uniform improvement over its maximum likelihood alternative. The performance is improved for all values of the unknown post-change parameter, as long as the number of the data streams is greater than three. Overall, the results suggest that shrinkage estimators, such as the James-Stein estimator, can provide substantial performance improvement in change detection problems with unknown parameters.

The problem of quickest change detection is studied in the context of detecting an arbitrary unknown mean-shift in multiple independent Gaussian data streams. The James-Stein estimator is used in constructing detection schemes that exhibit strong detection performance both asymptotically and non-asymptotically. Our results indicate that utilizing the James-Stein estimator in the recently developed window-limited CuSum test constitutes a uniform improvement over its typical maximum likelihood variant. That is, the proposed James-Stein version achieves a smaller detection delay simultaneously for all possible post-change parameter values and every false alarm rate constraint, as long as the number of parallel data streams is greater than three. Additionally, an alternative detection procedure that utilizes the James-Stein estimator is shown to have asymptotic detection delay properties that compare favorably to existing tests. The second-order asymptotic detection delay term is reduced in a predefined low-dimensional subspace of the parameter space, while second-order asymptotic minimaxity is preserved. The results are verified in simulations, where the proposed schemes are shown to achieve smaller detection delays compared to existing alternatives, especially when the number of data streams is large.

Detection of multiple spatial events in parallel is of wide interest in many modern applications, such as Internet of Things, environmental monitoring, and wireless communication. Sensor networks can be used for acquiring data and performing inference. In this paper, we take a Bayesian approach and model the detection of spatial events as a Bayesian multiple change point detection problem. The sensor network is assumed to be divided into distinct known clusters. In each cluster, a point source generates a spatial event that propagates omnidirectionally. The event causes a change in the local environment, which changes the distribution of observations at sensors located within the realm of this event. We propose a method for performing sequential multiple change-point detection under the Bayesian paradigm. It is shown analytically that the proposed procedure controls the false discovery rate (FDR), which is an appropriate criterion for statistically controlling the prevalence of false alarms in a setting where multiple decisions are made in parallel. It is numerically shown that exploiting spatial information decreases the average detection delay compared to procedures that do not properly use this information.

Several modern applications involve large-scale sensor networks for statistical inference. For example, such sensor networks are of significant interest for Internet of Things applications. In this paper, we consider Bayesian multiple changepoint detection using a sensor network in which a fusion center can receive a data stream from each sensor. Due to communication limitations, the fusion center monitors only a subset of the data streams at each time slot. We propose a detection procedure that handles these limitations by monitoring the sensors with the highest posterior probabilities of change points having occurred. It is shown that the proposed procedure attains an average detection delay that does not increase with the number of sensors, while controlling the false discovery rate. The proposed procedure is also shown to be useful for unveiling the tradeoff between reducing the average detection delay and reducing the average number of observations drawn until discovery.