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 biomedical signal processing. In all of these applications the observations being monitored undergo a change in distribution in response to a change or anomaly in the environment, and the goal is to detect the change as quickly as possibly, subject to false alarm constraints. In this chapter, two formulations of the quickest change detection problem, Bayesian and minimax, are introduced, and optimal or asymptotically optimal solutions to these formulations are discussed. Then some generalizations and extensions of the quickest change detection problem are described. The chapter is concluded with a discussion of applications and open issues.

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Quickest Change Detection

In some embodiments, a system and method for substantially real-time comparison of quality of interfaces by mobile devices over heterogeneous networks is disclosed The method can be performed using a dynamic and rapid comparison by distributed hosts, using a minimal number of injected network packets, using minimal path quality metrics, which path quality metrics are independent of how a Qol is measured, and in a manner suitable for both wireline and wireless networks

Real-time comparison of quality of interfaces

We show that humpback-whale vocalization behavior is synchronous with peak annual Atlantic herring spawning processes in the Gulf of Maine. With a passive, wide-aperture, densely-sampled, coherent hydrophone array towed north of Georges Bank in a Fall 2006 Ocean Acoustic Waveguide Remote Sensing (OAWRS) experiment, vocalizing whales could be instantaneously detected and localized over most of the Gulf of Maine ecosystem in a roughly 400-km diameter area by introducing array gain, of 18 dB, orders of magnitude higher than previously available in acoustic whale sensing. With humpback-whale vocalizations consistently recorded at roughly 2000/day, we show that vocalizing humpbacks (i) were overwhelmingly distributed along the northern flank of Georges Bank, coinciding with the peak spawning time and location of Atlantic herring, and (ii) their overall vocalization behavior was strongly diurnal, synchronous with the formation of large nocturnal herring shoals, with a call rate roughly ten-times higher at night than during the day. Humpback-whale vocalizations were comprised of (1) highly diurnal non-song calls, suited to hunting and feeding behavior, and (2) songs, which had constant occurrence rate over a diurnal cycle, invariant to diurnal herring shoaling. Before and during OAWRS survey transmissions: (a) no vocalizing whales were found at Stellwagen Bank, which had negligible herring populations, and (b) a constant humpback-whale song occurrence rate indicates the transmissions had no effect on humpback song. These measurements contradict the conclusions of Risch et al. Our analysis indicates that (a) the song occurrence variation reported in Risch et al. is consistent with natural causes other than sonar, (b) the reducing change in song reported in Risch et al. occurred days before the sonar survey began, and (c) the Risch et al. method lacks the statistical significance to draw the conclusions of Risch et al. because it has a 98–100% false-positive rate and lacks any true-positive confirmation.

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Ecosystem Scale Acoustic Sensing Reveals Humpback Whale Behavior Synchronous with Herring Spawning Processes and Re-Evaluation Finds No Effect of Sonar on Humpback Song Occurrence in the Gulf of Maine in Fall 2006

We pay tribute to the remarkable work of Frank Anscombe published in 1952, who invented the random central limit theorem (random CLT). This path-breaking contribution subsequently influenced practically the whole spectrum of sequential analysis very heavily. It is a humble attempt on our part to briefly sketch the breadth of its impact by connecting Anscombe's work with some of the major developments in sequential analysis that came afterwards.

A Tribute to Frank Anscombe and Random Central Limit Theorem from 1952

This paper studies the problem of sequential Gaussian shift-in-mean hypothesis testing in a distributed multi-agent network. A sequential probability ratio test (SPRT) type algorithm in a distributed framework of the \emph{consensus}+\emph{innovations} form is proposed, in which the agents update their decision statistics by simultaneously processing latest observations (innovations) sensed sequentially over time and information obtained from neighboring agents (consensus). For each pre-specified set of type I and type II error probabilities, local decision parameters are derived which ensure that the algorithm achieves the desired error performance and terminates in finite time almost surely (a.s.) at each network agent. Large deviation exponents for the tail probabilities of the agent stopping time distributions are obtained and it is shown that asymptotically (in the number of agents or in the high signal-to-noise-ratio regime) these exponents associated with the distributed algorithm approach that of the optimal centralized detector. The expected stopping time for the proposed algorithm at each network agent is evaluated and is benchmarked with respect to the optimal centralized algorithm. The efficiency of the proposed algorithm in the sense of the expected stopping times is characterized in terms of network connectivity. Finally, simulation studies are presented which illustrate and verify the analytical findings.

Distributed Sequential Detection for Gaussian Shift-in-Mean Hypothesis Testing

Passive Acoustic Detection of Marine Mammals Using Page's Test Two-Stage Procedures for Selecting the Best Component of a Multivariate Distribution Sequential Randomization Tests Sequential Methods for Multistate Processes Sequential Adaptive Designs for Clinical Trials with Longitudinal Responses Sequential Approaches to Data Mining Approximations and Bounds for Moving Sums of Discrete Random Variables Estimation of the Slope in a Measurement-Error Model Kernel Density Estimation of Wool Fiber Diameter Financial Applications of Sequential Nonparametric Curve Estimation

Applied Sequential Methodologies: Real- World Examples with Data Analysis

Prediction using a multiple-regression model is addressed when the penalties for overpredicting and underpredicting the true future value are not equal. Such asymmetric penalty functions are appropriate in many practical situations. If one imposes some preassigned precision on the prediction procedure, it is shown that in the presence of nuisance parameters in the model, the sample size needed to achieve the fixed precision is unknown. Some adaptive multistage sampling techniques are discussed that offer solutions to this problem. A prediction procedure based on a purely sequential sampling scheme is introduced, followed by a batch sequential scheme. Finally, a real-life example is provided to illustrate the use of these procedures, and computational evidence is supplied to demonstrate the efficiency of the latter procedure compared to the former one.

Asymmetric Penalized Prediction Using Adaptive Sampling Procedures

Sequential Estimation in the Agricultural Sciences

The author should be commended for his extremely informative, well-written and coherent review of one of the most celebrated results in the history of statistics–Wald's likelihood ratio identity. H...

Sujay Datta

Papers

Applied Sequential Methodologies: Real- World Examples with Data Analysis

Asymmetric Penalized Prediction Using Adaptive Sampling Procedures

Sequential Estimation in the Agricultural Sciences

Discussion on “Likelihood Ratio Identities and their Applications to Sequential Analysis” by Tze L. Lai