An Exact Formula for the Average Run Length to False Alarm of the Generalized Shiryaev-Roberts Procedure for Change-Point Detection under Exponential Observations

We derive analytically an exact closed-form formula for the standard minimax Average Run Length (ARL) to false alarm delivered by the Generalized Shiryaev-Roberts (GSR) change-point detection procedure devised to detect a shift in the baseline mean of a sequence of independent exponentially distributed observations. Specifically, the formula is found through direct solution of the respective integral (renewal) equation, and is a general result in that the GSR procedure's headstart is not restricted to a bounded range, nor is there a "ceiling" value for the detection threshold. Apart from the theoretical significance (in change-point detection, exact closed-form performance formulae are typically either difficult or impossible to get, especially for the GSR procedure), the obtained formula is also useful to a practitioner: in cases of practical interest, the formula is a function linear in both the detection threshold and the headstart, and, therefore, the ARL to false alarm of the GSR procedure can be easily computed.Comment: 9 pages; Accepted for publication in Proceedings of the 12-th German-Polish Workshop on Stochastic Models, Statistics and Their Application

Distributed Change Detection via Average Consensus over Networks

Distributed change-point detection has been a fundamental problem when performing real-time monitoring using sensor-networks. We propose a distributed detection algorithm, where each sensor only exchanges CUSUM statistic with their neighbors based on the average consensus scheme, and an alarm is raised when local consensus statistic exceeds a pre-specified global threshold. We provide theoretical performance bounds showing that the performance of the fully distributed scheme can match the centralized algorithms under some mild conditions. Numerical experiments demonstrate the good performance of the algorithm especially in detecting asynchronous changes.Comment: 15 pages, 8 figure

Using biomarkers to predict TB treatment duration (Predict TB): a prospective, randomized, noninferiority, treatment shortening clinical trial

Background : By the early 1980s, tuberculosis treatment was shortened from 24 to 6 months, maintaining relapse rates of 1-2%. Subsequent trials attempting shorter durations have failed, with 4-month arms consistently having relapse rates of 15-20%. One trial shortened treatment only among those without baseline cavity on chest x-ray and whose month 2 sputum culture converted to negative. The 4-month arm relapse rate decreased to 7% but was still significantly worse than the 6-month arm (1.6%, P<0.01).  We hypothesize that PET/CT characteristics at baseline, PET/CT changes at one month, and markers of residual bacterial load will identify patients with tuberculosis who can be cured with 4 months (16 weeks) of standard treatment.Methods: This is a prospective, multicenter, randomized, phase 2b, noninferiority clinical trial of pulmonary tuberculosis participants. Those eligible start standard of care treatment. PET/CT scans are done at weeks 0, 4, and 16 or 24. Participants who do not meet early treatment completion criteria (baseline radiologic severity, radiologic response at one month, and GeneXpert-detectable bacilli at four months) are placed in Arm A (24 weeks of standard therapy). Those who meet the early treatment completion criteria are randomized at week 16 to continue treatment to week 24 (Arm B) or complete treatment at week 16 (Arm C). The primary endpoint compares the treatment success rate at 18 months between Arms B and C.Discussion: Multiple biomarkers have been assessed to predict TB treatment outcomes. This study uses PET/CT scans and GeneXpert (Xpert) cycle threshold to risk stratify participants. PET/CT scans are not applicable to global public health but could be used in clinical trials to stratify participants and possibly become a surrogate endpoint. If the Predict TB trial is successful, other immunological biomarkers or transcriptional signatures that correlate with treatment outcome may be identified. TRIAL REGISTRATION: NCT02821832

Sanitation of blackwater via sequential wetland and electrochemical treatment

The discharge of untreated septage is a major health hazard in countries that lack sewer systems and centralized sewage treatment. Small-scale, point-source treatment units are needed for water treatment and disinfection due to the distributed nature of this discharge, i.e., from single households or community toilets. In this study, a high-rate-wetland coupled with an electrochemical system was developed and demonstrated to treat septage at full scale. The full-scale wetland on average removed 79 +/- 2% chemical oxygen demand (COD), 30 +/- 5% total Kjeldahl nitrogen (TKN), 58 +/- 4% total ammoniacal nitrogen (TAN), and 78 +/- 4% orthophosphate. Pathogens such as coliforms were not fully removed after passage through the wetland. Therefore, the wetland effluent was subsequently treated with an electrochemical cell with a cation exchange membrane where the effluent first passed through the anodic chamber. This lead to in situ chlorine or other oxidant production under acidifying conditions. Upon a residence time of at least 6 h of this anodic effluent in a buffer tank, the fluid was sent through the cathodic chamber where pH neutralization occurred. Overall, the combined system removed 89 +/- 1% COD, 36 +/- 5% TKN, 70 +/- 2% TAN, and 87 +/- 2% ortho-phosphate. An average 5-log unit reduction in coliform was observed. The energy input for the integrated system was on average 16 +/- 3 kWh/m(3), and 11 kWh/m(3) under optimal conditions. Further research is required to optimize the system in terms of stability and energy consumption

Asymptotically optimal pointwise and minimax quickest change-point detection for dependent data

International audienceWe consider the quickest change-point detection problem in pointwise and minimax settings for general dependent data models. Two new classes of sequential detection procedures associated with the maximal "local" probability of a false alarm within a period of some fixed length are introduced. For these classes of detection procedures, we consider two popular risks: the expected positive part of the delay to detection and the conditional delay to detection. Under very general conditions for the observations, we show that the popular Shiryaev-Roberts procedure is asymptotically optimal, as the local probability of false alarm goes to zero, with respect to both these risks pointwise (uniformly for every possible point of change) and in the minimax sense (with respect to maximal over point of change expected detection delays). The conditions are formulated in terms of the rate of convergence in the strong law of large numbers for the log-likelihood ratios between the "change" and "no-change" hypotheses, specifically as a uniform complete convergence of the normalized log-likelihood ratio to a positive and finite number. We also develop tools and a set of sufficient conditions for verification of the uniform complete convergence for a large class of Markov processes. These tools are based on concentration inequalities for functions of Markov processes and the Meyn-Tweedie geometric ergodic theory. Finally, we check these sufficient conditions for a number of challenging examples (time series) frequently arising in applications, such as autoregression, autoregressive GARCH, etc

A non-parametric cumulative sum approach for online diagnostics of cyber attacks to nuclear power plants

Both stochastic failures and cyber attacks can compromise the correct functionality of Cyber-Physical Systems (CPSs). Cyber attacks manifest themselves in the physical system and, can be misclassified as component failures, leading to wrong control actions and maintenance strategies. In this chapter, we illustrate the use of a nonparametric cumulative sum (NP-CUSUM) approach for online diagnostics of cyber attacks to CPSs. This allows for (i) promptly recognizing cyber attacks by distinguishing them from component failures, and (ii) guiding decisions for the CPSs recovery from anomalous conditions. We apply the approach to the Advanced Lead-cooled Fast Reactor European Demonstrator (ALFRED) and its digital Instrumentation and Control (I&amp;C) system. For this, an object-oriented model previously developed is embedded within a Monte Carlo (MC) engine that allows injecting into the I&amp;C system both components (stochastic) failures (such as sensor bias, drift, wider noise and freezing) and cyber attacks (such as Denial of Service (DoS) attacks mimicking component failures)