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

Social learning against data falsification in sensor networks

Sensor networks generate large amounts of geographically-distributed data. The conventional approach to exploit this data is to first gather it in a special node that then performs processing and inference. However, what happens if this node is destroyed, or even worst, if it is hijacked? To explore this problem, in this work we consider a smart attacker who can take control of critical nodes within the network and use them to inject false information. In order to face this critical security thread, we propose a novel scheme that enables data aggregation and decision-making over networks based on social learning, where the sensor nodes act resembling how agents make decisions in social networks. Our results suggest that social learning enables high network resilience, even when a significant portion of the nodes have been compromised by the attacker