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Timely detection of anomalous events in networks, particularly social networks, is a problem of increasing interest and relevance. A variety of methods have been proposed for monitoring such networks, including the window‐based scan method proposed by a previous study. However, research assessing the performance of this and other methods has been sparse. In this article, we use simulated social network structures to study the performance of the Priebe et al method. The detection power is high only when more than half of the social network experiences anomalous behavior or if the anomalous behavior is extreme. Both can be represented by high signal‐to‐noise ratios in the network. More precisely, Priebe's scan method performs well when the signal‐to‐noise ratio is above 20. Simulation studies are used to show that an improved detection rate and shortened monitoring delays can be achieved by lagging the moving window used for standardization, lowering the signaling threshold, and using shorter moving windows at the initial stage of monitoring. We suggest a community detection method to be used after an anomalous event has been identified to help determine the subnetwork associated with this anomalous behavior.

Daily data for fine (<2.5 µm) and coarse (2.5-10 µm) particles are available for 1995-1997 from the U.S. Environmental Protection Agency (EPA) research monitor in Phoenix, AZ. Mortality effects on the 65 and over population were studied for both the city of Phoenix and for a region of about 50 mi around Phoenix. Coarse particles in Phoenix are believed to be natural in origin and spatially homogeneous, whereas fine particles are primarily vehicular in origin and concentrated in the city itself. For this reason, it is natural to focus on city mortality data when considering fine particles, and on region mortality data when considering coarse particles, and most of the results reported here correspond to those assignments.After allowing for seasonality and long-term trend through a nonlinear (B-spline) trend curve, and also for meteorological effects based on temperature and specific humidity, a regression of mortality was performed on PM using several different measures for PM. Based on a linear PM effect, we found a statistically significant coefficient for coarse particles, but not for fine particles, contrary to what is widely believed about the effects of coarse and fine particles. An IMPLICATIONS The EPA standard for fine particles introduced in 1997 was based on the widespread belief that the most serious health effects occur for fine rather than coarse particles. The present study shows that coarse particles may still have an effect and, therefore, should not be neglected. It also confirms that fine particles have an effect, but in this analysis, it is only observed above a threshold in the region of 20-25 µg/m 3 ; there appears to be no effect below 15 µg/m 3 . Since the latter figure is the 1997 EPA standard for long-term average fine PM, the standard may possibly be more stringent than needed. However, the main message of the paper is that more study is needed of the comparative effects of coarse and fine PM, of possible threshold or nonlinear relationships, and of the effect of variations in the chemical composition of PM.analysis of nonlinear pollution-mortality relationships, however, suggests that the true picture is more complicated than that. For coarse particles, the evidence for any nonlinear or threshold-based effect is slight. For fine particles, we found evidence of a threshold, most likely with values in the range of 20-25 µg/m 3 . We also found some evidence of interactions of the PM effects with season and year.The main effect here is an apparent seasonal interaction in the coarse PM effect. An attempt was made to explain this in terms of seasonal variation in the chemical composition of PM, but this led to another counterintuitive result: the PM effect is highest in spring and summer, when the anthropogenic concentration of coarse PM is lowest as determined by a principal components analysis. There was no evidence of confounding between the fine and coarse PM effects. Although these results are based on one city and should be considered tentative until replicated in other studies,...

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