Detection of an anomalous cluster in a network

We consider the problem of detecting whether or not, in a given sensor network, there is a cluster of sensors which exhibit an "unusual behavior." Formally, suppose we are given a set of nodes and attach a random variable to each node. We observe a realization of this process and want to decide between the following two hypotheses: under the null, the variables are i.i.d. standard normal; under the alternative, there is a cluster of variables that are i.i.d. normal with positive mean and unit variance, while the rest are i.i.d. standard normal. We also address surveillance settings where each sensor in the network collects information over time. The resulting model is similar, now with a time series attached to each node. We again observe the process over time and want to decide between the null, where all the variables are i.i.d. standard normal, and the alternative, where there is an emerging cluster of i.i.d. normal variables with positive mean and unit variance. The growth models used to represent the emerging cluster are quite general and, in particular, include cellular automata used in modeling epidemics. In both settings, we consider classes of clusters that are quite general, for which we obtain a lower bound on their respective minimax detection rate and show that some form of scan statistic, by far the most popular method in practice, achieves that same rate to within a logarithmic factor. Our results are not limited to the normal location model, but generalize to any one-parameter exponential family when the anomalous clusters are large enough.Comment: Published in at http://dx.doi.org/10.1214/10-AOS839 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Constraints on the Formation of the Globular Cluster IC 4499 from Multi-Wavelength Photometry

We present new multiband photometry for the Galactic globular cluster IC 4499 extending well past the main sequence turn-off in the U, B, V, R, I, and DDO51 bands. This photometry is used to determine that IC4499 has an age of 12 pm 1 Gyr and a cluster reddening of E(B-V) = 0.22 pm 0.02. Hence, IC 4499 is coeval with the majority of Galactic GCs, in contrast to suggestions of a younger age. The density profile of the cluster is observed to not flatten out to at least r~800 arcsec, implying that either the tidal radius of this cluster is larger than previously estimated, or that IC 4499 is surrounded by a halo. Unlike the situation in some other, more massive, globular clusters, no anomalous color spreads in the UV are detected among the red giant branch stars. The small uncertainties in our photometry should allow the detection of such signatures apparently associated with variations of light elements within the cluster, suggesting that IC 4499 consists of a single stellar population.Comment: accepted to MNRA