We present an interpretable, multiscale model to detect anomalies in streaming data that strategically directs model complexity based on the difficulty of the underlying prediction task. The model is amenable to sequential updating, which is essential for scaleable computation. The core idea of our method has two parts. First, we propose a continuous-time stochastic process for predicting outcomes. This step can account for spatial or temporal trends that are known a priori or that can be assumed to be relatively stable. The second piece is a highly flexible, dynamic model for dependence between observations. If observations are on the scale of a geographic unit, then our approach will capture dependence between adjacent or nearby units. If we are, instead, modeling individual outcomes, then a similar approach could be used to model social structure between interacting individuals. We demonstrate the effectiveness of our model using data from users' social media interactions in response to both regional and local events.