Multivariate anomaly detection can be used to identify outages within large volumes of telemetry data for computing systems. However, developing an efficient anomaly detector that can provide users with relevant information is a challenging problem. We introduce our approach to hierarchical multivariate anomaly detection called DeCorus, a statistical multivariate anomaly detector which achieves linear complexity. It extends standard statistical techniques to improve their ability to find relevant anomalies within noisy signals and makes use of types of domain knowledge that system operators commonly possess to compute system-level anomaly scores. We describe the implementation of DeCorus an online log anomaly detection tool for network device syslog messages deployed at a cloud service provider. We use real-world data sets that consist of 1.5 billion network device syslog messages and hundreds of incident tickets to characterize the performance of DeCorus and compare its ability to detect incidents with five alternative anomaly detectors. While DeCorus outperforms the other anomaly detectors, all of them are challenged by our data set. We share how DeCorus provides value in the field and how we plan to improve its incident detection accuracy.