1. A method for monitoring dependent metric streams for anomalies, comprising: identifying a plurality of sets of dependent metric streams from a plurality of metric streams of a computer system by measuring an association of the plurality of metric streams using a statistical dependency measure analysis, wherein each set comprises a plurality of the dependent metric streams and each metric stream comprises a plurality of data; determining a subset of the plurality of sets of dependent metric streams to monitor by selecting a quantity of the sets of dependent metric streams that have a highest statistical dependency; cleaning the data of each set of dependent metric streams of the subset by identifying and removing outlier data; fitting a probability density function to the cleaned data of each set of dependent metric streams of the subset, wherein the probability density function is a likelihood function that provides a likelihood of an occurrence of the cleaned data; determining a detection threshold that is a lower threshold on the likelihood of the occurrence of the cleaned data of each set of dependent metric streams of the subset based on the likelihood function; detecting an anomaly if a likelihood of an occurrence of a new data of one of the sets of dependent metric streams of the subset is less than the detection threshold; and transmitting an alert signal in response to detecting the anomaly.