A method for detecting anomalies from multidimensional data comprises: a) receiving multidimensional data; b) estimating background parameters of a normal compositional model from the multidimensional data; c) estimating abundance values of the normal compositional model from the background parameters and the multidimensional data; d) determining an anomaly detection statistic from the multidimensional data, the background parameters, and abundance values; and e) classifying an observation from the multidimensional data as either a background reference or an anomaly from the anomaly detection statistic.