Hyperspectral data are often modeled using either a linear mixture or a statistical classification approach. The linear mixture model describes each spectral vector as a constrained linear combination of end-member spectra, whereas the classification approach models each spectra as a realization of a random vector having one of several normal distributions. In this work we describe a stochastic compositional model that synthesizes these two viewpoints and models each spectra as a constrained linear combination of random vectors. Maximum likelihood methods of estimating the parameters of the model, assuming normally distributed random vectors, are described, and anomaly and likelihood ratio detection statistics are defined. Detection algorithms derived from the classification, linear mixing, and stochastic compositional models are defined. Detection algorithms derived from the classification, linear mixing, and stochastic compositional models are compared using data consisting of ocean hyperspectral imagery to which the signature of a personal flotation device has been added at pixel fill fractions (PFF) of five and ten percent. These results show that detection algorithms based on the stochastic compositional model may significantly improve detection performance. For example, this study shows that, at a 5% PFF and a probability of detection of 0.8, the false alarm probabilities of anomaly and likelihood detection algorithms based on the stochastic compositional model are more than an order of magnitude lower than the false alarm probabilities of comparable algorithms based on either a linear unmixing algorithm or a Gaussian mixture model.