A study of model selection techniques for modeling synthetic aperture sonar backscatter statistics

High resolution acoustic imaging of the seafloor, such as with synthetic aperture sonar, can reveal complex environments due to the ability to resolve scatterers of different types. The statistical distribution of the backscattered field is appropriately modeled using a mixture distribution, which consists of a sum of a K pdf for each scatterer type, weighted by the relative frequency with which they occur. In this type of modeling, the number of distributions must be selected before parameters can be fit, and as the number of components increases, so does the danger of overfitting the data. Several methods of model selection are explored here. Two methods, the Bayesian information criterion and the Akaike information criterion are based on point parameter estimates, and a penalty due to the number of model parameters. The other two, the deviance information criterion and the Watanabe-Akaike information criterion, are based on Monte-Carlo sampling of the model parameter space. These four model selection criteria are compared to each other, and to the authors manual selection of the number of components.