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In this paper, we present an approach to selecting models for novelty (outlier) detection. Our approach minimizes the risk of accepting outliers at a fixed normal rejection rate, under the assumption that the distribution of abnormal (outlier) data is uniformly distributed in some bounded region of the input space. This risk is minimized by selecting the model with the smallest volume acceptance region, using a randomized volume estimation algorithm. The volume estimation algorithm can estimate the volume of a body in high-dimensional space and scales polynomially in dimension with the number of calls to the model. We have performed extensive experiments which show that the combined model selection criteria are able to select not only the best models from a given model class, but also among all model classes.