Natural stimulations caused by objects in the surrounding world do not stimulate single sensory receptors in isolation but lead to the activation of large numbers of neurons simultaneously. Thus, typical stimulus variables of interest are represented only implicitly in activation patterns across large neural populations. These patterns are statistical in nature since repeated presentation of the same stimulus usually leads to highly variable responses. The large dimensionality and randomness of the neural responses make it difficult to assess how well different stimuli can be discriminated. Depending on how effectively neurons share the labor of encoding, the accuracy with which stimuli are represented can change dramatically. Thus, studying the efficiency of population codes is important for our understanding of both which information is encoded in neural populations and how it is encoded.