The brain uses its past experience to draw conclusions from new sense data. We can quantify this idea using statistical principles that enable us to generate predictions about neural circuitry. One highly influential theory, efficient coding, applies this idea to visual processing. It proposes that the retina compresses natural images using center-surround receptive fields to remove natural correlations. I test this prediction and demonstrate that the spike trains of retinal ganglion cells are indeed decorrelated compared to the visual input. However, most of the decorrelation is accomplished not by the receptive fields, but by nonlinear processing. I show that these nonlinearities provide nearly optimal information transmission for noisy neurons. Extending the efficient coding theory to a nonlinear code thus provides a better explanation for the observed structure of retinal spike trains. I then discuss the role of statistics in neural computation more generally. I will contrast computation with information transmission, and emphasize the importance of nonlinearities and recurrent connectivity in extracting relevant information. As a concrete example I will describe my recent progress modelling contextual inference in the primary visual cortex. Hosts: Dora Angelaki (BCM), Behnaam Aazhang