Statistical representations, in which sensory signals are pooled over space and/or time, are believed to contribute to many aspects of perception. An example occurs in audition, where the background texture of the acoustic environment is represented with time-averaged sound statistics. How does this pooling over time occur in coordination with the competing need to segregate concurrent sound sources? I will present a series of experiments characterizing the averaging process underlying sound texture perception in auditory scenes. The results suggest time-averaging processes that can extend up to several seconds, but that operate selectively on individual sources. The resulting statistics are then “filled in”: textures that are intermittently obscured by louder sounds are inferred to continue, generating vivid percepts of illusory texture that support the subjective sense of a stable world despite unstable sensory input.