Context tree selection for functional data

It has been repeatedly conjectured that the brain retrieves statistical regularities from stimuli, so that their structural features are separated from noise. Here we present a new statistical approach allowing to address this conjecture. This approach is based on a new class of stochastic processes driven by context tree models. Also, it associates to a new experimental protocol in which structured auditory sequences are presented to volunteers while electroencephalographic signals are recorded from their scalp. A statistical model selection procedure for functional data is presented to analyze the electrophys-iological signals. This procedure is proved to be consistent. Applied to samples of electrophysiological trajectories collected during struc-tured auditory stimuli presentation, it produces results supporting the conjecture that the brain effectively identifies the context tree characterizing the source.