  It has been repeatedly conjectured that the brain retrieves statistical
regularities from stimuli. 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 chains with memory of variable length. It leads to a new
experimental protocol in which sequences of auditory stimuli generated by a
stochastic chain are presented to volunteers while electroencephalographic
(EEG) data is recorded from their scalp. A new statistical model selection
procedure for functional data is introduced and proved to be consistent.
Applied to samples of EEG data collected using our experimental protocol it
produces results supporting the conjecture that the brain effectively
identifies the structure of the chain generating the sequence of stimuli.
