标题： 功能数据的上下文树选择 显示英文标题

标题： Context tree selection for functional data

摘要： 人们多次推测，大脑会从刺激中提取统计规律。 在这里，我们提出了一种新的统计方法，可用于解决这一推测。 该方法基于一种由可变长度记忆链驱动的新一类随机过程。 它导致了一种新的实验协议，在该协议中，通过随机链生成的听觉刺激序列被呈现给志愿者，同时记录他们头皮上的脑电图（EEG）数据。 引入了一种用于功能数据的新统计模型选择程序，并证明其是一致的。 将其应用于使用我们实验协议收集的EEG数据样本，结果支持了大脑能够有效识别生成刺激序列的链结构的推测。 显示英文摘要

摘要： 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.