We initiate a mathematical analysis of hidden effects induced by binningspike trains of neurons. Assuming that the original spike train has beengenerated by a discrete Markov process, we show that binning generates astochastic process which is not Markov any more, but is instead a VariableLength Markov Chain (VLMC) with unbounded memory. We also show that the law ofthe binned raster is a Gibbs measure in the DLR (Dobrushin-Lanford-Ruelle)sense coined in mathematical statistical mechanics. This allows the derivationof several important consequences on statistical properties of binned spiketrains. In particular, we introduce the DLR framework as a natural setting tomathematically formalize anticipation, i.e. to tell "how good" our nervoussystem is at making predictions. In a probabilistic sense, this corresponds tocondition a process by its future and we discuss how binning may affect ourconclusions on this ability. We finally comment what could be the consequencesof binning in the detection of spurious phase transitions or in the detectionof wrong evidences of criticality.
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