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