How are analogue and digital signals similar/different?

Solving the neural code conundrum: digital or analogue - in layman term?

• Physicists have developed a technique that can tell which parts of the brain rely on analogue signals and which rely in digital signals. Reference: http://www.technologyreview.com/view/522066/solving-the-neural-code-conundrum-digital-or-analogue/

• Answer:

  In the article from which the question's citation is drawn ("Analog and digital codes in the brain" - http://arxiv.org/pdf/1311.4035v1.pdf) begins, "It has long been debated whether information in the brain is coded at the rate of neuronal spiking or at the precise timing of single spikes."  (NB: a series of spikes is called a, "spike train.") "Rate coding" presumes that the firing of a neuron occurs when a buildup or neuronal activity reaches a threshold which causes the neuron to fire.  In other words, the firing of a neuron is an "all" or "none" response and is thereby "digital" in nature. "Time-dependent firing" rate is defined as, "a simplification used to model large networks of neurons." (http://www.math.pitt.edu/~bdoiron/Course_files_Spring_2013/Ermentrout_Terman_Chapter11.pdf)  (Technically, it is, "the average number of spikes appearing during a short interval between times t and t+Δt, divided by the duration of the interval." - http://en.wikipedia.org/wiki/Neural_coding#Time-dependent_firing_rate)  This "simplification" is necessary because, "spiking events are probabilistic, so experimentalists repeat the same stimulus over many trials to obtain a poststimulus time histogram." (http://www.math.pitt.edu/~bdoiron/Course_files_Spring_2013/Ermentrout_Terman_Chapter11.pdf)  This translates into a spike train being a, "continuously varying analog signal." Different stochastic models (either "the empirical Bayes model - EBM - or the hidden Markov model - HMM") are selectively used by, "comparing their likelihood estimates for a given spike train." In short, if the data is best described by the "digital" EBM or "analog" HMM model, then the neuronal coding is decided to be one or the other. NB: I am NOT a scientist, but this methodology strikes me as empirically flawed; I would most certainly appreciate any further elucidation.