Ambiguity and nonidentifiability in the statistical analysis of neural codes

Abstract

Many experimental studies of neural coding rely on a statistical interpretation of the theoretical notion of the rate at which a neuron fires spikes. For example, neuroscientists often ask, "Does a population of neurons exhibit more synchronous spiking than one would expect from the covariability of their instantaneous firing rates?" For another example, "How much of a neuron's observed spiking variability is caused by the variability of its instantaneous firing rate, and how much is caused by spike timing variability?" However, a neuron's theoretical firing rate is not necessarily well-defined. Consequently, neuroscientific questions involving the theoretical firing rate do not have a meaning in isolation but can only be interpreted in light of additional statistical modeling choices. Ignoring this ambiguity can lead to inconsistent reasoning or wayward conclusions. We illustrate these issues with examples drawn from the neural-coding literature.temporal coding | spike timing | spike count variability | trial-to-trial variability | doubly stochastic A mong the most important open questions in neurophysiology are those regarding the nature of the code that neurons use to transmit information. Experimental approaches to such questions are challenging, because the spike outputs of a neuronal subpopulation, as typically recorded in behaving animals, are influenced by a vast array of factors. Such factors span all levels of description, from the microscopic (e.g., ion fluctuations and states of presynaptic neurons) to the macroscopic (e.g., sensation and attention), but only a small fraction of these is measured, or even understood. As a consequence, it is not clear to what degree variations in unknown and uncontrolled variables alternately reveal or confound the underlying signals that observed spikes are presumed to encode. Another consequence, very much related, is that these uncertainties also disturb our intuitive comfort with common models of statistical repeatability in neurophysiological signal analysis. In this context, there is an increasingly popular strain of thought in the neural-coding literature that "doubly stochastic point processes" (1-8) provide a way to think about and model fundamental questions about the relationship between sources of "trial-to-trial variability" (4, 9) and the observed variability of spike responses.Imagine an experiment consisting of repeated presentations of a sensory stimulus. In a typical probabilistic model of spike responses, the probability that a particular neuron emits (fires) a spike at one time is described by a theoretical firing rate function (a function of time relative to stimulus onset). [Note that theoretical firing rates are distinct from the basic "observed" or "empirical" firing rate, which is a report of how many spikes occur in a window of a specified time length. Here, we discuss the theoretical firing rate. Observed firing rates are used to infer theoretical firing rates or their properties (SI Appendix, section S1)]. For example, in a generic firing r...

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