Ambiguity and nonidentifiability in the statistical analysis of neural codes

In light of experimentally observed trial-to-trial variability, the notion of using a “doubly stochastic point process” as a mean to explain the variability has been gaining interest. This paints the following picture: when assuming a rate code, people assume that firing rate carries information while spike timing is random. The doubly stochastic point process assumes that the firing rate is also a random variable, which gives the spike train a two-layered variability. Under this assumption, we would be tempted to interpret the firing rate variability as something that affects behavior (i.e. informational), while spike time variability represents noise.

However, the authors of this paper show that without further constraints, this model is easily non-identifiable. This means that different firing rate processes can give rise to identical spike trains, rendering the aforementioned interpretation useless. The authors gave two examples to showcase this, and I encourage those that are interested to check it out.

Currently, what people usually do to obtain the firing rate process is to smooth the spike trains. The implicit constraint behind this practice is that firing rates operate at a timescale determined by the smoothing process. Another method people employ is to assume that the spiking process is Poisson. However, many studies cast doubt on that assumption, which is what led to discussions regarding doubly stochastic point processes to begin with. A relaxation of this assumption is to use the Cox process instead, which says that spiking is Poisson when conditioned on a random rate function. Both methods should be used with caution, as the conclusion one obtains is highly dependent on the validity of such assumptions.

Author: Pei-Hsien Liu

Original Paper: Amarasingham, A., Geman, S., & Harrison, M. T. (2015). Ambiguity and nonidentifiability in the statistical analysis of neural codes. Proceedings of the National Academy of Sciences, 112(20), 6455-6460.