Dynamic modeling of spike count data with Conway-Maxwell Poisson variability

TL;DR

This paper introduces a dynamic modeling framework using Conway-Maxwell Poisson (CMP) distribution to accurately track time-varying neural spike count variability, outperforming previous Poisson-based models in neuroscience data analysis.

Contribution

The paper develops a novel dynamic CMP model that captures both under- and over-dispersion in neural spike data, with an efficient approximation for parameter tracking.

Findings

The model accurately tracks neural response dynamics in visual cortex and hippocampus.

It outperforms previous Poisson-based models in fitting neural spike data.

The approach is flexible and applicable to non-Poisson count data beyond neuroscience.

Abstract

In many areas of the brain, neural spiking activity covaries with features of the external world, such as sensory stimuli or an animal's movement. Experimental findings suggest that the variability of neural activity changes over time and may provide information about the external world beyond the information provided by the average neural activity. To flexibly track time-varying neural response properties, here we developed a dynamic model with Conway-Maxwell Poisson (CMP) observations. The CMP distribution can flexibly describe firing patterns that are both under- and over-dispersed relative to the Poisson distribution. Here we track parameters of the CMP distribution as they vary over time. Using simulations, we show that a normal approximation can accurately track dynamics in state vectors for both the centering and shape parameters ($\lambda$ and $\nu$). We then fit our model to neural data from neurons in primary visual cortex and "place cells" in the hippocampus. We find that this method out-performs previous dynamic models based on the Poisson distribution. The dynamic CMP model provides a flexible framework for tracking time-varying non-Poisson count data and may also have applications beyond neuroscience.