  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.
