Dynamic Modeling of Spike Count Data With Conway-Maxwell Poisson Variability

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, we developed a dynamic model with Conway-Maxwell Poisson (CMP) observations. The CMP distribution can flexibly describe firing patterns that are both under- and overdispersed 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 (λ and ν). We then fit our model to neural data from neurons in primary visual cortex, “place cells” in the hippocampus, and a speed-tuned neuron in the anterior pretectal nucleus. We find that this method outperforms 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.

Calibrating Bayesian decoders of neural spiking activity

“…However, additional work is needed to better understand the alignment of perceptual/behavioral uncertainty and decoder posterior uncertainty (Panzeri et al, 2017). Models with more accurate descriptions of single neuron variability (Gao et al, 2015; Ghanbari et al, 2019), with nonstationarity (Shanechi et al, 2016; Wei and Stevenson, 2023), additional stimulus/movement nonlinearities (Schwartz and Simoncelli, 2001), state-dependence (Panzeri et al, 2016), and with more complex latent structure (Glaser et al, 2020a; Williams et al, 2020; Sokoloski et al, 2021; Williams and Linderman, 2021) may all show better coverage while maintaining coherence. Our results here indicate that Bayesian decoders of spiking activity are not necessarily well calibrated by default.…”