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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 (\u03bb and \u03bd). We then fit our model to neural data from neurons in primary visual cortex, \u201cplace cells\u201d 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.<\/jats:p>","DOI":"10.1162\/neco_a_01593","type":"journal-article","created":{"date-parts":[[2023,5,15]],"date-time":"2023-05-15T22:20:40Z","timestamp":1684189240000},"page":"1187-1208","update-policy":"http:\/\/dx.doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":3,"title":["Dynamic Modeling of Spike Count Data With Conway-Maxwell Poisson Variability"],"prefix":"10.1162","volume":"35","author":[{"given":"Ganchao","family":"Wei","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Connecticut, Storrs, CT 06269, U.S.A. ganchao.wei@uconn.edu"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ian H.","family":"Stevenson","sequence":"additional","affiliation":[{"name":"Department of Psychological Sciences and Department of Biomedical Engineering, 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