A novel point process model for neuronal spike trains - Ma, Yijia; Wu, Wei (Frontiers in Applied Mathematics and Statistics, 2024)
Point process provides a mathematical framework for characterizing neuronal spiking activities. Classical point process methods often focus on the conditional intensity function, which describes the likelihood at any time point given its spiking history. However, these models do not describe the central tendency or importance of the spike train observations. Based on the recent development on the notion of center-outward rank for point process, we propose a new modeling framework on spike train data. The new likelihood of a spike train is a product of the marginal probability on the number of spikes and the probability of spike timings conditioned on the same number. In particular, the conditioned distribution is calculated by adopting the well-known Isometric Log-Ratio transformation. We systematically compare the new likelihood with the state-of-the-art point process likelihoods in terms of ranking, outlier detection, and classification using simulations and real spike train data. This new framework can effectively identify templates as well as outliers in spike train data. It also provides a reasonable model, and the parameters can be efficiently estimated with conventional maximum likelihood methods. It is found that the proposed likelihood provides an appropriate ranking on the spike train observations, effectively detects outliers, and accurately conducts classification tasks in the given data.