Accurate statistical models of neural spike responses can characterize the information carried by neural populations. But the limited samples of spike counts during recording usually result in model overfitting. Besides, current models assume spike counts to be Poisson-distributed, which ignores the fact that many neurons demonstrate over-dispersed spiking behaviour. Although the Negative Binomial Generalized Linear Model (NB-GLM) provides a powerful tool for modeling over-dispersed spike counts, the maximum likelihood-based standard NB-GLM leads to highly variable and inaccurate parameter estimates. Thus, we propose a hierarchical parametric empirical Bayes method to estimate the neural spike responses among neuronal population. Our method integrates both Generalized Linear Models (GLMs) and empirical Bayes theory, which aims to (1) improve the accuracy and reliability of parameter estimation, compared to the maximum likelihood-based method for NB-GLM and Poisson-GLM; (2) effectively capture the over-dispersion nature of spike counts from both simulated data and experimental data; and (3) provide insight into both neural interactions and spiking behaviours of the neuronal populations. We apply our approach to study both simulated data and experimental neural data. The estimation of simulation data indicates that the new framework can accurately predict mean spike counts simulated from different models and recover the connectivity weights among neural populations. The estimation based on retinal neurons demonstrate the proposed method outperforms both NB-GLM and Poisson-GLM in terms of the predictive log-likelihood of held-out data. 1

中文翻译：

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通过经验贝叶斯构建高效灵活的尖峰列车模型


神经尖峰反应的准确统计模型可以表征神经群体携带的信息。但记录过程中尖峰计数样本有限通常会导致模型过度拟合。此外，当前模型假设尖峰计数呈泊松分布，忽略了许多神经元表现出过度分散的尖峰行为这一事实。尽管负二项式广义线性模型 (NB-GLM) 为过度分散的尖峰计数建模提供了强大的工具，但基于最大似然的标准 NB-GLM 会导致高度可变且不准确的参数估计。因此，我们提出了一种分层参数经验贝叶斯方法来估计神经元群体中的神经尖峰反应。我们的方法集成了广义线性模型（GLM）和经验贝叶斯理论，其目的是（1）与基于最大似然的 NB-GLM 和 Poisson-GLM 方法相比，提高参数估计的准确性和可靠性； （2）从模拟数据和实验数据中有效捕捉尖峰计数的过度分散性质； (3) 深入了解神经元群体的神经相互作用和尖峰行为。我们应用我们的方法来研究模拟数据和实验神经数据。模拟数据的估计表明，新框架可以准确预测不同模型模拟的平均尖峰计数，并恢复神经群体之间的连接权重。基于视网膜神经元的估计表明，所提出的方法在保留数据的预测对数似然方面优于 NB-GLM 和 Poisson-GLM。 1