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.
翻译:神经螺旋反应的精确统计模型可以成为神经人群所携带信息的特征。 但是,在记录期间的峰值测量样本有限通常导致模型的超配。 此外,目前模型假设峰值计数为Poisson分布式,这忽略了许多神经元表现出过度分散的弹簧行为的事实。虽然负二进制通用线性模型(NB-GLM)提供了一种强大的工具,用于模拟超分散的峰值计数,但基于最大可能性的标准NB-GLM 导致高度可变和不准确的参数估计。因此,我们提出一个等级参数性实验性贝斯测算法,用以估计神经人群神经峰值反应反应反应。我们的方法结合了通用线性模型(GLMS)和实验性贝斯理论,目的是(1) 提高参数估计的准确性和可靠性,而NBG-GLM和Poisson-GLM则提供了基于最大可能性的方法;(2) 有效地从模拟数据和实验数据中,测量了钉值的过度预测性预测性预测性质;(3) 对神经峰值的精确性模型进行了精确性分析;GLMeximal Studal Studal数据分析,以显示了我们进行了神经值数据流值的模型的精确性数据分析。