We derive exact analytical expressions for the cumulants of any orders of neuronal membrane potentials driven by spike trains in a multivariate Hawkes process model with excitation and inhibition. Such expressions can be used for the prediction and sensitivity analysis of the statistical behavior of the model over time, and to estimate the probability densities of neuronal membrane potentials using Gram-Charlier expansions. Our results are shown to provide a better alternative to Monte Carlo estimates via stochastic simulations, and computer codes based on combinatorial recursions are included.
翻译:我们得出精确分析的表达方式,说明在多变的霍克斯工艺模型中由钉钉火车驱动的神经膜潜能值的累积值,这种表达方式可以用来预测和敏感分析该模型在一段时间内的统计行为,并用Gram-Charlier扩展来估计神经膜潜能值的概率密度。我们的结果表明,通过蒸汽模拟,我们为蒙特卡洛估算值提供了更好的替代方法,并包括基于复数的计算机编码。