Point process regression models, based on generalized linear model (GLM) technology, have been widely used for spike train analysis, but a recent paper by Gerhard et al. described a kind of instability, in which fitted models can generate simulated spike trains with explosive firing rates. We analyze the problem by extending the methods of Gerhard et al. First, we improve their instability diagnostic and extend it to a wider class of models. Next, we point out some common situations in which instability can be traced to model lack of fit. Finally, we investigate distinctions between models that use a single filter to represent the effects of all spikes prior to any particular time t, as in a 2008 paper by Pillow et al., and those that allow different filters for each spike prior to time t, as in a 2001 paper by Kass and Ventura. We re-analyze the data sets used by Gerhard et al., introduce an additional data set that exhibits bursting, and use a well-known model described by Izhikevich to simulate spike trains from various ground truth scenarios. We conclude that models with multiple filters tend to avoid instability, but there are unlikely to be universal rules. Instead, care in data fitting is required and models need to be assessed for each unique set of data.

中文翻译：

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点过程加标神经元模型的稳定性。

基于广义线性模型（GLM）技术的点过程回归模型已被广泛用于尖峰序列分析，但是Gerhard等人最近发表了一篇论文。他描述了一种不稳定性，在这种不稳定性中，拟合模型可以生成具有爆炸射击速率的模拟尖峰序列。我们通过扩展Gerhard等人的方法来分析问题。首先，我们改进他们的不稳定性诊断并将其扩展到更广泛的模型类别。接下来，我们指出一些常见的情况，在这些情况下，可以将不稳定性追踪为缺乏拟合的模型。最后，我们研究了使用单个滤波器表示任何特定时间t之前所有尖峰的影响的模型之间的区别，例如在Pillow等人的2008年论文中，以及那些使用针对时间t之前的每个尖峰使用不同滤波器的模型之间的区别，例如Kass和Ventura在2001年的论文中。我们对Gerhard等人使用的数据集进行了重新分析，引入了另一个呈现爆发的数据集，并使用Izhikevich描述的众所周知的模型来模拟来自各种地面真实情况的峰值序列。我们得出的结论是，带有多个过滤器的模型倾向于避免不稳定性，但是不太可能存在通用规则。相反，需要注意数据拟合，并且需要针对每个唯一的数据集评估模型。