Many systems with propagation dynamics, such as spike propagation in neural networks and spreading of infectious diseases, can be approximated by autoregressive models. The estimation of model parameters can be complicated by the experimental limitation that one observes only a fraction of the system (subsampling) and potentially time-dependent parameters, leading to incorrect estimates. We show analytically how to overcome the subsampling bias when estimating the propagation rate for systems with certain non-stationary external input. This approach is readily applicable to trial-based experimental setups and seasonal fluctuations, as demonstrated on spike recordings from monkey prefrontal cortex and spreading of norovirus and measles.

中文翻译：

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表征具有非平稳外部输入的二次采样系统的扩散动力学

可以通过自回归模型来近似许多具有传播动力学的系统，例如神经网络中的尖峰传播和传染病传播。模型参数的估计可能会由于实验上的局限性而变得复杂，后者只能观察到系统的一小部分（二次采样）以及可能与时间相关的参数，从而导致估计不正确。我们分析性地显示了在估计具有某些非平稳外部输入的系统的传播速率时，如何克服二次采样偏差。这种方法很容易适用于基于试验的实验设置和季节性波动，如猴子前额叶皮层的峰值记录以及诺如病毒和麻疹的传播所证明的那样。