Discrete time rescaling theorem: determining goodness of fit for discrete time statistical models of neural spiking.
Discrete time rescaling theorem: determining goodness of fit for discrete time statistical models of neural spiking.
复制标题
DOI：
10.1162/neco_a_00015
复制
发表时间：
2010-10
影响因子：
2.9
通讯作者：
Brown E
中科院分区：
文献类型：
--
作者：
Haslinger R;Pipa G;Brown E
理解锋电位序列信息编码的一种方法是拟合统计模型，然后测试其拟合优度。时间重新标度定理提供了与尖峰序列的点过程性质一致的拟合优度检验。如果模型是准确的，则将峰间间隔（ISI）重新缩放（作为模型的峰电位概率的函数）为独立的和指数分布的。然后使用重新标度的ISI和指数分布之间的Kolmogorov Smirnov（KS）检验来检查拟合优度。这种重新缩放依赖于连续定义的时间和瞬时事件的假设。然而，尖峰脉冲具有有限的宽度，并且尖峰脉冲序列的统计模型几乎总是将时间离散化到箱中。在这里，我们证明了有限的时间分辨率的离散时间模型，防止其重新缩放的ISI是指数分布。即使模型完全正确，也可能错误地指示拟合优度差。我们提出了两个适应的时间重新标度定理离散时间模型。在第一个，我们建议，而不是假设重新标度的时间是指数，参考分布估计通过直接模拟的拟合模型。在第二，我们证明了一个离散时间版本的时间重新标度定理，分析纠正有限分辨率的影响。这使我们能够定义一个重新标度的时间是指数分布的，即使在任意的时间离散。我们证明了这两种技术的有效性，通过拟合广义线性模型（GLM），以模拟尖峰列车和尖峰列车实验记录在猴V1皮层。这两种技术给出了几乎相同的结果，降低了KS测试的假阳性率，并大大增加了基于时间重新标度定理的模型评估的可靠性。
One approach for understanding the encoding of information by spike trains is to fit statistical models and then test their goodness of fit. The time rescaling theorem provides a goodness of fit test consistent with the point process nature of spike trains. The interspike intervals (ISIs) are rescaled (as a function of the model’s spike probability) to be independent and exponentially distributed if the model is accurate. A Kolmogorov Smirnov (KS) test between the rescaled ISIs and the exponential distribution is then used to check goodness of fit. This rescaling relies upon assumptions of continuously defined time and instantaneous events. However spikes have finite width and statistical models of spike trains almost always discretize time into bins. Here we demonstrate that finite temporal resolution of discrete time models prevents their rescaled ISIs from being exponentially distributed. Poor goodness of fit may be erroneously indicated even if the model is exactly correct. We present two adaptations of the time rescaling theorem to discrete time models. In the first we propose that instead of assuming the rescaled times to be exponential, the reference distribution be estimated through direct simulation by the fitted model. In the second, we prove a discrete time version of the time rescaling theorem which analytically corrects for the effects of finite resolution. This allows us to define a rescaled time which is exponentially distributed, even at arbitrary temporal discretizations. We demonstrate the efficacy of both techniques by fitting Generalized Linear Models (GLMs) to both simulated spike trains and spike trains recorded experimentally in monkey V1 cortex. Both techniques give nearly identical results, reducing the false positive rate of the KS test and greatly increasing the reliability of model evaluation based upon the time rescaling theorem.