The time-rescaling theorem and its application to neural spike train data analysis
The time-rescaling theorem and its application to neural spike train data analysis
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DOI：
10.1162/08997660252741149
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发表时间：
2002-02-01
影响因子：
2.9
通讯作者：
Frank, LM
中科院分区：
文献类型：
--
作者：
Brown, EN;Barbieri, R;Frank, LM
测量统计模型和尖峰序列数据序列之间的一致性，即评估拟合优度，对于在使用模型对特定神经系统进行推断之前建立模型的有效性至关重要。评估拟合优度对于点过程神经锋电位训练模型是一个具有挑战性的问题，特别是对于基于直方图的模型，如Perstimulus时间直方图（PSTH）和通过锋电位训练平滑估计的速率函数。时间重标度定理是概率论中的一个著名结果，它指出任何具有可积条件强度函数的点过程都可以转化为具有单位速率的Poisson过程。我们描述了如何定理可用于开发拟合优度测试参数和直方图为基础的点过程模型的神经尖峰列车。我们应用这些测试中的两个例子：比较PSTH，非齐次泊松，和非齐次马尔可夫间隔模型的神经尖峰列车从补充眼领域的猕猴和时间和空间的平滑比较，非齐次泊松，非齐次伽马，和非齐次逆高斯模型大鼠海马位置细胞尖峰活动。为了帮助神经科学的研究人员更容易理解时间重新标度定理背后的逻辑，我们提出了一个只使用基本概率论论证的证明。我们还展示了如何定理可用于模拟一个一般的点过程模型的尖峰列车。我们的范例使得有可能直接比较参数和基于直方图的神经尖峰序列模型。这些结果表明，时间重标度定理可以为神经放电序列数据分析提供一个有价值的工具。
Measuring agreement between a statistical model and a spike train data series, that is, evaluating goodness of fit, is crucial for establishing the model's validity prior to using it to make inferences about a particular neural system. Assessing goodness-of-fit is a challenging problem for point process neural spike train models, especially for histogram-based models such as perstimulus time histograms (PSTH) and rate functions estimated by spike train smoothing. The time-rescaling theorem is a well-known result in probability theory, which states that any point process with an integrable conditional intensity function maybe transformed into a Poisson process with unit rate. We describe how the theorem may be used to develop goodness-of-fit tests for both parametric and histogram-based point process models of neural spike trains. We apply these tests in two examples: a comparison of PSTH, inhomogeneous Poisson, and inhomogeneous Markov interval models of neural spike trains from the supplementary eye field of a macque monkey and a comparison of temporal and spatial smoothers, inhomogeneous Poisson, inhomogeneous gamma, and inhomogeneous inverse gaussian models of rat hippocampal place cell spiking activity. To help make the logic behind the time-rescaling theorem more accessible to researchers in neuroscience, we present a proof using only elementary probability theory arguments. We also show how the theorem may be used to simulate a general point process model of a spike train. Our paradigm makes it possible to compare parametric and histogram-based neural spike train models directly. These results suggest that the time-rescaling theorem can be a valuable toot for neural spike train data analysis.