The time-rescaling theorem and its application to neural spike train data analysis

被引:377
作者
Brown, EN [1 ]
Barbieri, R
Ventura, V
Kass, RE
Frank, LM
机构
[1] Massachusetts Gen Hosp, Dept Anesthesia & Crit Care, Neurosci Stat Res Lab, Boston, MA 02114 USA
[2] MIT, Harvard Med Sch, Div Hlth Sci & Technol, Cambridge, MA 02139 USA
[3] Carnegie Mellon Univ, Dept Stat, Ctr Neural Basis Cognit, Pittsburgh, PA 15213 USA
关键词
D O I
10.1162/08997660252741149
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
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.
引用
收藏
页码:325 / 346
页数:22
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