%0 Journal Article %1 Brow_2002_325 %A Brown, Emery N %A Barbieri, Riccardo %A Ventura, Val�rie %A Kass, Robert E %A Frank, Loren M %D 2002 %J Neural Comput. %K 11802915 Action Animals, Gov't, Macaca, Models, Neurological, Neurons, Non-P.H.S., P.H.S., Pathways, Potentials, Probability Research Support, Theory, U.S. Visual %N 2 %P 325--346 %R 10.1162/08997660252741149 %T The time-rescaling theorem and its application to neural spike train data analysis. %U http://dx.doi.org/10.1162/08997660252741149 %V 14 %X 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 may be 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 tool for neural spike train data analysis.

@article{Brow_2002_325, abstract = {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 may be 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 tool for neural spike train data analysis.}, added-at = {2009-06-03T11:20:58.000+0200}, author = {Brown, Emery N and Barbieri, Riccardo and Ventura, Val�rie and Kass, Robert E and Frank, Loren M}, biburl = {https://www.bibsonomy.org/bibtex/2db144ff17fab41851ce5d1eaf4b49638/hake}, description = {The whole bibliography file I use.}, doi = {10.1162/08997660252741149}, file = {Brow_2002_325.pdf:Brow_2002_325.pdf:PDF}, interhash = {256caa78eca9a26cb98d2c62fb3fe8d2}, intrahash = {db144ff17fab41851ce5d1eaf4b49638}, journal = {Neural Comput.}, keywords = {11802915 Action Animals, Gov't, Macaca, Models, Neurological, Neurons, Non-P.H.S., P.H.S., Pathways, Potentials, Probability Research Support, Theory, U.S. Visual}, month = Feb, number = 2, pages = {325--346}, pmid = {11802915}, timestamp = {2009-06-03T11:21:06.000+0200}, title = {The time-rescaling theorem and its application to neural spike train data analysis.}, url = {http://dx.doi.org/10.1162/08997660252741149}, volume = 14, year = 2002 }