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.
%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
}