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.
- 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
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