PMID- 20608868
OWN - NLM
STAT- MEDLINE
DCOM- 20110627
LR  - 20211020
IS  - 1530-888X (Electronic)
IS  - 0899-7667 (Print)
IS  - 0899-7667 (Linking)
VI  - 22
IP  - 10
DP  - 2010 Oct
TI  - Discrete time rescaling theorem: determining goodness of fit for discrete time 
      statistical models of neural spiking.
PG  - 2477-506
LID - 10.1162/NECO_a_00015 [doi]
AB  - One approach for understanding the encoding of information by spike trains is to 
      fit statistical models and then test their goodness of fit. The time-rescaling 
      theorem provides a goodness-of-fit test consistent with the point process nature 
      of spike trains. The interspike intervals (ISIs) are rescaled (as a function of 
      the model's spike probability) to be independent and exponentially distributed if 
      the model is accurate. A Kolmogorov-Smirnov (KS) test between the rescaled ISIs 
      and the exponential distribution is then used to check goodness of fit. This 
      rescaling relies on assumptions of continuously defined time and instantaneous 
      events. However, spikes have finite width, and statistical models of spike trains 
      almost always discretize time into bins. Here we demonstrate that finite temporal 
      resolution of discrete time models prevents their rescaled ISIs from being 
      exponentially distributed. Poor goodness of fit may be erroneously indicated even 
      if the model is exactly correct. We present two adaptations of the time-rescaling 
      theorem to discrete time models. In the first we propose that instead of assuming 
      the rescaled times to be exponential, the reference distribution be estimated 
      through direct simulation by the fitted model. In the second, we prove a discrete 
      time version of the time-rescaling theorem that analytically corrects for the 
      effects of finite resolution. This allows us to define a rescaled time that is 
      exponentially distributed, even at arbitrary temporal discretizations. We 
      demonstrate the efficacy of both techniques by fitting generalized linear models 
      to both simulated spike trains and spike trains recorded experimentally in monkey 
      V1 cortex. Both techniques give nearly identical results, reducing the 
      false-positive rate of the KS test and greatly increasing the reliability of 
      model evaluation based on the time-rescaling theorem.
FAU - Haslinger, Robert
AU  - Haslinger R
AD  - Martinos Center for Biomedical Imaging, Massachusetts General Hospital, 
      Charlestown, MA 02129, USA. robhh@nmr.mgh.harvard.edu
FAU - Pipa, Gordon
AU  - Pipa G
FAU - Brown, Emery
AU  - Brown E
LA  - eng
GR  - K25 NS052422/NS/NINDS NIH HHS/United States
GR  - DP1 OD003646/OD/NIH HHS/United States
GR  - K25 NS052422-02/NS/NINDS NIH HHS/United States
GR  - MH59733-07/MH/NIMH NIH HHS/United States
GR  - R01 MH059733/MH/NIMH NIH HHS/United States
GR  - DP1 OD003646-01/OD/NIH HHS/United States
PT  - Journal Article
PT  - Research Support, N.I.H., Extramural
PT  - Research Support, Non-U.S. Gov't
PL  - United States
TA  - Neural Comput
JT  - Neural computation
JID - 9426182
SB  - IM
MH  - Action Potentials/*physiology
MH  - Algorithms
MH  - Animals
MH  - Computer Simulation/statistics & numerical data
MH  - Haplorhini
MH  - Humans
MH  - *Models, Neurological
MH  - *Models, Statistical
MH  - *Neural Networks, Computer
MH  - Poisson Distribution
MH  - Reaction Time/physiology
MH  - Reproducibility of Results
MH  - Time Factors
PMC - PMC2932849
MID - NIHMS186123
EDAT- 2010/07/09 06:00
MHDA- 2011/06/28 06:00
PMCR- 2011/10/01
CRDT- 2010/07/09 06:00
PHST- 2010/07/09 06:00 [entrez]
PHST- 2010/07/09 06:00 [pubmed]
PHST- 2011/06/28 06:00 [medline]
PHST- 2011/10/01 00:00 [pmc-release]
AID - 10.1162/NECO_a_00015 [doi]
PST - ppublish
SO  - Neural Comput. 2010 Oct;22(10):2477-506. doi: 10.1162/NECO_a_00015.