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45
The TimeRescaling Theorem and Its Application to Neural Spike Train Data Analysis
 NEURAL COMPUTATION
, 2001
"... 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 goodnessoffit is a challenging problem for point pro ..."
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Cited by 131 (23 self)
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, inhomogeneous Poisson, and inhomogeneous Markov interval models of neural spike trains from the sup
NOTE Communicated by Jonathan Victor The TimeRescaling Theorem and Its Application to Neural Spike Train
"... Measuring agreement between a statistical model and a spike train data series, that is, evaluating goodness of �t, is crucial for establishing the model’s validity prior to using it to make inferences about a particular neural system. Assessing goodnessof�t is a challenging problem for point proce ..."
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, inhomogeneous Poisson, and inhomogeneou s Markov interval models of neural spike trains from the supNeural Computation 14, 325–346 (2001)
Estimating statistics of neuronal dynamics via Markov chains
, 2000
"... We present an ecient computational method for estimating the mean and variance of interspike intervals dened by the timing of spikes in typical orbits of onedimensional neuronal maps. This is equivalent to nding the mean and variance of return times of orbits to particular regions of phase spac ..."
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Cited by 2 (0 self)
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space. Rather than computing estimates directly from time series, the system is modelled as a nite state Markov chain to extract stationary behaviour in the form of invariant measures and average absorption times. Ergodictheoretic formulae are then applied to produce the estimates without the need
Spikefrequency adapting neural ensembles: Beyond mean adaptation and renewal theories
 Neural Computation
, 2007
"... We propose a Markov process model for spikefrequency adapting neural ensembles which synthesizes existing meanadaptation approaches, population density methods, and inhomogeneous renewal theory, resulting in a unied and tractable framework which goes beyond renewal and meanadaptation theories by ..."
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Cited by 18 (1 self)
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We propose a Markov process model for spikefrequency adapting neural ensembles which synthesizes existing meanadaptation approaches, population density methods, and inhomogeneous renewal theory, resulting in a unied and tractable framework which goes beyond renewal and meanadaptation theories
Efficient spikesorting of multistate neurons using interspike nonparametric method for automatic neural spikes clustering 23 hal00639412, version 1  9 Nov 2011 intervals information. Journal of neuroscience methods
, 2006
"... We demonstrate the efficacy of a new spikesorting method based on a Markov Chain Monte Carlo (MCMC) algorithm by applying it to real data recorded from Purkinje cells (PCs) in young rat cerebellar slices. This algorithm is unique in its capability to estimate and make use of the firing statistics a ..."
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Cited by 15 (0 self)
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We demonstrate the efficacy of a new spikesorting method based on a Markov Chain Monte Carlo (MCMC) algorithm by applying it to real data recorded from Purkinje cells (PCs) in young rat cerebellar slices. This algorithm is unique in its capability to estimate and make use of the firing statistics
LETTER Communicated by Adrienne Fairhall Spike Train Probability Models for StimulusDriven Leaky IntegrateandFire Neurons
"... Mathematical models of neurons are widely used to improve understanding of neuronal spiking behavior. These models can produce artificial spike trains that resemble actual spike train data in important ways, but they are not very easy to apply to the analysis of spike train data. Instead, statistica ..."
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, statistical methods based on point process models of spike trains provide a wide range of dataanalytical techniques. Two simplified point process models have been introduced in the literature: the timerescaled renewal process (TRRP) and the multiplicative inhomogeneous Markov interval (mIMI) model
Journal of Neuroscience Methods 105 (2001) 25–37 Construction and analysis of nonPoisson stimulusresponse models of neural spiking activity
"... A paradigm for constructing and analyzing nonPoisson stimulusresponse models of neural spike train activity is presented. Inhomogeneous gamma (IG) and inverse Gaussian (IIG) probability models are constructed by generalizing the derivation of the inhomogeneous Poisson (IP) model from the exponenti ..."
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A paradigm for constructing and analyzing nonPoisson stimulusresponse models of neural spike train activity is presented. Inhomogeneous gamma (IG) and inverse Gaussian (IIG) probability models are constructed by generalizing the derivation of the inhomogeneous Poisson (IP) model from
A new look at statespace models for neural data
 Journal of Computational Neuroscience
, 2010
"... State space methods have proven indispensable in neural data analysis. However, common methods for performing inference in statespace models with nonGaussian observations rely on certain approximations which are not always accurate. Here we review direct optimization methods that avoid these appro ..."
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Cited by 53 (25 self)
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these approximations, but that nonetheless retain the computational efficiency of the approximate methods. We discuss a variety of examples, applying these direct optimization techniques to problems in spike train smoothing, stimulus decoding, parameter estimation, and inference of synaptic properties. Along the way
Slice Normalized Dynamic Markov Logic Networks
"... Markov logic is a widely used tool in statistical relational learning, which uses a weighted firstorder logic knowledge base to specify a Markov random field (MRF) or a conditional random field (CRF). In many applications, a Markov logic network (MLN) is trained in one domain, but used in a differe ..."
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model, slice normalized dynamic Markov logic networks (SNDMLN), that suffers from none of these issues. It supports efficient online inference, and can directly model influences between variables within a time slice that do not have a causal direction, in contrast with fully directed models (e.g., DBNs
Sampling Properties of the Spectrum and Coherency of Sequences of Action Potentials
 Neural Computation
"... The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This paper begins with a review of these quantities, their interpretation and how they may be estimated. A discussion of how to assess the statis ..."
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Cited by 54 (4 self)
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on a doubly stochastic inhomogeneous Poisson process model in which the rate functions are drawn from a low variance Gaussian process. It is found that, in contrast to continuous processes, the variance of the estimators cannot be reduced by smoothing beyond a scale which is set by the number of point
Results 1  10
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