Likelihood Methods for Neural Spike Train Data Analysis

Brown, Emery; Barbieri, Riccardo; Eden, Uri T.; Frank, L. Matthew

doi:10.1201/9780203494462.ch9

Cited by 120 publications

(188 citation statements)

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“…To simplify model estimation, we further assumed the multiplicative form of the conditional intensity function (t͉H t ) ϭ 1 (t) ⅐ 2 (). In the multiplicative IMI process, the first component 1 (t) describes the time-dependent modulation of the spiking activity of the neuron reflecting its responsiveness to different stimuli (Berry and Meister, 1998;Brown et al, 2003;Schaette et al, 2005). The second component 2 (), which might be called "postimpulse probability" following Poggio and Viernstein (1964), reflects the membrane properties of the neuron including its refractory periods.…”

Section: Discussionmentioning

confidence: 99%

Variability of Visual Responses of Superior Colliculus Neurons Depends on Stimulus Velocity

Mochol

Wójcik²,

Wypych³

et al. 2010

J. Neurosci.

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Visually responding neurons in the superficial, retinorecipient layers of the cat superior colliculus receive input from two primarily parallel information processing channels, Y and W, which is reflected in their velocity response profiles. We quantified the timedependent variability of responses of these neurons to stimuli moving with different velocities by Fano factor (FF) calculated in discrete time windows. The FF for cells responding to low-velocity stimuli, thus receiving W inputs, increased with the increase in the firing rate. In contrast, the dynamics of activity of the cells responding to fast moving stimuli, processed by Y pathway, correlated negatively with FF whether the response was excitatory or suppressive. These observations were tested against several types of surrogate data. Whereas Poisson description failed to reproduce the variability of all collicular responses, the inclusion of secondary structure to the generating point process recovered most of the observed features of responses to fast moving stimuli. Neither model could reproduce the variability of low-velocity responses, which suggests that, in this case, more complex time dependencies need to be taken into account. Our results indicate that Y and W channels may differ in reliability of responses to visual stimulation. Apart from previously reported morphological and physiological differences of the cells belonging to Y and W channels, this is a new feature distinguishing these two pathways.

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Section: Discussionmentioning

confidence: 99%

Variability of Visual Responses of Superior Colliculus Neurons Depends on Stimulus Velocity

Mochol

Wójcik²,

Wypych³

et al. 2010

J. Neurosci.

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“…Because there is significant overlap between adjacent local likelihood intervals, we start the Newton-Raphson procedure at t with the previous local maximum-likelihood estimate at time t − . Model goodness-of-fit is based on the Kolmogorov-Smirnov (KS) test and associated KS statistics [23,28], along with autocorrelation plots testing the independence of the model-transformed intervals [23].…”

Section: Methodsmentioning

confidence: 99%

Inhomogeneous point-process entropy: An instantaneous measure of complexity in discrete systems

et al. 2014

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Measures of entropy have been widely used to characterize complexity, particularly in physiological dynamical systems modeled in discrete time. Current approaches associate these measures to finite single values within an observation window, thus not being able to characterize the system evolution at each moment in time. Here, we propose a new definition of approximate and sample entropy based on the inhomogeneous point-process theory. The discrete time series is modeled through probability density functions, which characterize and predict the time until the next event occurs as a function of the past history. Laguerre expansions of the Wiener-Volterra autoregressive terms account for the long-term nonlinear information. As the proposed measures of entropy are instantaneously defined through probability functions, the novel indices are able to provide instantaneous tracking of the system complexity. The new measures are tested on synthetic data, as well as on real data gathered from heartbeat dynamics of healthy subjects and patients with cardiac heart failure and gait recordings from short walks of young and elderly subjects. Results show that instantaneous complexity is able to effectively track the system dynamics and is not affected by statistical noise properties.

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“…In Equation (6), both the factors λ S (x(t)) and r(t − s * ) are dynamic, evolving simultaneously according to a state-space model specified by a point process adaptive filter Brown et al, 2003). This allowed the authors to describe the way the receptive fields evolve across space and time.…”

Section: Tracking Plasticity In Hippocampal Place Fieldsmentioning

confidence: 99%

“…The point-process likelihood function is then given by the simple and explicit pdf (Snyder and Miller, 1991;Brown et al, 2003;Paninski, 2004;Truccolo et al, 2005) …”

Section: Approximating the If Model Via Simpler Point-process Modelsmentioning

confidence: 99%

Statistical Models of Spike Trains

Paninski¹,

Brown²,

Iyengar³

2009

Stochastic Methods in Neuroscience

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Likelihood Methods for Neural Spike Train Data Analysis

Cited by 120 publications

References 1 publication

Variability of Visual Responses of Superior Colliculus Neurons Depends on Stimulus Velocity

Variability of Visual Responses of Superior Colliculus Neurons Depends on Stimulus Velocity

Inhomogeneous point-process entropy: An instantaneous measure of complexity in discrete systems

Statistical Models of Spike Trains

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