The Time-Rescaling Theorem and Its Application to Neural Spike Train Data Analysis

Brown, Emery N.; Barbieri, Riccardo; Ventura, Valérie; Kass, Robert E.; Frank, Loren M.

doi:10.1162/08997660252741149

Cited by 480 publications

(514 citation statements)

References 16 publications

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“…To find out how much the observed phenomena depend on the probabilistic structure of the recorded spike trains, the experimental results were compared with the results of the analysis of surrogate data. We used a stochastic modeling approach: the experimental spike trains were treated as realizations of a point process under the assumption that such a process is completely characterized by the conditional intensity function (Johnson, 1996;Brown et al, 2002) defined as the probability to observe a spike at time t given the spiking history H t up to t:…”

Section: Resultsmentioning

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: Resultsmentioning

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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show abstract

“…The theory of point process [14], which has been introduced in not only marketing science [4] but also such diverse disciplines as neuroscience [15] and seismology [16], provides a powerful tool for modeling and analyzing the stochastic structure of point events occurring in continuous time. In the point process framework, the purchase behavior of a customer is characterized by the purchase rate, that is, the instantaneous probability for a customer to make a purchase decision at each point in time [4], [7], [17].…”

Section: Estimating Purchase Behavior Via Point Processmentioning

confidence: 99%

“…The theorem has been applied in such fields as neuroscience [15] and seismology [16], mainly for evaluating the goodness-of-fit of point process models to data. In this paper, we utilize the idea of time-rescaling for constructing our flexible and tractable model (Sect.…”

Section: Time-rescaling Theoremmentioning

confidence: 99%

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Analyzing Temporal Dynamics of Consumer's Behavior Based on Hierarchical Time-Rescaling

Kim

Takaya

Sawada

2017

IEICE Trans. Inf. & Syst.

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SUMMARYImprovements in information technology have made it easier for industry to communicate with their customers, raising hopes for a scheme that can estimate when customers will want to make purchases. Although a number of models have been developed to estimate the timevarying purchase probability, they are based on very restrictive assumptions such as preceding purchase-event dependence and discrete-time effect of covariates. Our preliminary analysis of real-world data finds that these assumptions are invalid: self-exciting behavior, as well as marketing stimulus and preceding purchase dependence, should be examined as possible factors influencing purchase probability. In this paper, by employing the novel idea of hierarchical time rescaling, we propose a tractable but highly flexible model that can meld various types of intrinsic history dependency and marketing stimuli in a continuous-time setting. By employing the proposed model, which incorporates the three factors, we analyze actual data, and show that our model has the ability to precisely track the temporal dynamics of purchase probability at the level of individuals. It enables us to take effective marketing actions such as advertising and recommendations on timely and individual bases, leading to the construction of a profitable relationship with each customer.

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“…To evaluate goodness-of-fit for the heart beat probability model-point process adaptive filter algorithm, i.e., determine how well this model describes the sequence of ECG R -wave events, we use the Kolmogorov-Smirnov test based on the time-rescaling theorem for point processes (Brown et al, 2002, Barbieri et al, 2005Barbieri et al, 2006). Close agreement between the uniform transformation of the ordered observations (empirical quantiles) and the ordered observations from a uniform probability density (model quantiles) is true if and only if there is close agreement between the point process probability model and the series of R-R intervals.…”

Section: Model Goodness-of-fitmentioning

confidence: 99%

Application of dynamic point process models to cardiovascular control

Barbieri

Brown

2008

Biosystems

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The development of statistical models that accurately describe the stochastic structure of biological signals is a fast growing area in quantitative research. In developing a novel statistical paradigm based on Bayes' theorem applied to point processes, we are focusing our recent research on characterizing the physiological mechanisms involved in cardiovascular control. Results from a Tilt Table study point at our statistical framework as a valid model for the heart beat, as generated from complex mechanisms underlying cardiovascular control. The point process analysis provides new quantitative indices that could have important implications for research studies of cardiovascular and autonomic regulation and for monitoring of heart rate and heart rate variability measures in clinical settings.

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The Time-Rescaling Theorem and Its Application to Neural Spike Train Data Analysis

Cited by 480 publications

References 16 publications

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

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

Analyzing Temporal Dynamics of Consumer's Behavior Based on Hierarchical Time-Rescaling

Application of dynamic point process models to cardiovascular control

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