On Firing Rate Estimation for Dependent Interspike Intervals

@article{Benedetto2015OnFR,
  title={On Firing Rate Estimation for Dependent Interspike Intervals},
  author={Elisa Benedetto and Federico Polito and Laura Sacerdote},
  journal={Neural Computation},
  year={2015},
  volume={27},
  pages={699-724}
}
Abstract If interspike intervals are dependent, the instantaneous firing rate does not catch important features of spike trains. In this case, the conditional instantaneous rate plays the role of the instantaneous firing rate for the case of samples of independent interspike intervals. If the conditional distribution of the interspikes intervals (ISIs) is unknown, it becomes difficult to evaluate the conditional firing rate. We propose a nonparametric estimator for the conditional instantaneous… 
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4 Citations
Background Citations
2
Methods Citations
1

4 Citations

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This paper uses equilibrium renewal and Markov renewal processes as spike train models as Spike train models to describe the Fano factor in the operational time and provides an illustration on experimental data.
Stochastic methods and models for neuronal activity and motor proteins
The main topic of this thesis is to specialize mathematical methods and construct stochastic models for describing and predict biological dynamics such as neuronal firing and acto-myosin sliding. …
Minimum divergence estimators for the Radon–Nikodym derivatives of the semi-Markov kernel
In this paper we face the problem of estimating the elements that define a homogeneous semi-Markov process. Given an observed sample path of the process in a finite interval , non-parametric…

References

SHOWING 1-10 OF 77 REFERENCES
Calculation of Interspike Intervals for Integrate-and-Fire Neurons with Poisson Distribution of Synaptic Inputs
TLDR
The results indicate that neurons functioning near their critical threshold, where the inputs are just sufficient to cause firing, display a large variability in their spike timings.
Mean Instantaneous Firing Frequency Is Always Higher Than the Firing Rate
TLDR
Three different definitions of firing frequency are compared in an effort to contribute to a better understanding of the input-output properties of a neuron.
Optimizing Time Histograms for Non-Poissonian Spike Trains
TLDR
Improvement in the goodness of fit of the time histogram is assessed and confirmed by numerically simulated non-Poissonian spike trains derived from the given fluctuating rate.
Neuronal spike trains and stochastic point processes. I. The single spike train.
Serial correlation in neural spike trains: experimental evidence, stochastic modeling, and single neuron variability.
TLDR
It is argued that the feature of a negative serial correlation is likely to be common to the class of spike-frequency-adapting neurons and that it might have been largely overlooked in extracellular single-unit recordings due to spike sorting errors.
Kernel bandwidth optimization in spike rate estimation
TLDR
It is revealed that the classical kernel smoother may exhibit goodness-of-fit comparable to, or even better than, that of modern sophisticated rate estimation methods, provided that the bandwidth is selected properly for a given set of spike data, according to the optimization methods presented here.
Adaptation reduces variability of the neuronal population code.
TLDR
A master equation for generalized non-renewal processes is employed to calculate the interval and count statistics of superimposed processes governed by a slow adaptation variable for an ensemble of neurons with spike-frequency adaptation, which results in the regularization of the population activity and an enhanced postsynaptic signal decoding.
Significance of joint-spike events based on trial-shuffling by efficient combinatorial methods
TLDR
A Monte-Carlo-based resampling procedure is suggested and it is demonstrated that the procedure yields an appropriate estimate of the distribution and reliable significance estimation and is able to systematically sample the coincidence counts from all trial combinations.
Parametric inference of neuronal response latency in presence of a background signal
Entropy and Information in Neural Spike Trains
TLDR
It is shown how to quantify this information, in bits, free from any assumptions about which features of the spike train or input signal are most important, and this approach is applied to the analysis of experiments on a motion sensitive neuron in the fly visual system.
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