Abstract
Analysis of sinusoidal noisy leaky integrate-and-fire models and comparison with experimental data are important to understand the neural code and neural synchronization and rhythms. In this paper, we propose two methods to estimate input parameters using interspike interval data only. One is based on numerical solutions of the Fokker–Planck equation, and the other is based on an integral equation, which is fulfilled by the interspike interval probability density. This generalizes previous methods tailored to stationary data to the case of time-dependent input. The main contribution is a binning method to circumvent the problems of nonstationarity, and an easy-to-implement initializer for the numerical procedures. The methods are compared on simulated data.List of AbbreviationsLIF: Leaky integrate-and-fireISI: Interspike intervalSDE: Stochastic differential equationPDE: Partial differential equation
Highlights
Information processing in the nervous system is carried out by spike timings in neurons
A common assumption is that the data are well described by a renewal process, basing the statistical inference on the interspike intervals (ISIs), assuming these are realizations of independent and identically distributed random variables
In [3, 4], certain explicit moment relations derived from the Laplace transform of the first-passage time distribution are applied, but these are only valid under stimulation
Summary
Information processing in the nervous system is carried out by spike timings in neurons. To study the neural code in such a complicated system, a first step is to understand signal processing and transmission in single neurons. Stochastic leaky integrate-and-fire (LIF) neuronal models are a good compromise between biophysical realism and mathematical tractability, and are commonly applied as theoretical tools to study properties of real neuronal systems. A central issue is to perform statistical inference from experimental data and estimate model parameters. Many electrophysiological experiments on neurons, namely extra-cellular recordings, are only capable of detecting the time of the spike and not the detailed voltage trajectory leading up to the spike. Estimating the parameters of the LIF model from this type of data is equivalent to estimating the parameters of a stochastic model from the statistics of the first-passage times only. Since only partial information about the process is available, the statistical problem becomes more difficult, and no explicit expression for the likelihood is available
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