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Article Neuron Modeling: Estimating the Parameters of a Neuron Model From Neural Spiking Data(Tubitak Scientific & Technological Research Council Turkey, 2018) Doruk, Resat OzgurWe present a modeling study aiming at the estimation of the parameters of a single neuron model from neural spiking data. The model receives a stimulus as input and provides the firing rate of the neuron as output. The neural spiking data will be obtained from point process simulation. The resultant data will be used in parameter estimation based on the inhomogeneous Poisson maximum likelihood method. The model will be stimulated by various forms of stimuli, which are modeled by a Fourier series (FS), exponential functions, and radial basis functions (RBFs). Tabulated results presenting cases with different sample sizes (# of repeated trials), stimulus component sizes (FS and RBF), amplitudes, and frequency ranges (FS) will be presented to validate the approach and provide a means of comparison. The results showed that regardless of the stimulus type, the most effective parameter on the estimation performance appears to be the sample size. In addition, the lowest variance of the estimates is obtained when a Fourier series stimulus is applied in the estimation.Article Citation - WoS: 13Citation - Scopus: 16Estimating the Parameters of Fitzhugh-Nagumo Neurons From Neural Spiking Data(Mdpi, 2019) Doruk, Resat Ozgur; Abosharb, LailaA theoretical and computational study on the estimation of the parameters of a single Fitzhugh-Nagumo model is presented. The difference of this work from a conventional system identification is that the measured data only consist of discrete and noisy neural spiking (spike times) data, which contain no amplitude information. The goal can be achieved by applying a maximum likelihood estimation approach where the likelihood function is derived from point process statistics. The firing rate of the neuron was assumed as a nonlinear map (logistic sigmoid) relating it to the membrane potential variable. The stimulus data were generated by a phased cosine Fourier series having fixed amplitude and frequency but a randomly shot phase (shot at each repeated trial). Various values of amplitude, stimulus component size, and sample size were applied to examine the effect of stimulus to the identification process. Results are presented in tabular and graphical forms, which also include statistical analysis (mean and standard deviation of the estimates). We also tested our model using realistic data from a previous research (H1 neurons of blowflies) and found that the estimates have a tendency to converge.
