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Article Citation - WoS: 4Citation - Scopus: 6Statistical Inference for a Class of Startup Demonstration Tests(Taylor & Francis inc, 2019) Eryilmaz, SerkanIn this article, we develop a general statistical inference procedure for the probability of successful startup p in the case of startup demonstration tests when only the number of trials until termination of the experiment are observed. In particular, we define a class of startup demonstration tests and present expectation-maximization (EM) algorithm to get the maximum likelihood estimate of p for this class. Most of well-known startup testing procedures are involved in this class. Extension of the results to Markovian startups is also presented.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: 1Citation - Scopus: 1Adaptive Stimulus Design for Dynamic Recurrent Neural Network Models(Frontiers Media Sa, 2019) Doruk, R. Ozgur; Zhang, KechenWe present an adaptive stimulus design method for efficiently estimating the parameters of a dynamic recurrent network model with interacting excitatory and inhibitory neuronal populations. Although stimuli that are optimized for model parameter estimation should, in theory, have advantages over nonadaptive random stimuli, in practice it remains unclear in what way and to what extent an optimal design of time-varying stimuli may actually improve parameter estimation for this common type of recurrent network models. Here we specified the time course of each stimulus by a Fourier series whose amplitudes and phases were determined by maximizing a utility function based on the Fisher information matrix. To facilitate the optimization process, we have derived differential equations that govern the time evolution of the gradients of the utility function with respect to the stimulus parameters. The network parameters were estimated by maximum likelihood from the spike train data generated by an inhomogeneous Poisson process from the continuous network state. The adaptive design process was repeated in a closed loop, alternating between optimal stimulus design and parameter estimation from the updated stimulus-response data. Our results confirmed that, compared with random stimuli, optimally designed stimuli elicited responses with significantly better likelihood values for parameter estimation. Furthermore, all individual parameters, including the time constants and the connection weights, were recovered more accurately by the optimal design method. We also examined how the errors of different parameter estimates were correlated, and proposed heuristic formulas to account for the correlation patterns by an approximate parameter-confounding theory. Our results suggest that although adaptive optimal stimulus design incurs considerable computational cost even for the simplest excitatory-inhibitory recurrent network model, it may potentially help save time in experiments by reducing the number of stimuli needed for network parameter 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.
