Fokker–Planck and Fortet Equation-Based Parameter Estimation for a Leaky Integrate-and-Fire Model with Sinusoidal and Stochastic Forcing
نویسندگان
چکیده
UNLABELLED 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 ABBREVIATIONS LIF Leaky integrate-and-fireISI: Interspike intervalSDE: Stochastic differential equationPDE: Partial differential equation.
منابع مشابه
Statistical Analysis of Neural Data: the Integrate-and-fire Neuron and Other Continuous-time State-space Models *
3 The “Fokker-Planck” equation is a partial differential equation that controls the evolution of the forward (and backward) probabilities 9 3.1 Deriving the “free” Fokker-Planck equation (no spike observations) . . . . . . 10 3.1.1 Conductance-based model . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.2 Computing mean firing rates in a network of GLM neurons . . . . . . 13 3.2 Incorpo...
متن کاملComputing likelihoods in the stochastic integrate-and-fire model: numerical methods
Recent work has examined the estimation of models of stimulus-driven neural activity in which a linear filtering process is followed by a nonlinear, probabilistic spiking stage. We analyze the estimation of one such model for which this nonlinear step is implemented by a noisy, leaky, integrate-and-fire mechanism with a spike-dependent after-current. We have formulated this problem in terms of ...
متن کاملNoisy threshold in neuronal models: connections with the noisy leaky integrate-and-fire model.
Providing an analytical treatment to the stochastic feature of neurons' dynamics is one of the current biggest challenges in mathematical biology. The noisy leaky integrate-and-fire model and its associated Fokker-Planck equation are probably the most popular way to deal with neural variability. Another well-known formalism is the escape-rate model: a model giving the probability that a neuron ...
متن کاملEscape rates in periodically driven Markov processes
We present an approximate analytical expression for the escape rate of time-dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrateand-fire model for neural spiking. The novel approximation is based on a discrete state Markovian modeling of the full long-time dynamics with time-dependent rates. It is valid in a wide parameter regime beyond the restrai...
متن کاملOptimal Design for Estimation in Diffusion Processes from First Hitting Times | SIAM/ASA Journal on Uncertainty Quantification | Vol. 5, NO. 1 | Society for Industrial and Applied Mathematics
We consider the optimal design problem for the Ornstein–Uhlenbeck process with fixed threshold, commonly used to describe a leaky, noisy integrate-and-fire neuron. We present a solution to the problem of devising the best external time-dependent perturbation to the process in order to facilitate the estimation of the characteristic time parameter for this process. The optimal design problem is ...
متن کامل