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Abstract:
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Estimating the parameters of stochastic models using only observed first-passage times (FPTs) is an important area of research that has direct applications in computational neural modeling. Here we present a sequential monte carlo (SMC) approach to estimate from an Ornstein-Uhlenbeck (OU) process parameters related to the asymptotic mean, the decay rate, and the process noise using only an observed set of FPTs. The challenge is to efficiently compute trajectories from a particular OU model with the observed FPTs. We construct a new iterative algorithm that allows us to estimate the (distribution of) parameters for an OU process, or more general dynamical models, by deriving a set of forward and backward iterative equations to compute the required conditional distribution. We implemented our algorithm on a small set of simulated data (20-50 FPTs), and found that it could accurately and efficiently estimate (distribution of) all identifiable parameters simultaneously. We also show that our estimator is consistent and explore its convergence rate. Finally, we discuss how this approach can be generalized to a wide class of dynamic models for neural spiking systems.
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