The Annals of Applied Statistics

Estimation in the partially observed stochastic Morris–Lecar neuronal model with particle filter and stochastic approximation methods

Susanne Ditlevsen and Adeline Samson

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Abstract

Parameter estimation in multidimensional diffusion models with only one coordinate observed is highly relevant in many biological applications, but a statistically difficult problem. In neuroscience, the membrane potential evolution in single neurons can be measured at high frequency, but biophysical realistic models have to include the unobserved dynamics of ion channels. One such model is the stochastic Morris–Lecar model, defined by a nonlinear two-dimensional stochastic differential equation. The coordinates are coupled, that is, the unobserved coordinate is nonautonomous, the model exhibits oscillations to mimic the spiking behavior, which means it is not of gradient-type, and the measurement noise from intracellular recordings is typically negligible. Therefore, the hidden Markov model framework is degenerate, and available methods break down. The main contributions of this paper are an approach to estimate in this ill-posed situation and nonasymptotic convergence results for the method. Specifically, we propose a sequential Monte Carlo particle filter algorithm to impute the unobserved coordinate, and then estimate parameters maximizing a pseudo-likelihood through a stochastic version of the Expectation–Maximization algorithm. It turns out that even the rate scaling parameter governing the opening and closing of ion channels of the unobserved coordinate can be reasonably estimated. An experimental data set of intracellular recordings of the membrane potential of a spinal motoneuron of a red-eared turtle is analyzed, and the performance is further evaluated in a simulation study.

Article information

Source
Ann. Appl. Stat. Volume 8, Number 2 (2014), 674-702.

Dates
First available in Project Euclid: 1 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1404229510

Digital Object Identifier
doi:10.1214/14-AOAS729

Mathematical Reviews number (MathSciNet)
MR3262530

Zentralblatt MATH identifier
06333772

Keywords
Sequential Monte Carlo diffusions pseudo likelihood Stochastic Approximation Expectation Maximization motoneurons conductance-based neuron models membrane potential

Citation

Ditlevsen, Susanne; Samson, Adeline. Estimation in the partially observed stochastic Morris–Lecar neuronal model with particle filter and stochastic approximation methods. Ann. Appl. Stat. 8 (2014), no. 2, 674--702. doi:10.1214/14-AOAS729. https://projecteuclid.org/euclid.aoas/1404229510


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