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

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Standard

Estimation in the partially observed stochastic Morris-Lecar neuronal model with particle filter and stochastic approximation methods. / Ditlevsen, Susanne; Samson, Adeline.

I: Annals of Applied Statistics, Bind 8, Nr. 2, 2014, s. 674-702.

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Ditlevsen, S & Samson, A 2014, 'Estimation in the partially observed stochastic Morris-Lecar neuronal model with particle filter and stochastic approximation methods', Annals of Applied Statistics, bind 8, nr. 2, s. 674-702. https://doi.org/10.1214/14-AOAS729

APA

Ditlevsen, S., & Samson, A. (2014). Estimation in the partially observed stochastic Morris-Lecar neuronal model with particle filter and stochastic approximation methods. Annals of Applied Statistics, 8(2), 674-702. https://doi.org/10.1214/14-AOAS729

Vancouver

Ditlevsen S, Samson A. Estimation in the partially observed stochastic Morris-Lecar neuronal model with particle filter and stochastic approximation methods. Annals of Applied Statistics. 2014;8(2):674-702. https://doi.org/10.1214/14-AOAS729

Author

Ditlevsen, Susanne ; Samson, Adeline. / Estimation in the partially observed stochastic Morris-Lecar neuronal model with particle filter and stochastic approximation methods. I: Annals of Applied Statistics. 2014 ; Bind 8, Nr. 2. s. 674-702.

Bibtex

@article{44a1ee6d72514b669b2f8d7ca74bd595,
title = "Estimation in the partially observed stochastic Morris-Lecar neuronal model with particle filter and stochastic approximation methods",
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.",
author = "Susanne Ditlevsen and Adeline Samson",
year = "2014",
doi = "10.1214/14-AOAS729",
language = "English",
volume = "8",
pages = "674--702",
journal = "Annals of Applied Statistics",
issn = "1932-6157",
publisher = "Institute of Mathematical Statistics",
number = "2",

}

RIS

TY - JOUR

T1 - Estimation in the partially observed stochastic Morris-Lecar neuronal model with particle filter and stochastic approximation methods

AU - Ditlevsen, Susanne

AU - Samson, Adeline

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

U2 - 10.1214/14-AOAS729

DO - 10.1214/14-AOAS729

M3 - Journal article

VL - 8

SP - 674

EP - 702

JO - Annals of Applied Statistics

JF - Annals of Applied Statistics

SN - 1932-6157

IS - 2

ER -

ID: 122431320