@article{5c34645683594b1bb3309c0acd5b5a25,
title = "Data Assimilation Methods for Neuronal State and Parameter Estimation",
abstract = "This tutorial illustrates the use of data assimilation algorithms to estimate unobserved variables and unknown parameters of conductance-based neuronal models. Modern data assimilation (DA) techniques are widely used in climate science and weather prediction, but have only recently begun to be applied in neuroscience. The two main classes of DA techniques are sequential methods and variational methods. We provide computer code implementing basic versions of a method from each class, the Unscented Kalman Filter and 4D-Var, and demonstrate how to use these algorithms to infer several parameters of the Morris–Lecar model from a single voltage trace. Depending on parameters, the Morris–Lecar model exhibits qualitatively different types of neuronal excitability due to changes in the underlying bifurcation structure. We show that when presented with voltage traces from each of the various excitability regimes, the DA methods can identify parameter sets that produce the correct bifurcation structure even with initial parameter guesses that correspond to a different excitability regime. This demonstrates the ability of DA techniques to perform nonlinear state and parameter estimation and introduces the geometric structure of inferred models as a novel qualitative measure of estimation success. We conclude by discussing extensions of these DA algorithms that have appeared in the neuroscience literature.",
keywords = "Conductance-based models, Data assimilation, Neuronal excitability, Parameter estimation",
author = "Moye, {Matthew J.} and Diekman, {Casey O.}",
note = "Funding Information: Acknowledgements We thank Tyrus Berry and Franz Hamilton for helpful discussions about the UKF and for sharing code, and Nirag Kadakia and Paul Rozdeba for helpful discussions about 4D-Var methods and for sharing code. MM also benefited from lectures and discussions at the Mathematics and Climate Summer Graduate Program held at the University of Kansas in 2016, which was sponsored by the Institute for Mathematics and its Applications and the Mathematics and Climate Research Network. Funding Information: We thank Tyrus Berry and Franz Hamilton for helpful discussions about the UKF and for sharing code, and Nirag Kadakia and Paul Rozdeba for helpful discussions about 4D-Var methods and for sharing code. MM also benefited from lectures and discussions at the Mathematics and Climate Summer Graduate Program held at the University of Kansas in 2016, which was sponsored by the Institute for Mathematics and its Applications and the Mathematics and Climate Research Network. The MATLAB code used in this study is provided as Supplementary Material. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Funding Information: Funding This work was supported in part by NSF grants DMS-1412877 and DMS-1555237, and U.S. Army Research Office grant W911NF-16-1-0584. The funding bodies had no role in the design of the study and collection, analysis, and interpretation of data and in writing the manuscript should be declared. Publisher Copyright: {\textcopyright} 2018, The Author(s).",
year = "2018",
month = dec,
day = "1",
doi = "10.1186/s13408-018-0066-8",
language = "English (US)",
volume = "8",
journal = "Journal of Mathematical Neuroscience",
issn = "2190-8567",
publisher = "Springer Verlag",
number = "1",
}