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Using Monte Carlo Particle Methods to Estimate and Quantify Uncertainty in Periodic Parameters (Research)

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Advances in Mathematical Sciences

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 21))

Abstract

Estimating and quantifying uncertainty in system parameters remains a big challenge in applied and computational mathematics. A subset of these problems includes estimating periodic parameters that have unknown dynamics. Along with their time series, the period of these parameters may also be unknown and need to be estimated. The aim of this paper is to address the periodic parameter estimation problem, with particular focus on exploring the associated uncertainty, using Monte Carlo particle methods, such as the ensemble Kalman filter. Both parameter tracking and piecewise function approximations of periodic parameters are considered, highlighting aspects of parameter uncertainty in each approach when considering factors such as the frequency of available data and the number of piecewise segments used in the approximation. Estimation of the period of the periodic parameters and related uncertainty is also analyzed in the piecewise formulation. The pros and cons of each approach are discussed relative to a numerical example estimating the external voltage parameter in the FitzHugh–Nagumo system for modeling the spiking dynamics of neurons.

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Acknowledgement

This work is supported by the National Science Foundation under grant number NSF/DMS-1819203.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA, USA

    Andrea Arnold

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  1. Andrea Arnold
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Correspondence to Andrea Arnold .

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Editors and Affiliations

  1. Department of Mathematics, Northwestern University, Evanston, IL, USA

    Bahar Acu

  2. Department of Mathematics, Purdue University, West Lafayette, IN, USA

    Donatella Danielli

  3. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA

    Marta Lewicka

  4. Department of Mathematics, St. Thomas University, Houston, TX, USA

    Arati Pati

  5. Security and Privacy, Bosch Research and Technology Center, Pittsburgh, PA, USA

    Saraswathy RV

  6. Department of Mathematics, Lehigh University, Bethlehem, PA, USA

    Miranda Teboh-Ewungkem

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Arnold, A. (2020). Using Monte Carlo Particle Methods to Estimate and Quantify Uncertainty in Periodic Parameters (Research). In: Acu, B., Danielli, D., Lewicka, M., Pati, A., Saraswathy RV, Teboh-Ewungkem, M. (eds) Advances in Mathematical Sciences. Association for Women in Mathematics Series, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-030-42687-3_14

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