Using Monte Carlo Particle Methods to Estimate and Quantify Uncertainty in Periodic Parameters
Using Monte Carlo Particle Methods to Estimate and Quantify Uncertainty in Periodic Parameters
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使用蒙特卡罗粒子方法估计和量化周期性参数的不确定性
DOI：
10.1007/978-3-030-42687-3_14
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Arnold, Andrea
中科院分区：
文献类型：
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作者：
Arnold, Andrea
估计和量化系统参数中的不确定性仍然是应用数学和计算数学中的一大挑战。这些问题的一个子集包括估计具有未知动态的周期参数。连同它们的时间序列，这些参数的周期也可能是未知的，需要估计。本文的目的是解决周期参数估计问题，特别关注探索相关的不确定性，使用蒙特卡罗粒子方法，如集合卡尔曼滤波。同时考虑了周期参数的参数跟踪和分段函数近似，强调了当考虑可用数据的频率和近似中使用的分段分段的数量等因素时，每种方法中的参数不确定性的方面。在分段公式中还分析了周期参数的周期估计和相关的不确定性。结合一个数值例子讨论了每种方法的优缺点，该方法估计了Fitzhugh-Nagumo系统中的外部电压参数，用于模拟神经元的放电动力学。
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.