研究WENDy-IRLS算法在多种动态方程下的参数估计偏差与覆盖性。
Bias and Coverage Properties of the WENDy-IRLS Algorithm
- 基于非线性微分方程的参数估计，采用迭代重加权最小二乘法。
- 在高噪声水平下仍保持良好估计覆盖性，噪声分布多样。
- 适用于生物、生态等复杂系统建模，适合关注稳健性研究者。
弱形式非线性动力学（WENDy）方法是一类近期提出的参数估计算法，具有显著的抗噪鲁棒性和计算高效性。本文研究了原始WENDy-IRLS算法在逻辑斯蒂、洛特卡-沃尔泰拉、菲茨休-纳古莫、辛德马什-罗斯及蛋白质转导基准模型这五类微分方程中，参数与状态估计器的覆盖性与偏差特性。通过模拟数据，在四种不同噪声分布（正态、对数正态、加性截尾正态、加性右截断正态）下进行测试，覆盖了远高于以往研究的噪声水平。
原文摘要 · Abstract (English)
The Weak form Estimation of Nonlinear Dynamics (WENDy) method is a recently proposed class of parameter estimation algorithms that exhibits notable noise robustness and computational efficiency. This work examines the coverage and bias properties of the original WENDy-IRLS algorithm's parameter and state estimators in the context of the following differential equations: Logistic, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark. The estimators' performance was studied in simulated data examples, under four different noise distributions (normal, log-normal, additive censored normal, and additive truncated normal), and a wide range of noise, reaching levels much higher than previously tested for this algorithm.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。