Bias and Coverage Properties of the WENDy-IRLS Algorithm
This work provides a detailed analysis of an existing algorithm's statistical properties, which is incremental but important for researchers using WENDy in systems biology and related fields.
The paper examined the bias and coverage properties of the WENDy-IRLS algorithm for parameter and state estimation in five differential equation models under four noise distributions and high noise levels, finding that the estimators performed robustly in simulations.
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.