ArticleJournal of the American Statistical Association2008
Parameter Estimation for Differential Equation Models Using a Framework of Measurement Error in Regression Models.
Article in Journal of the American Statistical Association, 2008. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 57 papers.
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Who cites it
57 citing papers in PubMed.
- Hazard-based distributional regression via ordinary differential equations.Statistical methods in medical research · 2026Article
- gNODE: gLV model-informed neural ordinary differential equations for modeling microbial community dynamics.Frontiers in cellular and infection microbiology · 2026Article
- Maximum likelihood inference for multivariate delay differential equation models.Scientific reports · 2025Article
- Measuring Regulatory Network Inheritance in Dividing Yeast Cells Using Ordinary Differential Equations.bioRxiv : the preprint server for biology · 2025Article
- The Michaelis-Menten Reaction at Low Substrate Concentrations: Pseudo-First-Order Kinetics and Conditions for Timescale Separation.Bulletin of mathematical biology · 2024Article
- Parameter estimation and forecasting with quantified uncertainty for ordinary differential equation models using QuantDiffForecast: A MATLAB toolbox and tutorial.Statistics in medicine · 2024Article
- Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics.Bulletin of mathematical biology · 2023Article
- Direct Estimation of Parameters in ODE Models Using WENDy: Weak-form Estimation of Nonlinear Dynamics.ArXiv · 2023Article
- Efficient inference and identifiability analysis for differential equation models with random parameters.PLoS computational biology · 2022Article
- Learning delay dynamics for multivariate stochastic processes, with application to the prediction of the growth rate of COVID-19 cases in the United States.Journal of mathematical analysis and applications · 2022Article
- Kernel Ordinary Differential Equations.Journal of the American Statistical Association · 2022Article
- A Joint estimation approach to sparse additive ordinary differential equations.Statistics and computing · 2022Article
- Dynamic estimation of epidemiological parameters of COVID-19 outbreak and effects of interventions on its spread.Journal of public health research · 2021Article
- Non-invasive Inference of Thrombus Material Properties with Physics-Informed Neural Networks.Computer methods in applied mechanics and engineering · 2021Article
- Gene expression dynamic analysis reveals co-activation of Sonic Hedgehog and epidermal growth factor followed by dynamic silencing.Oncotarget · 2020Article
- Modelling of hypoxia gene expression for three different cancer cell lines.International journal of computational biology and drug design · 2020Article
- Integration of single-cell multi-omics for gene regulatory network inference.Computational and structural biotechnology journal · 2020Review
- Nonparametric inference of interaction laws in systems of agents from trajectory data.Proceedings of the National Academy of Sciences of the United States of America · 2019Article
- Parametric and non-parametric gradient matching for network inference: a comparison.BMC bioinformatics · 2019Article
- Parameter Estimation for Semiparametric Ordinary Differential Equation Models.Communications in statistics: theory and methods · 2019Article
Corrections and comments
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Authors and funding
2 authors.
Funding
Abstract
Differential equation (DE) models are widely used in many scientific fields that include engineering, physics and biomedical sciences. The so-called "forward problem", the problem of simulations and predictions of state variables for given parameter values in the DE models, has been extensively studied by mathematicians, physicists, engineers and other scientists. However, the "inverse problem", the problem of parameter estimation based on the measurements of output variables, has not been well explored using modern statistical methods, although some least squares-based approaches have been proposed and studied. In this paper, we propose parameter estimation methods for ordinary differential equation models (ODE) based on the local smoothing approach and a pseudo-least squares (PsLS) principle under a framework of measurement error in regression models. The asymptotic properties of the proposed PsLS estimator are established. We also compare the PsLS method to the corresponding SIMEX method and evaluate their finite sample performances via simulation studies. We illustrate the proposed approach using an application example from an HIV dynamic study.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.