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In this paper, different strands of literature are combined in order to obtain algorithms for semi-parametric estimation of discrete choice models that include the modelling of unobserved heterogeneity by using mixing distributions for the…

Methodology · Statistics 2022-12-12 Dietmar Bauer , Sebastian Büscher , Manuel Batram

We investigate an optimization problem governed by an elliptic partial differential equation with uncertain parameters. We introduce a robust optimization framework that accounts for uncertain model parameters. The resulting non-linear…

Optimization and Control · Mathematics 2019-09-24 Alessandro Alla , Michael Hinze , Philip Kolvenbach , Oliver Lass , Stefan Ulbrich

We introduce and analyze a method of learning-informed parameter identification for partial differential equations (PDEs) in an all-at-once framework. The underlying PDE model is formulated in a rather general setting with three unknowns:…

Optimization and Control · Mathematics 2023-08-25 Christian Aarset , Martin Holler , Tram Thi Ngoc Nguyen

We consider the problem of parameter estimation in dynamic systems described by ordinary differential equations. A review of the existing literature emphasizes the need for deterministic global optimization methods due to the nonconvex…

Optimization and Control · Mathematics 2025-06-16 M. Fernández de Dios , Ángel M. González-Rueda , Julio R. Banga , Julio González-Díaz , David R. Penas

Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model…

Computation · Statistics 2014-06-24 Douglas Bates , Martin Mächler , Ben Bolker , Steve Walker

State estimation aims at approximately reconstructing the solution $u$ to a parametrized partial differential equation from $m$ linear measurements, when the parameter vector $y$ is unknown. Fast numerical recovery methods have been…

Numerical Analysis · Mathematics 2020-11-25 Albert Cohen , Wolfgang Dahmen , Olga Mula , James Nichols

Nonlinearity and endogeneity are prevalent challenges in causal analysis using observational data. This paper proposes an inference procedure for a nonlinear and endogenous marginal effect function, defined as the derivative of the…

Econometrics · Economics 2024-06-19 Qingliang Fan , Zijian Guo , Ziwei Mei , Cun-Hui Zhang

Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this work…

Optimization and Control · Mathematics 2020-10-09 Olena Burkovska , Christian Glusa , Marta D'Elia

Inverse problem for the identification of the parameters for large-scale systems of nonlinear ordinary differential equations (ODEs) arising in systems biology is analyzed. In a recent paper in \textit{Mathematical Biosciences, 305(2018),…

Quantitative Methods · Quantitative Biology 2020-12-07 Ugur G. Abdulla , Roby Poteau

Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\bm\theta$ of physical significance…

Statistics Theory · Mathematics 2014-11-05 Prithwish Bhaumik , Subhashis Ghosal

Ordinary differential equations (ODE) are widely used for modeling in Systems Biology. As most commonly only some of the kinetic parameters are measurable or precisely known, parameter estimation techniques are applied to parametrize the…

Quantitative Methods · Quantitative Biology 2016-01-19 Christoph Zimmer , Frank T. Bergmann , Sven Sahle

In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…

Numerical Analysis · Mathematics 2024-12-20 Max Winkler

We consider the problem of asymptotic reconstruction of the state and parameter values in systems of ordinary differential equations. A solution to this problem is proposed for a class of systems of which the unknowns are allowed to be…

Optimization and Control · Mathematics 2015-03-13 Ivan Y. Tyukin , Erik Steur , Henk Nijmeijer , Cees van Leeuwen

A novel approach to the problem of partial state estimation of nonlinear systems is proposed. The main idea is to translate the state estimation problem into one of estimation of constant, unknown parameters related to the systems initial…

Systems and Control · Computer Science 2016-04-08 Ortega Romeo , Bobtsov Alexey , Pyrkin Anton , Aranovskiy Stanislav

We consider nonlinear mixed effects models including high-dimensional covariates to model individual parameters variability. The objective is to identify relevant covariates among a large set under sparsity assumption and to estimate model…

Statistics Theory · Mathematics 2025-08-06 Antoine Caillebotte , Estelle Kuhn , Sarah Lemler

We study the problem of estimating the coefficients in linear ordinary differential equations (ODE's) with a diverging number of variables when the solutions are observed with noise. The solution trajectories are first smoothed with local…

Statistics Theory · Mathematics 2008-04-29 Heng Lian

We investigate the use of neural networks (NNs) for the estimation of hidden model parameters and uncertainty quantification from noisy observational data for inverse parameter estimation problems. We formulate the parameter estimation as a…

Numerical Analysis · Mathematics 2025-10-17 German Villalobos , Johann Rudi , Andreas Mang

In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations…

Classical Analysis and ODEs · Mathematics 2009-12-16 Olexandr Nakonechnyi , Yury Podlipenko , Yury Shestopalov

The problem of nonlinear functional of parameters, such as differential entropy, has received much attention in information theory and statistics. In many situations, prior information about the parameters is available in the form of order…

Statistics Theory · Mathematics 2026-03-10 Somnath Mandal , Lakshmi Kanta Patra

Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would…

Machine Learning · Computer Science 2024-07-22 Jonas Beck , Nathanael Bosch , Michael Deistler , Kyra L. Kadhim , Jakob H. Macke , Philipp Hennig , Philipp Berens