Parameter estimation in continuous-time dynamic models using principal differential analysis

TL;DR: This paper gives a comprehensive review of the application of metaheuristics to optimization problems in systems biology, mainly focusing on the parameter estimation problem (also called the inverse problem or model calibration).

TL;DR: Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy.

TL;DR: In this article, the authors propose a general method for estimating the parameters indexing ODEs from times series by using a nonparametric estimator of regression functions as a first step in the construction of an M-estimator and show the consistency of the derived estimator under general conditions.

TL;DR: In this paper, a hybrid approach using Gaussian processes and differential equations is presented to combine data-driven modeling with a physical model of the system, and different, physically inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system.

TL;DR: This book presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines as well as specific approximation methods, interpolation, smoothing and least-squares approximation, the solution of an ordinary differential equation by collocation, curve fitting, and surface fitting.

TL;DR: This book is based on the author's experience with calculations involving polynomial splines.

TL;DR: This book offers a balanced presentation of the theoretical, practical, and computational aspects of nonlinear regression and provides background material on linear regression, including the geometrical development for linear and nonlinear least squares.