Differential equations in data analysis. (30th November 2020) - Dattner, Itai
Abstract: Differential equations have proven to be a powerful mathematical tool in science and engineering, leading to better understanding, prediction, and control of dynamic processes. In this paper, we review the role played by differential equations in data analysis. More specifically, we consider the intersection between differential equations and data analysis in the light of modern statistical learning methodologies. This article is categorized under: Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Statistical Models > Nonlinear Models Abstract : Parameter estimation of a biochemical system using the simode R package (Yaari & Dattner (2019)). System parameters were estimated using the Separable Integral Matching method (Dattner, Ship & Voit (2020)). Biochemical system taken from Chapter 2, Page 54 of Voit (2000). Solutions x1 and x2 of the biochemical system in solid red lines. Simulated stochastic observations in circles. Model fits in dashed blue lines.