UCPH Statistics Seminar: Yuto Miyatake

Title: Isotonic regression for quantifying the error in numerical integration of differential equations

Speaker: Yuto Miyatake from Osaka University

Abstract: We investigate the problem of parameter estimation in ordinary differential equation (ODE) models using noisy observations. Traditional approaches often involve fitting numerical solutions, such as those obtained via Euler or Runge-Kutta methods, to the observed data. However, these methods do not account for discretization errors inherent in numerical integration, thereby limiting the accuracy of the parameter estimates.

In this context, quantifying discretization errors can significantly improve both the accuracy and the reliability evaluation of the parameter estimates. Although the literature on numerical analysis does not offer straightforward methods for quantifying these errors, we propose novel approaches to address this gap.

In this talk, we introduce several models that treat discretization error as a random variable. We demonstrate that the variance of this random variable can be effectively updated using isotonic regression algorithms. Furthermore, we show that this updated variance provides a reliable quantification of the actual discretization error for several test problems.

[1] T. Matsuda, Y. Miyatake: Estimation of ordinary differential equation models with discretization error quantification, SIAM/ASA J. Uncertain. Quantif. 9 (2021) 302–331.
https://epubs.siam.org/doi/10.1137/19M1278405

[2] T. Matsuda, Y. Miyatake: Genaralized nearly isotonic regression, arXiv:2108.13010.

[3] N. Marumo, T. Matsuda, Y. Miyatake, Modelling the discretization error of initial value problems using the Wishart distribution, Appl. Math. Lett. available online.