Fast Approximate Bayesian Computation for Estimating Parameters in Differential Equations

TL;DR

This paper introduces a novel Gaussian process-based approach to approximate Bayesian computation that reduces computational costs in estimating parameters for differential equations, maintaining accuracy.

Contribution

The paper presents a new method that avoids explicit numerical integration in ABC by leveraging derivatives of Gaussian processes for smoothing observations.

Findings

Achieves comparable accuracy to existing ABC methods

Significantly reduces computational time

Effective on biological system models with differential equations

Abstract

Approximate Bayesian computation (ABC) using a sequential Monte Carlo method provides a comprehensive platform for parameter estimation, model selection and sensitivity analysis in differential equations. However, this method, like other Monte Carlo methods, incurs a significant computational cost as it requires explicit numerical integration of differential equations to carry out inference. In this paper we propose a novel method for circumventing the requirement of explicit integration by using derivatives of Gaussian processes to smooth the observations from which parameters are estimated. We evaluate our methods using synthetic data generated from model biological systems described by ordinary and delay differential equations. Upon comparing the performance of our method to existing ABC techniques, we demonstrate that it produces comparably reliable parameter estimates at a significantly reduced execution time.