# Fast Approximate Bayesian Computation for Estimating Parameters in Differential Equations

arXiv: https://arxiv.org/abs/1507.05117 · HTML: https://mlsanity.com/paper/1507.05117/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jul 2015.

## Built on by (most cited first, 1 of 1)

- [Data-Adaptive Probabilistic Likelihood Approximation for Ordinary Differential Equations](https://mlsanity.com/paper/2306.05566/) (2023)

## Abstract (arXiv)

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.