Fast Approximate Bayesian Computation for Estimating Parameters in Differential Equations
This work addresses computational bottlenecks for researchers in fields like systems biology, though it is incremental as it builds on existing ABC techniques.
The paper tackled the high computational cost of parameter estimation in differential equations using Approximate Bayesian Computation by proposing a method that avoids explicit numerical integration through Gaussian process derivatives, resulting in comparably reliable estimates at significantly reduced execution times.
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.