ABC-RF-rejection: A two-stage machine-learning-enhanced framework for efficient likelihood-free inference

Accurate parameter estimation is fundamental to quantitative epidemiology as it provides the foundation for robust modelling and evidence-based decision-making. We present a novel two-stage framework, that is designed to enhance computational efficiency for parameter estimation of complex, stochastic, or spatially explicit models. Traditional Approximate Bayesian Computation (ABC) methods often face prohibitive costs when likelihoods are analytically intractable and acceptance rates are low. Our hybrid approach, ABC-RF-rejection, integrates ABC rejection sampling with Random Forest (RF) classification to selectively identify parameter sets likely to satisfy observed data constraints. In the first stage, a small-scale ABC rejection step generates a labelled training dataset of accepted and rejected particles. In the second stage, a trained RF model decouples posterior exploration from expensive forward simulations by predicting acceptance probabilities for a substantially larger candidate set. This allows the algorithm to focus computational resources on high-probability regions of the parameter space. We apply the ABC-RF-rejection approach to three distinct epidemiological contexts: stochastic simulations of onchocerciasis vector control, spatially explicit modelling of cassava brown streak virus spread in Uganda, and the 2014-2015 West Africa Ebola outbreak in heterogeneous populations. This framework provides an adaptable and robust solution for rapid, evidence-based decision-making in settings characterised by spatial heterogeneity, stochasticity, and limited surveillance data.