Accelerating Bayesian inference for stochastic models by preconditioning with approximate continuum limit descriptions

Ecological and biological sciences rely on the characterisation of populations of interacting individuals. Random walks are standard in modelling the stochastic nature of individual movement, growth and death. Due to the computationally burdensome task of stochastic simulation, it is routine to employ mean-field assumptions to derive approximate continuum limit descriptions of these kinds of stochastic models. Bayesian parameter inference is especially prohibitive for random walks since expensive likelihood-free methods are required. Conversely, the approximate continuum limit description yields a closed-form likelihood. However, for parameter regimes where the mean-field approximation is inaccurate, statistical inferences are biased. We propose that, despite this bias, the approximate continuum limit may still be exploited to accelerate Bayesian inference for expensive random walk models. Specifically, we extend sequential Monte Carlo sampling algorithms for approximate Bayesian computation. Our methods utilise samples from the continuum limit posterior as a precondtioner to inform efficient sampling from the target posterior for the random walk model. The resulting methods are demostrated to be effective at significantly reducing the number of expensive stochastic simulations while maintaining accuracy in parameter and uncertainty estimates