Approximate Bayesian Computation sequential Monte Carlo via random forests

Abstract

Approximate Bayesian Computation (ABC) is a popular inference method when likelihoods are hard to come by. Practical bottlenecks of ABC applications include selecting statistics that summarize the data without losing too much information or introducing uncertainty, and choosing distance functions and tolerance thresholds that balance accuracy and computational efficiency. Recent studies have shown that ABC methods using random forest (RF) methodology perform well while circumventing many of ABC's drawbacks. However, RF construction is computationally expensive for large numbers of trees and model simulations, and there can be high uncertainty in the posterior if the prior distribution is uninformative. Here we adapt distributional random forests to the ABC setting, and introduce Approximate Bayesian Computation sequential Monte Carlo with random forests (ABC-SMC-(D)RF). This updates the prior distribution iteratively to focus on the most likely regions in the parameter space. We show that ABC-SMC-(D)RF can accurately infer posterior distributions for a wide range of deterministic and stochastic models in different scientific areas.