  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.
