Robust adaptive distance functions for approximate Bayesian inference on outlier-corrupted data

Approximate Bayesian Computation (ABC) is a likelihood-free parameter inference method for complex stochastic models in systems biology and other research areas. While conceptually simple, its practical performance relies on the ability to efficiently compare relevant features in simulated and observed data via distance functions. Complications can arise particularly from the presence of outliers in the data, which can severely impair the inference. Thus, robust methods are required that provide reliable estimates also from outlier-corrupted data. We illustrate how established ABC distance functions are highly sensitive to outliers, and can in practice yield erroneous or highly uncertain parameter estimates and model predictions. We introduce self-tuned outlier-insensitive distance functions, based on a popular adaptive distance weighting concept, complemented by a simulation-based online outlier detection and downweighting routine. We evaluate and compare the presented methods on six test models covering different model types, problem features, and outlier scenarios. Our evaluation demonstrates substantial improvements on outlier-corrupted data, while giving at least comparable performance on outlier-free data. The developed methods have been made available as part of the open-source Python package pyABC (https://github.com/icb-dcm/pyabc).