“…Consequently, methods have been developed that aim to detect and remove outliers, prior to and independent of the inference method used [Ben-Gal, 2005, Hodge and Austin, 2004, Niu et al, 2011. However, for noise-corrupted high-dimensional or highly structured data with few replicates, which are common in biological problems and also as applications of ABC [Durso-Cain et al, 2021, Jagiella et al, 2017, such methods may be unreliable, and the complete removal of points that are not actually outliers can increase uncertainty [Motulsky and Christopoulos, 2003]. To circumvent this, estimators that are robust in the presence of outliers have been developed, using heavy-tailed distributions [Berger et al, 1994, Fernández and Steel, 1999, Huber et al, 1964, Tarantola, 2005 or pseudo-likelihoods with robust loss functions or divergences [Basu et al, 1998, Chérief-Abdellatif and Alquier, 2020, Jewson et al, 2018.…”