  Operating system (OS) updates introduce numerical perturbations that impact
the reproducibility of computational pipelines. In neuroimaging, this has
important practical implications on the validity of computational results,
particularly when obtained in systems such as high-performance computing
clusters where the experimenter does not control software updates. We present a
framework to reproduce the variability induced by OS updates in controlled
conditions. We hypothesize that OS updates impact computational pipelines
mainly through numerical perturbations originating in mathematical libraries,
which we simulate using Monte-Carlo arithmetic in a framework called "fuzzy
libmath" (FL). We applied this methodology to pre-processing pipelines of the
Human Connectome Project, a flagship open-data project in neuroimaging. We
found that FL-perturbed pipelines accurately reproduce the variability induced
by OS updates and that this similarity is only mildly dependent on simulation
parameters. Importantly, we also found between-subject differences were
preserved in both cases, though the between-run variability was of comparable
magnitude for both FL and OS perturbations. We found the numerical precision in
the HCP pre-processed images to be relatively low, with less than 8 significant
bits among the 24 available, which motivates further investigation of the
numerical stability of components in the tested pipeline. Overall, our results
establish that FL accurately simulates results variability due to OS updates,
and is a practical framework to quantify numerical uncertainty in neuroimaging.
