  The strength or weakness of an algorithm is ultimately governed by the
confidence of its result. When the domain of the problem is large (e.g.
traversal of a high-dimensional space), a perfect solution cannot be obtained,
so approximations must be made. These approximations often lead to a reported
quantity of interest (QOI) which varies between runs, decreasing the confidence
of any single run. When the algorithm further computes this final QOI based on
uncertain or noisy data, the variability (or lack of confidence) of the final
QOI increases. Unbounded, these two sources of uncertainty (algorithmic
approximations and uncertainty in input data) can result in a reported
statistic that has low correlation with ground truth.
  In biological applications, this is especially applicable, as the search
space is generally approximated at least to some degree (e.g. a high percentage
of protein structures are invalid or energetically unfavorable) and the
explicit conversion from continuous to discrete space for protein
representation implies some uncertainty in the input data. This research
applies uncertainty quantification techniques to the difficult protein-protein
docking problem, first showing the variability that exists in existing
software, and then providing a method for computing probabilistic certificates
in the form of Chernoff-like bounds. Finally, this paper leverages these
probabilistic certificates to accurately bound the uncertainty in docking from
two docking algorithms, providing a QOI that is both robust and statistically
meaningful.
