  The usual figure of merit characterizing the performance of neural networks
applied to problems in the quantum domain is their accuracy, being the
probability of a correct answer on a previously unseen input. Here we append
this parameter with the uncertainty of the prediction, characterizing the
degree of confidence in the answer. A powerful technique for estimating both
the accuracy and the uncertainty is provided by Bayesian neural networks
(BNNs). We first give simple illustrative examples of advantages brought
forward by BNNs, out of which we wish to highlight their ability of reliable
uncertainty estimation even after training with biased data sets. Then we apply
BNNs to the problem of recognition of quantum contextuality which shows that
the uncertainty itself is an independent parameter identifying the chance of
misclassification of contextuality.
