  We review various methods used to estimate uncertainties in quantum
correlation functions, such as parton distribution functions (PDFs). Using a
toy model of a PDF, we compare the uncertainty estimates yielded by the
traditional Hessian and data resampling methods, as well as from explicitly
Bayesian analyses using nested sampling or hybrid Markov chain Monte Carlo
techniques. We investigate how uncertainty bands derived from neural network
approaches depend on details of the network training, and how they compare to
the uncertainties obtained from more traditional methods with a specific
underlying parametrization. Our results show that utilizing a neural network on
a simplified example of PDF data has the potential to inflate uncertainties, in
part due to the cross validation procedure that is generally used to avoid
overfitting data.
