A Bayesian interpretation is given for regularization terms for
parameter functions in inverse problems. Fluctuations about the
extremal solution depend on the regularization terms - which encode
prior knowledge - provide quantification of uncertainty. After
reviewing a general path-integral framework, we set up a number of
applications that arise in biophysics. The inference of bond energies
and bond coordinate mobilities from dynamic force spectroscopy
experiments are worked out in detail.