  We consider the problem of assigning a meaningful degree of belief to
uncertainty estimates of perturbative series. We analyse the assumptions which
are implicit in the conventional estimates made using renormalisation scale
variations. We then formulate a Bayesian model that, given equivalent initial
hypotheses, allows one to characterise a perturbative theoretical uncertainty
in a rigorous way in terms of a credibility interval for the remainder of the
series. We compare its outcome to the conventional uncertainty estimates in the
simple case of the calculation of QCD corrections to the e+e- -> hadrons
process. We find comparable results, but with important conceptual differences.
This work represents a first step in the direction of a more comprehensive and
rigorous handling of theoretical uncertainties in perturbative calculations
used in high energy phenomenology.
