  We update constraints on the Hubble function H(phi) during inflation, using
the most recent cosmic microwave background (CMB) and large scale structure
(LSS) data. Our main focus is on a comparison between various commonly used
methods of calculating the primordial power spectrum via analytical
approximations and the results obtained by integrating the exact equations
numerically. In each case, we impose naive, minimally restrictive priors on the
duration of inflation. We find that the choice of priors has an impact on the
results: the bounds on inflationary parameters can vary by up to a factor two.
Nevertheless, it should be noted that within the region allowed by the minimal
prior of the exact method, the accuracy of the approximations is sufficient for
current data. We caution however that a careless minimal implementation of the
approximative methods allows models for which the assumptions behind the
analytical approximations fail, and recommend using the exact numerical method
for a self-consistent analysis of cosmological data.
