  There has been much recent discussion, and some confusion, regarding the use
of existing observational data to estimate the likelihood that next-generation
cosmic microwave background (CMB) polarization experiments might detect a
nonzero tensor signal, possibly associated with inflation. We examine this
issue in detail here in two different ways: (1) first we explore the effect of
choice of different parameter priors on the estimation of the tensor-to-scalar
ratio r and other parameters describing inflation, and (2) we examine the
Bayesian complexity in order to determine how effectively existing data can
constrain inflationary parameters. We demonstrate that existing data are not
strong enough to render full inflationary parameter estimates in a
parametrization- and prior-independent way and that the predicted tensor signal
is particularly sensitive to different priors. For parametrizations where the
Bayesian complexity is comparable to the number of free parameters we find that
a flat prior on the scale of inflation (which is to be distinguished from a
flat prior on the tensor-to-scalar ratio) leads us to infer a larger, and in
fact slightly nonzero tensor contribution at 68% confidence level. However, no
detection is claimed. Our results demonstrate that all that is statistically
relevant at the current time is the (slightly enhanced) upper bound on r, and
we stress that the data remain consistent with r = 0.
