  We investigate constraints on power spectra of the primordial curvature and
tensor perturbations with priors based on single-field slow-roll inflation
models. We stochastically draw the Hubble slow-roll parameters and generate the
primordial power spectra using the inflationary flow equations. Using data from
recent observations of CMB and several measurements of geometrical distances in
the late Universe, Bayesian parameter estimation and model selection are
performed for models that have separate priors on the slow-roll parameters. The
same analysis is also performed adopting the standard parameterization of the
primordial power spectra. We confirmed that the scale-invariant
Harrison-Zel'dovich spectrum is disfavored with increased significance from
previous studies. While current observations appear to be optimally modeled
with some simple models of single-field slow-roll inflation, data is not enough
constraining to distinguish these models.
