The shapes of the primordial power spectra are the key quantities to unravel the physics of the inflationary epoch. We propose a new framework for parametrizing the spectra of primordial scalar and tensor perturbations, stressing the statistical trajectory nature of the relevant quantities and the importance of priors which can lead to spurious results like an apparent detection of tensor modes. We clarify the impact of prior probabilities, demonstrate strategies to adjust the prior distributions and as an example investigate a model inspired by high energy theory that exhibits intrinsic statistical elements.