  We present a generic inference method for inflation models from observational
data by the usage of higher-order statistics of the curvature perturbation on
uniform density hypersurfaces. This method is based on the calculation of the
posterior for the primordial non-Gaussianity parameters $f_\text{NL}$ and
$g_\text{NL}$, which in general depend on specific parameters of inflation and
reheating models, and enables to discriminate among the still viable inflation
models. To keep analyticity as far as possible to dispense with numerically
expensive sampling techniques a saddle-point approximation is introduced, whose
precision is validated for a numerical toy example. The mathematical
formulation is done in a generic way so that the approach remains applicable to
cosmic microwave background data as well as to large scale structure data.
Additionally, we review a few currently interesting inflation models and
present numerical toy examples thereof in two and three dimensions to
demonstrate the efficiency of the higher-order statistics method. A second
quantity of interest is the primordial power spectrum. Here, we present two
Bayesian methods to infer it from observational data, the so called critical
filter and an extension thereof with smoothness prior, both allowing for a
non-parametric spectrum reconstruction. These methods are able to reconstruct
the spectra of the observed perturbations and the primordial ones of curvature
perturbation even in case of non-Gaussianity and partial sky coverage. We argue
that observables like $T-$ and $B-$modes permit to measure both spectra. This
also allows to infer the level of non-Gaussianity generated since inflation.
