  Cosmic inflation may have led to non-Gaussian initial conditions that cannot
be fully parametrised by 3- and/or 4-point functions. In this work, we discuss
various strategies to search for primordial non-Gaussianity beyond polyspectra
with the help of cosmological data. Our starting point is a generalised local
ansatz for the primordial curvature perturbation $\zeta$ of the form $\zeta =
\zeta_{\rm G} + \mathcal{F}_{\rm NG} (\zeta_{\rm G})$, where $\zeta_{\rm G}$ is
a Gaussian random field and $\mathcal{F}_{\rm NG}$ is an arbitrary function
parametrising non-Gaussianity that, in principle, could be reconstructed from
data. Noteworthily, in the case of multi-field inflation, the function
$\mathcal{F}_{\rm NG}$ can be shown to be determined by the shape of
tomographic sections of the landscape potential responsible for driving
inflation. We discuss how this generalised local ansatz leads to a probability
distribution functional that may be used to extract information about inflation
from current and future observations. In particular, we derive various classes
of probability distribution functions suitable for the statistical analysis of
the cosmic microwave background and large-scale structure.
