  Primordial perturbations with wavelengths greater than the observable
universe shift the effective background fields in our observable patch from
their global averages over the inflating space. This leads to a landscape
picture where the properties of our observable patch depend on its location and
may significantly differ from the expectation values predicted by the
underlying fundamental inflationary model. We show that if multiple fields are
present during inflation, this may happen even if our horizon exit would be
preceded by only a few e-foldings of inflation. Non-Gaussian statistics are
especially affected: for example models of local non-Gaussianity predicting
|f_NL|>> 10 over the entire inflating volume can have a probability up to a few
tens of percent to generate a non-detectable bispectrum in our observable patch
|fNL^{obs.}|<10. In this work we establish systematic connections between the
observable local properties of primordial perturbations and the global
properties of the inflating space which reflect the underlying high energy
physics. We study in detail the implications of both a detection and
non-detection of primordial non-Gaussianity by Planck, and discover novel ways
of characterising the naturalness of different observational configurations.
