Primordial perturbations with wavelengths greater than the observable universe shift the effective background fields in our 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. They may significantly differ from the expectation values predicted by the fundamental inflationary model reflecting the underlying high-energy physics. Non-Gaussian statistics are especially affected with interesting ramifications for the interpretation of the non-detection of local f_NL by Planck. In this talk I will develop methods to quantify the naturalness of different signatures in the inflationary perturbations and establish systematic connections between the observable properties of primordial perturbations and the underlying global properties of the inflating space. For example, I will demonstrate that models with a small f_NL as required by the Planck data but sizeable non-Gaussianity in the form of g_NL imply an inherent tuning of the number of e-foldings.