  The simplest inflationary models present us with few observable parameters to
discriminate between them. A detection of features in the spectra of primordial
density perturbations could provide valuable insights and lead to stringent
tests of models of the early Universe. So far, searches for oscillatory
features have not produced statistically significant results. In this work we
consider a combined search for features in the power spectrum and bispectrum.
We show that possible dependencies between the estimates of feature model
amplitudes based on the two- and three-point correlators are largely
statistically independent under the assumption of the null hypothesis of a
nearly Gaussian featureless CMB. Building on this conclusion we propose an
optimal amplitude estimator for a combined search and study the look-elsewhere
effect in feature model surveys. In particular we construct analytic models for
the distribution of amplitude estimates that allow for a reliable assessment of
the significance of potential findings. We also propose a well-behaved
integrated statistic that is designed to detect evidence for models exhibiting
features at multiple frequencies.
