  In this paper, we use a complete model of classical primordial standard
clocks as an example to develop a methodology of directly comparing numerical
predictions from complicated multi-field feature models with the Planck data,
including the Planck 2018 Plik unbinned likelihood and the statistically most
powerful CamSpec 2020 likelihood for temperature and polarization data. As this
two-field inflationary model offers a plethora of primordial feature spectra
that represent combinations of sharp and resonance feature signals
non-trivially distributed over extended cosmological scales, its data
comparison has not been satisfactorily addressed by previous attempts using
analytical templates. The method of this paper, consisting of numerical
prediction, effective parameter construction and nested sampling data
comparison, allows us to efficiently explore every possible spectra from the
model. We classify the resulting feature candidates in three different
frequency ranges. We use the Bayesian evidences to assess the statistical
significance of the candidates over the baseline model, taking into account the
effect of additional parameters and the look-elsewhere effect. Although none of
the candidates is statistically significant, the methodology of this paper can
be used to facilitate the future model-building and data-screening process of
primordial features, and the candidates can be subjected to further tests with
data from the upcoming cosmic microwave background polarization observations
and galaxy surveys.
