  The asteroseismic analysis of stellar power density spectra is often
computationally expensive. The models used in the analysis may use several
dozen parameters to accurately describe features in the spectra caused by
oscillation modes and surface granulation. Many parameters are often highly
correlated, making the parameter space difficult to quickly and accurately
sample. They are, however, all dependent on a smaller set of parameters, namely
the fundamental stellar properties. We aim to leverage this to simplify the
process of sampling the model parameter space for the asteroseismic analysis of
solar-like oscillators, with an emphasis on mode identification. Using a large
set of previous observations, we applied principal component analysis to the
sample covariance matrix to select a new basis on which to sample the model
parameters. Selecting the subset of basis vectors that explains the majority of
the sample variance, we redefine the model parameter prior probability density
distributions in terms of a smaller set of latent parameters. We are able to
reduce the dimensionality of the sampled parameter space by a factor of two to
three. The number of latent parameters needed to accurately model the stellar
oscillation spectra cannot be determined exactly but is likely only between
four and six. Using two latent parameters, the method is able to describe the
bulk features of the oscillation spectrum, while including more latent
parameters allows for a frequency precision better than $\approx10\%$ of the
small frequency separation for a given target. We find that sampling a
lower-rank latent parameter space still allows for accurate mode identification
and parameter estimation on solar-like oscillators over a wide range of
evolutionary stages. This allows for the potential to increase the complexity
of spectrum models without a corresponding increase in computational expense.
