From Nonparametric Power Spectra to Inference About Cosmological
  Parameters: A Random Walk in the Cosmological Parameter Space
  What do the data, as distinguished from cosmological models, tell us about
cosmological parameters that determined the model of the universe? In this
paper, we address this question in the context of the WMAP angular power
spectra for the cosmic microwave background radiation. Nonparametric methods
are ideally suited for this purpose because they are model-independent by
construction, and therefore allow inferences that are as data-driven as
possible. Our analysis is based on a nonparametric fit to the WMAP 7-year power
spectrum data, with uncertainties characterized in the form of a
high-dimensional confidence set centered at this fit. For the purpose of making
inferences about cosmological parameters, we have devised a sampling method to
explore the projection of this confidence set around the nonparametric fit,
into the space of seven cosmological parameters Omega_b, Omega_c, Omega_Lambda,
Omega_k, H_0, n_s, tau). Our sampling method is justified by its computational
simplicity, and validated by the fact that well-known degeneracies in this
cosmological parameter space are correctly reproduced in our results. Our
results show that cosmological parameters are not as tightly constrained by
these data alone. However, incorporating additional prior information in the
analysis (e.g., constraining the values of H_0 or Omega_k) leads to tighter
confidence intervals on parameters that are consistent with uncertainties
estimated by the mainstream parametric methods.
