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What do the data, as distinguished from cosmological models, tell us aboutcosmological parameters that determined the model of the universe? In thispaper, we address this question in the context of the WMAP angular powerspectra for the cosmic microwave background radiation. Nonparametric methodsare ideally suited for this purpose because they are model-independent byconstruction, and therefore allow inferences that are as data-driven aspossible. Our analysis is based on a nonparametric fit to the WMAP 7-year powerspectrum data, with uncertainties characterized in the form of ahigh-dimensional confidence set centered at this fit. For the purpose of makinginferences about cosmological parameters, we have devised a sampling method toexplore 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 computationalsimplicity, and validated by the fact that well-known degeneracies in thiscosmological parameter space are correctly reproduced in our results. Ourresults show that cosmological parameters are not as tightly constrained bythese data alone. However, incorporating additional prior information in theanalysis (e.g., constraining the values of H_0 or Omega_k) leads to tighterconfidence intervals on parameters that are consistent with uncertaintiesestimated by the mainstream parametric methods.

From Nonparametric Power Spectra to Inference About Cosmological Parameters: A Random Walk in the Cosmological Parameter Space