Frequentist estimation of cosmological parameters from the MAXIMA1 cosmic microwave background anisotropy data
Abstract
We use a frequentist statistical approach to set confidence intervals on the values of cosmological parameters using the MAXIMA1 and COBE measurements of the angular power spectrum of the cosmic microwave background. We define a Δχ^{2} statistic, simulate the measurements of MAXIMA1 and COBE, determine the probability distribution of the statistic, and use it and the data to set confidence intervals on several cosmological parameters. We compare the frequentist confidence intervals with Bayesian credible regions. The frequentist and Bayesian approaches give best estimates for the parameters that agree within 15 per cent, and confidence interval widths that agree to within 30 per cent. The results also suggest that a frequentist analysis gives slightly broader confidence intervals than a Bayesian analysis. The frequentist analysis gives values of \Omega =0.89^{+0.26}_{0.19}, \Omega _{B}\,h^{2}=0.026^{+0.020}_{0.011} and n=1.02^{+0.31}_{0.10}, and the Bayesian analysis gives values of \Omega =0.98^{+0.14}_{0.19}, \Omega _{B}\,h^{2}=0.029^{+0.015}_{0.010} and n=1.18^{+0.10}_{0.23}, all at the 95 per cent confidence level.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 July 2002
 DOI:
 10.1046/j.13658711.2002.05383.x
 arXiv:
 arXiv:astroph/0111010
 Bibcode:
 2002MNRAS.334...11A
 Keywords:

 methods: data analysis;
 methods: statistical;
 cosmic microwave background;
 Astrophysics
 EPrint:
 10 pages, 9 Postscript figures, changes made to reflect published version