LAUSR

The Megamaser Cosmology Project inferred a value for the Hubble constant given by H0=73.9±3.0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$H_{0}=73.9 \pm 3.0 $\end{document} km/sec/Mpc. This value was obtained using Bayesian inference by marginalizing over six nuisance parameters, corresponding to the velocities of the megamaser galaxy systems. We obtain an independent estimate of the Hubble constant with the same data using frequentist inference. For this purpose, we use profile likelihood to dispense with the aforementioned nuisance parameters. The frequentist estimate of the Hubble constant is given by H0=73.5−2.9+3.0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$H_{0}=73.5^{+3.0}_{-2.9}$\end{document} km/sec/Mpc and agrees with the Bayesian estimate to within 0.2σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$0.2\sigma $\end{document}, and both approaches also produce consistent confidence/credible intervals. Therefore, this analysis provides a proof-of-principle application of profile likelihood in dealing with nuisance parameters in cosmology, which is complementary to Bayesian analysis.