Bayesian `Hyper-Parameters' Approach to Joint Estimation: The Hubble Constant from CMB Measurements

Preprint

6 December 1999

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.astro-ph/9912105

Abstract

Recently several studies have jointly analysed data from different cosmological probes with the motivation of estimating cosmological parameters. Here we generalise this procedure to take into account the relative weights of various probes. This is done by including in the joint \chi^2 function a set of `Hyper-Parameters', which are dealt with using Bayesian considerations. The resulting algorithm (in the case of uniform priors on the log of the Hyper-Parameters) is very simple: instead of minimising \sum \chi_j^2 (where \chi_j^2 is per data set j) we propose to minimise \sum N_j \ln (\chi_j^2) (where N_j is the number of data points per data set j). We illustrate the method by estimating the Hubble constant H_0 from different sets of recent CMB experiments (including Saskatoon, Python V, MSAM1, TOCO and Boomerang).

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Version 1, 1999-12-06, ArXiv
Published version: Monthly Notices of the Royal Astronomical Society, 315 (4), L45.

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