Bayesian Methods for Cosmological Parameter Estimation from Cosmic Microwave Background Measurements

TL;DR

The paper addresses the challenge of estimating cosmological parameters from CMB anisotropy data within a rigorous Bayesian framework. It advocates using Markov chain Monte Carlo, specifically the Metropolis-Hastings algorithm, to sample from the joint posterior without explicit multidimensional integration and to handle high-dimensional marginalization. It outlines how to integrate existing tools like CMBFAST or CAMB with MH sampling, including guidance on priors, likelihood construction from $C_l$, and convergence diagnostics, to produce full posterior distributions and parameter correlations. This approach scales to many parameters and remains robust to non-Gaussian noise, enabling more reliable cosmological inferences from current and future CMB measurements.

Abstract

We present a strategy for a statistically rigorous Bayesian approach to the problem of determining cosmological parameters from the results of observations of anisotropies in the cosmic microwave radiation background. We propose the application of Markov chain Monte Carlo methods, specifically the Metropolis-Hastings algorithm, to estimate the parameters. A complete statistical analysis is presented, with the Metropolis-Hastings algorithm described in detail.