II: Bayesian Methods for Cosmological Parameter Estimation from Cosmic Microwave Background Measurements

TL;DR

This work addresses cosmological parameter estimation from CMB anisotropy data within a Bayesian framework, tackling the challenge of high-dimensional posterior integration. It advocates Markov chain Monte Carlo, specifically Metropolis–Hastings, to sample from the posterior $p( heta|z)$ and to marginalize over nuisance parameters, enabling robust uncertainty quantification under varying priors. The authors introduce a Fisher-matrix–based proposal strategy and demonstrate the approach on a four-parameter toy model with a fast $C_l$ calculator, achieving convergence and recovering true parameter values; they also discuss extending to ~10 parameters and applying to real CMB measurements. The work highlights the practical viability and scalability of MCMC for complex cosmological models, offering a pathway to rigorous posterior inference where grid-based methods become prohibitive.

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 background. Our strategy relies on Markov chain Monte Carlo methods, specifically the Metropolis-Hastings algorithm, to perform the necessary high-dimensional integrals. We describe the Metropolis-Hastings algorithm in detail and discuss the results of our test on simulated data.