Cosmological Parameter Estimation from the CMB

TL;DR

This paper presents an efficient and optimal method for estimating cosmological parameters from the CMB using a generalized eigenvalue problem, enabling data compression and addressing multi-parameter estimation challenges.

Contribution

It introduces a generalized eigenvalue approach for maximum likelihood estimation of CMB parameters, improving efficiency and data compression capabilities.

Findings

Method achieves minimal information loss in parameter estimation.

Enables substantial data compression without sacrificing accuracy.

Provides solutions for simultaneous multi-parameter estimation.

Abstract

We discuss the problems of applying Maximum Likelihood methods to the CMB and how one can make it both efficient and optimal. The solution is a generalised eigenvalue problem that allows virtually no loss of information about the parameter being estimated, but can allow a substantial compression of the data set. We discuss the more difficult question of simultaneous estimation of many parameters, and propose solutions. A much fuller account of most of this work is available (Tegmark, Taylor & Heavens 1997)