Statistical techniques in cosmology

TL;DR

This paper discusses statistical techniques for cosmological data analysis, emphasizing Bayesian methods, survey design analysis, numerical parameter estimation, and model selection, applicable broadly in scientific data interpretation.

Contribution

It provides a comprehensive overview of general statistical methods used in cosmology, including survey analysis, parameter estimation, and model comparison, with practical numerical approaches.

Findings

Fisher matrices help optimize survey designs.

Monte Carlo methods are effective for parameter estimation.

Model selection techniques can distinguish between theoretical frameworks.

Abstract

In these lectures I cover a number of topics in cosmological data analysis. I concentrate on general techniques which are common in cosmology, or techniques which have been developed in a cosmological context. In fact they have very general applicability, for problems in which the data are interpreted in the context of a theoretical model, and thus lend themselves to a Bayesian treatment. We consider the general problem of estimating parameters from data, and consider how one can use Fisher matrices to analyse survey designs before any data are taken, to see whether the survey will actually do what is required. We outline numerical methods for estimating parameters from data, including Monte Carlo Markov Chains and the Hamiltonian Monte Carlo method. We also look at Model Selection, which covers various scenarios such as whether an extra parameter is preferred by the data, or answering wider questions such as which theoretical framework is favoured, using General Relativity and braneworld gravity as an example. These notes are not a literature review, so there are relatively few references.