Statistical techniques in cosmology

In these four 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 which are firmly model-based, 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. Some of the derivations follow the excellent notes of Licia Verde [24] and Andrew Hamilton [8]. After this introduction, the sections are: