Bayesian analysis of cosmological models.

Abstract

In this thesis, we utilise the framework of Bayesian statistics to discriminate between models of the cosmological mass function. We first review the cosmological model and the formation and distribution of galaxy clusters before formulating a statistic within the Bayesian framework, namely the Bayesian razor, that allows model testing of probability distributions. The Bayesian razor is used to discriminate between three popular mass functions, namely the Press-Schechter, Sheth-Tormen and normalisable Tinker models. With a small number of particles in the simulation, we find that the simpler model is preferred due to the Occam’s razor effect, but as the size of the simulation increases the more complex model, if taken to be the true model, is preferred. We establish criteria on the size of the simulation that is required to decisively favour a given model and investigate the dependence of the simulation size on the threshold mass for clusters, and prior probability distributions. Finally we outline how our method can be extended to consider more realistic N-body simulations or be applied to observational data.