Physical modelling of galaxy clusters and Bayesian inference in
  astrophysics
  I compare the mass values obtained with data taken from the Arcminute
Microkelvin Imager (AMI) radio interferometer system and from the Planck
satellite. The former of these uses a Bayesian analysis pipeline that
parameterises a cluster in terms of its physical quantities, and models the
dark matter \& baryonic components of a cluster using Navarro-Frenk-White (NFW)
and generalised-NFW profiles respectively. I also analyse simulated AMI data
with input values based on PwS mass estimates. I then compare three cluster
models using AMI data for the 54 cluster sample. The two observational models
considered only model the gas content of the cluster. To compare the physical
and observational models I consider their posterior parameter estimates,
including the calculation of a metric defined between two probability
distributions. The models' fit to the cluster data is evaluated by looking at
the Bayesian evidence values. Improvements to the physical modelling of galaxy
clusters are then considered, either by relaxing some of the assumptions
underlying the physical model, or by introducing a new profile for the dark
matter component of clusters. The final part of the cluster analysis work
focuses on Bayesian analysis using a joint likelihood function of data from
both AMI and the Planck satellite simultaneously. Finally, a new Bayesian
inference algorithm based on nested sampling is presented. The algorithm, named
the "geometric nested sampler", is an adaption of the Metropolis-Hastings
nested sampler and makes use of the geometrical interpretation of sets of
parameters to sample from their domains efficiently. The geometric nested
sampler is tested on several toy models as well as a model representing the
emission of gravitational waves from binary black hole mergers.
