Comparison of physical and observational galaxy cluster modelling
  We present a comparison between three cluster models applied to data obtained
by the Arcminute Microkelvin Imager radio interferometer system. The physical
model (PM) parameterises a cluster in terms of its physical quantities to model
the dark matter and baryonic components of the cluster using NFW and GNFW
profiles respectively. The observational models (OM I and OM II) model only the
gas content of the cluster. The two OMs vary only in the priors they use in
Bayesian inference: OM I has a joint prior on angular radius $\theta$ and
integrated Comptonisation $Y$, derived from simulations, while OM II uses
separable priors on $\theta$ and $Y$ which are based on calculations of the
physical model. For the comparison we consider a sample of $54$ clusters which
are a subsample of the second Planck catalogue of Sunyaev-Zel'dovich sources.
We first compare the $Y$ estimates of the three models, and find that the PM
generally yields lower estimates relative to the OMs. We then compute the Earth
Mover's Distance between the $\theta$ - $Y$ posterior distributions obtained
from each model for each cluster, and find that the two models which are most
discrepant are PM and OM I. Finally, we compare the Bayesian evidence values
obtained from each model for each cluster. OM I generally provides the best fit
to the data but not at a statistically significant level, according to the
Jeffreys scale. The highest evidence ratio obtained is actually in favour of
the PM over OM I.
