Bayesian Methods for Astrophysics and Particle Physics

LIST OF FIGURES
5.1 Spectral index distribution from Waldram et al. (2007) used as the
prior on α, normalized to unit probability at maximum. The final
normalization depends on the adopted prior range. . . . . . . . . 130
5.2 Maps formed from channel 4 (14.992 GHz) of the simulations
considered in this work. The unCLEANed maps are 512 × 512
pixels at 15 ′′ resolution. Both data sets have different realisa-
tions of primary CMB and instrumental noise. The three radio
sources have the same fluxes and spectral indices in each simula-
tion, but two of them are at different locations. Simulation ‘A’ has
a spherically-symmetric, isothermal β-model cluster at the centre
of the map. Simulation ‘B’ has no cluster. . . . . . . . . . . . . . 135
5.3 Priors and 1D marginalized posterior probability distributions for
the parameters of the simulated cluster and point sources discussed
in Section 5.5. The true parameter values used in the simulation
are shown by crosses. . . . . . . . . . . . . . . . . . . . . . . . . . 136
5.4 2D marginalized posterior probability distributions for the para-
meters of the cluster simulation ‘A’ discussed in Section 5.5. The
true parameter values used in the simulation are shown by crosses. 137
5.5 2D marginalized posterior probability distributions for T and Mgas
for the analysis of the cluster simulation ‘A’ discussed in Section
5.5. The true parameter values used in the simulation are shown
by crosses. Uniform U(0, 20) keV and Gaussian (8 ± 2) keV prior
on T were used for the figures on the left and right hand–panels
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.6 1D marginalized posterior probability distributions for Mgas for the
analysis of the cluster simulation ‘A’ discussed in Section 5.5. The
true Mgas used in the simulation is shown by a ‘plus’ symbol. . . . 138
5.7 2D marginalized posterior probability distributions for the para-
meters of cluster MACS 0647+70. . . . . . . . . . . . . . . . . . . 142
6.1 Depiction of our likelihood constraint on the predicted value of
ΩDMh 2 due to lightest neutralinos, compared to a simple Gaussian
with WMAP5 central value and a 1σ uncertainty of 0.02. . . . . . 155
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