The work presented in my thesis develops advanced Bayesian statistical methods for
using astrophysical data to probe our understanding of the Universe, I cover three
main areas:
Should we doubt the cosmological constant?
While Bayesian model selection is a useful tool to discriminate between competing
cosmological models, it only gives a relative rather than an absolute measure of how
good a model is. Bayesian doubt introduces an unknown benchmark model against
which the known models are compared, thereby obtaining an absolute measure of
model performance in a Bayesian framework. I apply this new methodology to the
problem of the dark energy equation of state, comparing an absolute upper bound
on the Bayesian evidence for a presently unknown dark energy model against a
collection of known models including a flat Lambda cold dark matter ( CDM )
scenario. I find a strong absolute upper bound to the Bayes factor between the
unknown model and CDM. The posterior probability for doubt is found to be less
than 13 per cent (with a 1 per cent prior doubt) while the probability for CDM rises
from an initial 25 per cent to almost 70 per cent in light of the data. I conclude
that CDM remains a sufficient phenomenological description of currently available
observations and that there is little statistical room for model improvement
Improved constraints on cosmological parameters from supernovae type Ia data:
I present a new method based on a Bayesian hierarchical model to extract constraints
on cosmological parameters from SNIa data obtained with the SALT-II lightcurve
fitter. I demonstrate with simulated data sets that our method delivers considerably
tighter statistical constraints on the cosmological parameters and that it outperforms
the usual chi-square approach 2/3 of the times. As a further benefit, a full posterior
probability distribution for the dispersion of the intrinsic magnitude of SNe is obtained.
I apply this method to recent SNIa data and find that it improves statistical
constraints on cosmological parameters from SNIa data. From the combination of
SNIa, CMB and BAO data I obtain Ωm = 0:28 ± 0:02; ΩΛ
= 0:73 ± 0:01 (assuming w = -1) and Ωm = 0:28 ± 0:01, w = -0:90 ± 0:05 (assuming flatness; statistical
uncertainties only). I constrain the intrinsic dispersion of the B-band magnitude of
the SNIa population, obtaining σ int μ = 0:13 ± 0:01[mag].
Robustness to systematics for future dark energy probes:
I extend the Figure of Merit formalism usually adopted to quantify the statistical
performance of future dark energy probes to assess the robustness of a future mission
to plausible systematic bias. I introduce a new robustness Figure of Merit which
can be computed in the Fisher Matrix formalism given arbitrary systematic biases
in the observable quantities. I argue that robustness to systematics is an important
new quantity that should be taken into account when optimizing future surveys. I
illustrate our formalism with toy examples, and apply it to future type Ia supernova
(SNIa) and baryonic acoustic oscillation (BAO) surveys. For the simplified systematic
biases that I consider, I find that SNIa are a somewhat more robust probe of
dark energy parameters than the BAO. I trace this back to a geometrical alignment
of systematic bias direction with statistical degeneracy directions in the dark energy
parameter space.