Title:

Advanced statistical methods for astrophysical probes of cosmology

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 SALTII 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 chisquare 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 Bband 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.
