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Title: Cosmology in the presence of non-Gaussianity
Author: Schuhmann, R. L.
ISNI:       0000 0004 7224 1102
Awarding Body: UCL (University College London)
Current Institution: University College London (University of London)
Date of Award: 2017
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Modern observational cosmology relies on statistical inference, which models measurable quantities (including their systematic and statistical uncertainties) as random variates, examples are model parameters ('cosmological parameters') to be estimated via regression, as well as the observable data itself. In various contexts, these exhibit non-Gaussian distribution properties, e.g., the Bayesian joint posterior distribution of cosmological parameters from different data sets, or the random fields affected by late-time nonlinear structure formation like the convergence of weak gravitational lensing or the galaxy density contrast. Gaussianisation provides us with a powerful toolbox to model this non-Gaussian structure: a non-linear transformation from the original non-Gaussian random variate to an auxiliary random variate with (approximately) Gaussian distribution allows one to capture the full distribution structure in the first and second moments of the auxiliary. We consider parametric families of non-linear transformations, in particular Box-Cox transformations and generalisations thereof. We develop a framework that allows us to choose the optimally-Gaussianising transformation by optimising a loss function, and propose methods to assess the quality of the optimal transform a posteriori. First, we apply our maximum-likelihood framework to the posterior distribution of Planck data, and demonstrate how to reproduce the contours of credible regions without bias - our method significantly outperforms the current gold standard, kernel density estimation. Next, we use Gaussianisation to compute the model evidence for a combination of CFHTLenS and BOSS data, and compare to standard techniques. Third, we find Gaussianising transformations for simulated weak lensing convergence maps. This increases the information content accessible to two-point statistics (e.g., the power spectrum) and potentially allows for rapid production of independent mock maps with non-Gaussian correlation structure. With these examples, we demonstrate how Gaussianisation expands our current inference toolbox, and permits us to accurately extract information from non-Gaussian contexts.
Supervisor: Joachimi, B. ; Peiris, H. V. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available