Application of Bayesian statistics in Supernovae Ia cosmology
File(s)
Author(s)
Shariff, Hikmatali Ansar
Type
Thesis
Abstract
The purpose of this thesis is to apply Bayesian analysis to supernovae type Ia (SNIa)
cosmology to derive more accurate parameter estimation including cosmological parameters.
Additionally, it aims to improve the standard SALT2 light-curve fitting procedure by providing empirical and physically motivated correction to the linear
Tripp formalism. \n
BAHAMAS \n
We develop BAyesian HierArchical Modelling for the Analysis of Supernova cosmology
(BAHAMAS) software package for the analysis of SNIa cosmology in a statistically consistent manner. We apply our algorithm to a sample of 740 spectroscopically confirmed SNIa from the Joint Light-curve Analysis (JLA) dataset and simultaneously
determine cosmological parameters and population level parameters, including residual scatter. Combining JLA and Planck Cosmic Microwave Background data, we find significant discrepancies in cosmological parameter constraints with respect
to the standard analysis: we find
omega_m = 0.399 \pm 0.027, 2.8 \sigma higher than previously reported and w = -0.910 \pm 0.045, 1.6 \sigma higher than the standard analysis. \n
Extensions to SALT2 \n
BAHAMAS provides a framework for analysing to extensions the classical SALT2 light-curve fitting procedure including empirical corrections to the standard Phillips relationship. We analyse four extensions in this thesis. We use the host galaxy mass
as an additional covariate in the linear regression and allow for a redshift dependence for the colour-magnitude slope, \beta(z). We use the time of the second peak in the NIR band due to re-brightening, t_2, as an alternative standardization parameter of SNIa peak brightness. Finally we split the SNIa into two groups based on the distance to their host galaxy and investigate if SNIa further from the host galaxy are better standard candles. \n
Simple-BayeSN \n
Conventional SNIa cosmology analyses currently use a simplistic linear regression of magnitude versus colour and light curve shape. We construct a probabilistic generative model for the dusty distribution of extinguished absolute magnitudes
and apparent colours as the convolution of an intrinsic SNIa colour-magnitude distribution
and a host galaxy dust reddening-extinction distribution. Additionally, we combine Simple-BayeSN and BAHAMAS to allow for cosmological parameter
estimation of "dusty" SNIa light curves. \n
Selection Effects \n
Most modern SNIa cosmological analyses account for selection effects by a bias correction to the apparent magnitude (or distance modulus). However, within a
Bayesian framework, it is possible to consistently account for selection effects by associating a selection probability to each observation. We use SNANA simulations and supervised classifiers to predict the selection probability conditional on the
latent variables. Additionally, we use Monte Carlo simulations to integrate the latent variables and derive the selection probability conditional on the hyper-parameters (and redshift).
cosmology to derive more accurate parameter estimation including cosmological parameters.
Additionally, it aims to improve the standard SALT2 light-curve fitting procedure by providing empirical and physically motivated correction to the linear
Tripp formalism. \n
BAHAMAS \n
We develop BAyesian HierArchical Modelling for the Analysis of Supernova cosmology
(BAHAMAS) software package for the analysis of SNIa cosmology in a statistically consistent manner. We apply our algorithm to a sample of 740 spectroscopically confirmed SNIa from the Joint Light-curve Analysis (JLA) dataset and simultaneously
determine cosmological parameters and population level parameters, including residual scatter. Combining JLA and Planck Cosmic Microwave Background data, we find significant discrepancies in cosmological parameter constraints with respect
to the standard analysis: we find
omega_m = 0.399 \pm 0.027, 2.8 \sigma higher than previously reported and w = -0.910 \pm 0.045, 1.6 \sigma higher than the standard analysis. \n
Extensions to SALT2 \n
BAHAMAS provides a framework for analysing to extensions the classical SALT2 light-curve fitting procedure including empirical corrections to the standard Phillips relationship. We analyse four extensions in this thesis. We use the host galaxy mass
as an additional covariate in the linear regression and allow for a redshift dependence for the colour-magnitude slope, \beta(z). We use the time of the second peak in the NIR band due to re-brightening, t_2, as an alternative standardization parameter of SNIa peak brightness. Finally we split the SNIa into two groups based on the distance to their host galaxy and investigate if SNIa further from the host galaxy are better standard candles. \n
Simple-BayeSN \n
Conventional SNIa cosmology analyses currently use a simplistic linear regression of magnitude versus colour and light curve shape. We construct a probabilistic generative model for the dusty distribution of extinguished absolute magnitudes
and apparent colours as the convolution of an intrinsic SNIa colour-magnitude distribution
and a host galaxy dust reddening-extinction distribution. Additionally, we combine Simple-BayeSN and BAHAMAS to allow for cosmological parameter
estimation of "dusty" SNIa light curves. \n
Selection Effects \n
Most modern SNIa cosmological analyses account for selection effects by a bias correction to the apparent magnitude (or distance modulus). However, within a
Bayesian framework, it is possible to consistently account for selection effects by associating a selection probability to each observation. We use SNANA simulations and supervised classifiers to predict the selection probability conditional on the
latent variables. Additionally, we use Monte Carlo simulations to integrate the latent variables and derive the selection probability conditional on the hyper-parameters (and redshift).
Version
Open Access
Date Issued
2017-12
Date Awarded
2018-09
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Trotta, Roberto
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)