Embedding the Big Bang Cosmological Model into a Bayesian Hierarchical Model for Super Nova Light Curve Data

• Activity Number: 47
• Type: Invited
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): David van Dyk*+ and Xiyun Jiao and Roberto Trotta
• Companies: Imperial College London and Imperial College London and Imperial College London
• Keywords: Astrostatistics ; Model Diagnostics ; Computer Model ; Partially Collapsed Gibbs Sampler ; ASIS Sampling

Abstract

The 2011 Nobel Prize in Physics was awarded for the discovery that the expansion of the Universe is accelerating. This talk describes a Bayesian model that relates the difference between the apparent and intrinsic brightnesses of object to their distance which in turn depends on parameters that describe this expansion. While apparent brightness can be readily measured, intrinsic brightness can only be obtained for certain objects. Type Ia Supernova occur when material accreting onto a white dwarf drives mass above a threshold and triggers a powerful supernova explosion. Because this occurs only in a particular physical scenario, we can use covariates to estimate intrinsic brightness. We use a hierarchical Bayesian model to leverage this information to study the expansion history of the Universe. The model includes computer models that relate expansion parameters to observed brightnesses along with components that account for measurement error, data contamination, dust absorption, repeated measures, and covariate adjustment uncertainty. Sophisticated MCMC methods are employed for model fitting and a secondary Bayesian analysis is conducted for residual analysis and model checking.