A Transdimensional Perspective on Dark Matter

Abstract

Robust uncertainty propagation and marginalization over nuisance parameters is the key to per- form robust inference. This thesis introduces a transdimensional, hierarchical, threshold-free, and Bayesian inference framework. Colloquially referred to as probabilistic cataloging, the paradigm propagates within and across model covariances, reduces mismodeling and information loss due to thresholding based on statistical significance, and accelerates computation to ensure scalability. The main product is a Python implementation of probabilistic cataloging called the Probabilistic Cataloger (PCAT). The code and its documentation are available on GitHub and readthedocs, respectively, for the use of the scientific community. A central problem in contemporary cosmology is dark matter. Astrophysical data sets such as telescope images that aim to probe the characteristics of dark matter, require covariant models and aim to recover information contained in data features potentially caused by model elements with low statistical significance. Using probabilistic cataloging, the thesis presents two inferences of the properties of dark matter, e.g., self-annihilation of Weakly Interacting Massive Particles (WIMPs) in the inner Milky, and the small-scale structure of dark matter in galactic halos. The role of various priors in probabilistic cataloging are also studied.