Hierarchical Bayesian Models for inference using RR Lyrae as standard candles in the Gaia Era

RR Lyrae stars are periodic variable stars considered standard candles, allowing their distances to be estimated from their intrinsic brightness, which depends on their pulsation period and chemical composition through Period-Luminosity-Metallicity relations. These stars are well represented in components of our galaxy like the disc, bulge, and halo, suggesting they could also trace the geometry of composite objects like the Large Magellanic Cloud (LMC).

Traditional methods using RR Lyrae stars as standard candles have shortcomings, including inadequate uncertainty treatment, omission of relevant information for improved model fitting, and lack of continuity between model fitting and distance estimation. These issues partly arise from the scarcity of trigonometric parallaxes, crucial for fitting Period-Luminosity-Metallicity relations. The thesis proposes an alternative methodological framework combining probabilistic models for directed graphs as a knowledge representation formalism and Bayesian statistical inference for learning and prediction. This framework allows constructing unified generative models representing domain knowledge at different levels, including characterising RR Lyrae populations based on their spatial distribution, luminosity, period, and chemical composition, as well as modelling intrinsic and observable properties of individual stars and their relationships.

The thesis applies the hierarchical Bayesian modelling framework to ab-type RR Lyrae stars in the Milky Way field and globular clusters, as well as in its satellite galaxy, the Large Magellanic Cloud. Using semi-synthetic data, it demonstrates correlations between metallicity, period, and parallax for RR Lyrae ab stars in the field of the Milky Way, proposing a 3D Gaussian mixture prior to better recover Period-Luminosity-Metallicity relation parameters under large parallax uncertainties. It infers these relations from multi-band photometry and {\it Gaia} parallaxes, derives spatial distributions, and performs comparative analyses across populations. It introduces techniques to estimate metallicity of RR Lyrae ab stars from light curve Fourier parameters, and characterise local {\it Gaia} parallax systematic errors in the LMC using radial basis function regression. For RR Lyrae ab star population in the LMC, it constructs a chemo-spatial model with two metallicity-dependent geometric components, but finds convergence issues suggesting a more complex geometry beyond the two-component assumption.