Type Ia supernovæ (SNæ Ia) are extremely powerful stellar explosions used for measuring cosmographical distances and constraining parameters of the cosmological model via standardisation: the process of inferring their intrinsic brightness from properties of the observed light curves. Inference from current data sets (≈2000 objects) is already dominated not by statistical noise but by systematic uncertainties and modelling choices. The very near future promises vast amounts of new data (∼100 000 SNæ Ia), accompanied by new modelling challenges like the unavailability of spectroscopic classification and precise redshift measurements.
Embedded within the framework of neural simulation-based Bayesian inference (SBI), this thesis presents solutions for no-compromise analyses of future large SN surveys on three fronts: model realism, scalability, and probabilistic rigour. We develop a modern GPU-accelerated simulator for SN light curves that incorporates realistic uncertainties in the SN Ia flux template and physically motivated dust extinction in the host and Milky Way. We then use it to analyse a low-redshift SN Ia sample, inferring simultaneously all global and object-specific parameters with truncated marginal neural ratio estimation in excellent agreement with conventional methods. Moreover, we describe a procedure to construct calibrated regions with exact frequentist confidence from the approximate Bayesian results. With minimal extra training and re-using simulations, we also perform fully Bayesian model comparison of host mass-dependent standardisation and dust models, deemed extremely challenging computationally for high-dimensional problems. We furthermore demonstrate scalable set-based neural inference from up to 100 000 mock SNæ Ia, elucidating the biases introduced by model simplifications used for handling photometric redshift uncertainties and selection effects. Finally, we combine SN and host-galaxy modelling in a one-stop SBI framework for SN cosmology.
