Statistical methods with machine learning in astroparticle physicsBortolato, Blaž (Avtor) Kamenik, Jernej (Mentor) kozmični žarkisestavastatistična inferencaverjetnostna funkcijaklasifikacijaobservatorij Pierre AugerUnderstanding the composition of ultra-high-energy cosmic rays (UHECRs) is essential for constraining their origins, unveiling acceleration mechanisms, and potentially studying hadron interactions at extreme energies. This thesis presents a comprehensive analysis of UHECR composition through a novel method, using publicly available data from the Pierre Auger Observatory and simulated events generated with four hadronic models—EPOS, Sibyll, QGSJet01, and QGSJetII-04—across multiple energy intervals. The proposed method compares features of measured and simulated events while accounting for systematic and statistical uncertainties in both datasets. This approach enables exploration of a broad range of possible compositions, from protons to iron and up to uranium. We compute rejection confidence levels for each hadronic model based on inferred compositions and introduce a method for generating lists of distinguishable nuclei for inference, as well as determining the minimum number of nuclei required for unbiased composition inference. Key results include bounds on the fraction of primaries with atomic numbers greater than a given $Z$, from $Z=1$ (proton) to $Z=94$ (plutonium), and event classification by primary type. Additionally, we propose a method to effectively increase the number of fluorescence events by leveraging correlations between fluorescence-based observable $\X_{\max}$ and ground-based observables. The developed methods provide a flexible and efficient framework for UHECR composition inference, advancing research in the field and offering statistical techniques applicable across various domains.20252025-01-24 08:15:05Doktorsko delo/naloga166750sl