Bayesian Hierarchical Model for cross calibration of hybrid air shower detectors

Anatoli Fedynitch¹, Anton Prosekin^1*, Kozo Fujisue¹

¹High Energy Theory Group, Institute of Physics, Academia Sinica, Taipei, Taiwan

* Presenter:Anton Prosekin, email:antonpr@gate.sinica.edu.tw

Energy calibration in indirect air shower detection presents a challenging problem due to the impossibility of controlled laboratory validation. Traditionally, hybrid measurements combining fluorescence detectors (FD) and surface detectors (SD) have relied on calibrating the SD using FD data, assuming that fluorescence measurements closely reflect the calorimetric principle. However, SD energy estimations depend on approximate empirical relationships or Monte Carlo simulations, both of which require reliable extrapolation beyond the limited energy range covered by high-statistics FD observations. Crucially, systematic uncertainties in fluorescence yield, invisible energy fraction, atmospheric conditions, detection efficiency, mass composition dependence, and proxy variable reconstruction are often overlooked or oversimplified, potentially introducing biases into calibration results and subsequent analyses. In this work, we introduce an unbinned Bayesian Hierarchical Model capable of integrating detection uncertainties event-by-event, ensuring unbiased calibration and systematic error propagation. Using toy simulations, we illustrate how common simplifications lead to biased outcomes and quantify the impact of detection and systematic uncertainties on energy calibration accuracy at ultra-high energies.

Keywords: UHECR, Air shower detection, Energy calibration, Bayesian hierarchical modeling, Systematic uncertainties