Accelerated Bayesian inference techniques for event based datasets

Westerkamp, Margret (2025): Accelerated Bayesian inference techniques for event based datasets: in nested sampling and X-ray astronomy. Dissertation, LMU München: Fakultät für Physik

Abstract

The updating of our knowledge in response to new information can prove to be complex, both in everyday life and in science. Bayes' theorem provides a systematic, probabilistic framework for updating our knowledge given new data. In any case of Bayesian inference - parameter estimation, model comparison, or field inference - probability distributions are used to encode our knowledge about the quantity of interest. This quantity is referred to as the signal. To compute the posterior probability of the signal in the presence of new data, Bayes' theorem combines prior knowledge of the signal with knowledge of the data measurement process, represented by the likelihood. This probabilistic approach not only provides a posterior estimate of the signal, but also allows for uncertainty quantification. This thesis focuses on Bayesian field inference built upon information field theory. Inferring a field from an inherently finite data set is an under-constrained problem. Hence, the inclusion of prior knowledge is essential. In the present work, the implementation of generative, non-parametric prior models allows to exploit possibly complex and a priori unknown correlation structures of the signal during inference. Two distinct applications of Bayesian field inference are discussed: Bayesian evidence calculation and imaging. The methodological part addresses the calculation of the posterior normalization - the Bayesian evidence. The evidence plays an important role in Bayesian model comparison. However, the evidence may be computationally intractable, for example due to complex relationships between the prior and posterior. Nested sampling provides a numerical estimate of the evidence by examining the likelihood as a function of enclosed prior volumes. In particular, the algorithm is based on statistical estimates of the prior volumes, introducing a stochastic error. For this reason a one-dimensional Bayesian field inference problem is formulated to obtain improved estimates of the prior volumes and the corresponding evidence. The second and main part is dedicated to advancing Bayesian imaging of the X-ray sky. Observed by space-based telescopes, X-rays allow us to study some of the most energetic phenomena in the universe. However, the interpretability of the data is limited by overlapping X-ray sources, Poisson noise, and instrumental effects such as the point spread function. In this context, Bayesian forward models are constructed for the X-ray telescopes Chandra and eROSITA, tailored to their instrumental properties, to obtain denoised, deconvolved, decomposed, and spatio-spectral resolved images of the X-ray object of interest. The work presented includes the development of the JAX-accelerated open source software package J-UBIK to support future and existing Bayesian imaging models. Imaging results for the supernova remnant of SN1006 and for the Large Magellanic Cloud provide a detailed view of the diffuse X-ray structures and the separated point sources. This paves the way for future analysis of such fine-scale structures, such as shock fronts of supernova remnants, the construction of point source catalogs, and possibly improved instrument calibration.

• Dokumententyp: Dissertationen (Dissertation, LMU München)
• Themengebiete: 500 Naturwissenschaften und Mathematik ; 500 Naturwissenschaften und Mathematik > 530 Physik
• Fakultäten: Fakultät für Physik
• Sprache der Hochschulschrift: Englisch
• Datum der mündlichen Prüfung: 6. März 2025
• 1. Bericht­erstatter:in: Enßlin, Torsten