Abstract: 
In this talk, I will discuss two applications of Bayesian surrogate models. Firstly, I'll detail how we construct a datadriven surrogate model for quasar emission, using Bayesian model selection to probabilistically detect damped Lyman alpha absorbers (DLAs) and metal absorbers in SDSS quasar spectra. Our model encodes the full covariance of quasar emissions and the redshift evolution of optical depth, enabling us to offer probabilistic detections even for low SNR spectra. This technique has been adopted by DESI, improving the accuracy of the Lya 1D flux power spectrum. In the second part, I'll demonstrate how we employ a multifidelity technique to build a surrogate model (emulator) for cosmological hydrodynamical simulations with varying qualities. I will present an application using PRIYA simulations, a galaxy formation simulation suite, based on the ASTRID simulation model, with 9dimensional cosmological and astrophysical feedback parameters. We apply this model to the eBOSS Lya flux 1D power spectrum, yielding new cosmological constraints. The emulator infers σ₈ = 0.733 ± 0.026, a result that aligns with DES and other smallscale probes and presenting tension with CMB measurements. Additionally, I will discuss other astrophysical inference results, including the notable excess of Lyman limit systems in the data.
