The Challenge in Illuminating the Invisible: Constraining LyC Escape with Bayesian Modelling and Symbolic Regression

Direct observations of Lyman continuum (LyC) radiation from galaxies during the Epoch of Reionization (EoR) are impeded by absorption in the intergalactic medium, requiring indirect methods to infer the escape fraction of ionizing photons ($f_{\rm esc}^{\rm LyC}$). One approach is to develop and validate such methods on local analogues of the high-redshift galaxies with directly detected LyC leakage. In this study, we constrain $f_{\rm esc}^{\rm LyC}$ using a Bayesian spectral energy distribution (SED) fitting framework built on Prospector, which incorporates a non-parametric star-formation history, a flexible dust attenuation curve, self-consistent nebular emission, and fiber aperture-loss corrections. Our methodology jointly fits broadband photometry and emission line fluxes. We apply six models to the Low-redshift LyC Survey (LzLCS), a sample of local galaxies with physical properties comparable to EoR galaxies, and evaluate them based on their ability to recover the observed flux and their relative Bayesian evidence. The best-performing model is further assessed through a parameter recovery test, demonstrating that $f_{\rm esc}^{\rm LyC}$ can be recovered within uncertainties. Building on these results, we present updated $f_{\rm esc}^{\rm LyC}$ estimates for the LzLCS sample, with a median of 4\%, and values reaching as high as 51\%, with 26 of 64 galaxies having a cosmologically relevant $f_{\rm esc}^{\rm LyC}$($\gtrsim5\%$). Additionally, we present a revised UV $\beta$-slope vs $\log_{10}(f_{\rm esc}^{\rm LyC})$ relation, derived using symbolic regression with PySR trained on a synthetic dataset generated with \texttt{Prospector}:$\log_{10}(f_{\rm esc}^{\rm LyC}) = (-2.30 \pm 1.28)\beta - (6.26 \pm 2.91)$, ($\sigma = 0.43$~dex). The relation successfully reproduces the $f_{\rm esc}^{\rm LyC}$ obtained from full SED fitting of the LzLCS sample within $1\sigma$.