SimSIMS: Simulation-based Supernova Ia Model Selection with thousands of latent variables

We present principled Bayesian model selection through simulation-based neural classification applied to SN Ia analysis. We validate our approach on realistically simulated SN Ia lightcurve data, demonstrating its ability to recover posterior model probabilities while marginalizing over > 4000 latent variables. We briefly explore the dependence of Bayes factors on the true parameters of simulated data, demonstrating Occam's razor for nested models. When applied to a sample of 86 low-redshift SNae Ia from the CSP, our method prefers a model with a single dust law and no magnitude step with host mass, while disfavouring different dust laws for low- and high-mass hosts with odds in excess of 100:1.