Accounting for Selection Effects in Supernova Cosmology with Simulation-Based Inference and Hierarchical Bayesian Modelling

TL;DR

This paper introduces a simulation-based inference method using normalizing flows and hierarchical Bayesian modeling to correct for selection biases like Malmquist bias in supernova cosmology, improving parameter estimation accuracy.

Contribution

It presents a novel approach combining normalizing flows and hierarchical Bayesian models to account for selection effects in supernova data analysis.

Findings

Achieved accurate posterior estimates on toy models within 1 sigma.

Demonstrated the method's effectiveness in correcting for observational biases.

Provided a framework adaptable to real supernova survey data.

Abstract

Type Ia supernovae (SNe Ia) are thermonuclear exploding stars that can be used to put constraints on the nature of our universe. One challenge with population analyses of SNe Ia is Malmquist bias, where we preferentially observe the brighter SNe due to limitations of our telescopes. If untreated, this bias can propagate through to our posteriors on cosmological parameters. In this paper, we develop a novel technique of using a normalising flow to learn the non-analytical likelihood of observing a SN Ia for a given survey from simulations, that is independent of any cosmological model. The learnt likelihood is then used in a hierarchical Bayesian model with Hamiltonian Monte Carlo sampling to put constraints on different sets of cosmological parameters conditioned on the observed data. We verify this technique on toy model simulations finding excellent agreement with analytically-derived posteriors to within $1 \sigma$.