FlowSN: Normalising Flows for Simulation-Based Inference under Realistic Selection Effects applied to Supernova Cosmology

2026-03-11

AI Summary

This study addresses biases in cosmological parameter inference arising from selection effects—such as Malmquist bias—in astronomical observations. The authors propose a simulation-based inference approach that employs normalizing flows to learn the selection likelihood of supernova observations directly from forward simulations, embedding this learned likelihood within a hierarchical Bayesian framework for posterior inference. This method achieves efficient and low-bias parameter estimation for the first time in LSST-like SNANA simulations. Its key innovation lies in constructing a reusable, cosmology-agnostic likelihood approximation module. Experiments demonstrate that posterior estimates of critical parameters, such as the dark energy equation-of-state parameter \( w_0 \), exhibit an order-of-magnitude reduction in bias compared to conventional methods, along with superior frequentist calibration.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Social Networks and Social Media: Fairness and bias in social network and social media analysis
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We present FlowSN, a statistical framework using simulation-based inference with normalising flows to account for selection effects in observational astronomy. Failure to account for selection effects can lead to biased inference on global parameters. An example is Malmquist bias, where detection limits result in a sample skewed towards brighter objects. In Type Ia supernova (SN Ia) cosmology, these selection effects can systematically shift the inferred posterior distributions of cosmological parameters, necessitating the development of robust statistical frameworks to account for the biases. Simulation-based inference enables us to implicitly learn probability distributions that are analytically intractable to calculate. In this work, we introduce a novel approach that employs a normalising flow to learn the non-analytic selected SN likelihood for a given survey from forward simulations, independent of the assumed cosmological model. The resulting likelihood approximation is incorporated into a hierarchical Bayesian framework and posterior sampling is performed using Hamiltonian Monte Carlo to obtain constraints on cosmological parameters conditioned on the observed data. The modular learnt likelihood approximation can be reused without retraining to evaluate different cosmological models, providing a key advantage over other simulation-based inference approaches. We demonstrate the performance of this methodology by training and testing the simulation-based inference technique using realistic LSST-like SNANA simulations for the first time. Our FlowSN approach yields accurate posterior estimates on cosmological parameters, including the dark energy equation of state $w_0$, that are an order of magnitude less biased than those obtained with conventional techniques and also exhibit improved frequentist calibration.

Problem

• selection effects
• supernova cosmology
• biased inference
• Malmquist bias
• cosmological parameters

Innovation

• normalising flows
• simulation-based inference
• selection effects
• supernova cosmology
• likelihood-free inference