We present FlowSN, a statistical framework using simulation-based inference (SBI) 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. SBI 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 SBI approaches. We demonstrate the performance of this methodology by training and testing the SBI 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.

翻译：我们提出FlowSN，一种利用归一化流（normalising flows）进行基于模拟的推断（SBI）的统计框架，用于处理观测天文学中的选择效应。未能考虑选择效应可能导致对全局参数的推断产生偏差。一个典型例子是马尔姆奎斯特偏差（Malmquist bias），其中探测极限导致样本偏向于更亮的天体。在Ia型超新星（SN Ia）宇宙学中，这些选择效应会系统性偏移宇宙学参数的后验推断分布，因此需要开发稳健的统计框架来处理这些偏差。SBI使我们能够隐式学习那些解析上难以计算的概率分布。在本工作中，我们引入了一种新方法，利用归一化流从正向模拟中学习给定巡天的非解析选定超新星似然函数，且该过程独立于假定的宇宙学模型。由此得到的似然近似被纳入分层贝叶斯框架，并通过哈密顿蒙特卡洛（Hamiltonian Monte Carlo）进行后验采样，以获得基于观测数据的宇宙学参数约束。这种模块化的学习似然近似可重复使用于评估不同宇宙学模型，而无需重新训练，这为其他SBI方法提供了关键优势。我们首次通过使用类似LSST的SNANA模拟来训练和测试SBI技术，展示了该方法的性能。我们的FlowSN方法在宇宙学参数（包括暗能量状态方程$w_0$）上获得了准确的后验估计，其偏差比传统技术低一个数量级，并展现出改进的频率论校准特性。