标题： 基于模拟推断和分层贝叶斯建模的超新星宇宙学中选择效应的处理 显示英文标题

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

摘要： I型超新星（SNe Ia）是热核爆炸恒星，可用于对我们的宇宙本质施加约束。 SNe Ia群体分析的一个挑战是马尔姆奎斯特偏差，由于望远镜的限制，我们倾向于观察更明亮的SNe。 如果不处理，这种偏差可能会传播到我们对宇宙学参数的后验分布上。 在本文中，我们开发了一种新技术，使用归一化流从模拟中学习给定调查下观测到SNe Ia的非解析似然，该似然独立于任何宇宙学模型。 然后将学习到的似然用于分层贝叶斯模型，并使用哈密顿蒙特卡洛采样来对不同的一组宇宙学参数施加约束，这些参数基于观测数据。 我们在玩具模型模拟上验证了这项技术，发现与解析推导的后验分布在$1 \sigma$以内有很好的一致性。 显示英文摘要

摘要： 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 $1 \sigma$.