Type Ia supernovae (SNe Ia) are standarizable candles whose observed light curves can be used to infer their distances, which can in turn be used in cosmological analyses. As the quantity of observed SNe Ia grows with current and upcoming surveys, increasingly scalable analyses are necessary to take full advantage of these new datasets for precise estimation of cosmological parameters. Bayesian inference methods enable fitting SN Ia light curves with robust uncertainty quantification, but traditional posterior sampling using Markov Chain Monte Carlo (MCMC) is computationally expensive. We present an implementation of variational inference (VI) to accelerate the fitting of SN Ia light curves using the BayeSN hierarchical Bayesian model for time-varying SN Ia spectral energy distributions (SEDs). We demonstrate and evaluate its performance on both simulated light curves and data from the Foundation Supernova Survey with two different forms of surrogate posterior -- a multivariate normal and a custom multivariate zero-lower-truncated normal distribution -- and compare them with the Laplace Approximation and full MCMC analysis. To validate of our variational approximation, we calculate the pareto-smoothed importance sampling (PSIS) diagnostic, and perform variational simulation-based calibration (VSBC). The VI approximation achieves similar results to MCMC but with an order-of-magnitude speedup for the inference of the photometric distance moduli. Overall, we show that VI is a promising method for scalable parameter inference that enables analysis of larger datasets for precision cosmology.

翻译：Ia型超novae（SNe Ia）是可标准化的标准烛光，其观测到的光变曲线可用于推断距离，进而应用于宇宙学分析。随着当前及未来巡天项目观测到的SNe Ia数量不断增长，为充分利用这些新数据集以精确估计宇宙学参数，亟需发展更具可扩展性的分析方法。贝叶斯推断方法能够通过稳健的不确定性量化来拟合SNe Ia光变曲线，但传统的马尔可夫链蒙特卡洛（MCMC）后验采样计算成本高昂。本文提出一种变分推断（VI）实现方案，利用BayeSN层次贝叶斯模型对时变SNe Ia光谱能量分布（SEDs）进行建模，从而加速SNe Ia光变曲线拟合。我们通过模拟光变曲线和Foundation超新星巡天实测数据，采用两种替代后验分布形式——多元正态分布和自定义的多元零下限截断正态分布——对该方法进行验证与评估，并与拉普拉斯近似及完整MCMC分析进行对比。为验证变分近似效果，我们计算了帕累托平滑重要性采样（PSIS）诊断指标，并执行了基于变分推断的模拟校准（VSBC）。实验表明，在测光距离模数推断任务中，VI近似能够取得与MCMC相近的结果，同时实现数量级的速度提升。总体而言，我们证明VI是一种具有前景的可扩展参数推断方法，能够为精确宇宙学研究提供更大规模数据集的分析能力。