Many modern applications of Bayesian inference, such as in cosmology, are based on complicated forward models with high-dimensional parameter spaces. This considerably limits the sampling of posterior distributions conditioned on observed data. In turn, this reduces the interpretability of posteriors to their one- and two-dimensional marginal distributions, when more information is available in the full dimensional distributions. We show how to learn smooth and differentiable representations of posterior distributions from their samples using normalizing flows, which we train with an added evidence error loss term, to improve accuracy in multiple ways. Motivated by problems from cosmology, we implement a robust method to obtain one and two-dimensional posterior profiles. These are obtained by optimizing, instead of integrating, over other parameters, and are thus less prone than marginals to so-called projection effects. We also demonstrate how this representation provides an accurate estimator of the Bayesian evidence, with log error at the 0.2 level, allowing accurate model comparison. We test our method on multi-modal mixtures of Gaussians up to dimension 32 before applying it to simulated cosmology examples. Our code is publicly available at https://github.com/mraveri/tensiometer.
Fast Parameter Inference on Pulsar Timing Arrays with Normalizing Flows
Rutgers University（罗格斯大学）；Cornell University（康奈尔大学）；Vanderbilt University（范德堡大学）；University of Florida（佛罗里达大学）；University of California Santa Cruz（加州大学圣克鲁兹分校）
Learned harmonic mean estimation of the Bayesian evidence with normalizing flows
Mullard Space Science Laboratory, University College London（穆拉德空间科学实验室，伦敦大学学院）；Centre Universitaire d'Informatique, Université de Genève（日内瓦大学计算机中心，日内瓦大学）；Department of Physics, Royal Holloway, University of London（物理系，伦敦大学皇家霍洛威学院）；Alan Turing Institute（艾伦·图灵研究所）
Marginal Post Processing of Bayesian Inference Products with Normalizing Flows and Kernel Density Estimators
Cavendish Laboratory（卡文迪许实验室）；Kavli Institute for Cosmology, Cambridge（剑桥卡弗里宇宙学研究所）；University College London（伦敦大学学院）；University of Sussex（萨塞克斯大学）；McGill University（麦吉尔大学）；University of Cambridge（剑桥大学）；Stockholm University（斯德哥尔摩大学）
A normalizing flow approach for the inference of star cluster properties from unresolved broadband photometry I: Comparison to spectral energy distribution fitting
Universität Heidelberg（海德堡大学）；Université Côte d’Azur（蔚蓝海岸大学）；Universidad Nacional Autónoma de México（墨西哥国立自治大学）；INAF – Arcetri Astrophysical Observatory（意大利国家天体物理研究所阿切特里天文台）；University of Wyoming（怀俄明大学）；Australian National University（澳大利亚国立大学）；The Johns Hopkins University（约翰斯·霍普金斯大学）
Assessment of normalizing flows for parameter estimation on time-frequency representations of gravitational-wave data
Universidad de Oviedo（奥维耶多大学）；Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA)（阿斯图里亚斯宇宙科学与技术大学研究所）；Universitat de València（瓦伦西亚大学）；Centro de Física das Universidades do Minho e do Porto (CF-UM-UP), Universidade do Minho（米尼奥与波尔图大学物理中心（CF-UM-UP），米尼奥大学）
Simulation-based Inference for Exoplanet Atmospheric Retrieval: Insights from winning the Ariel Data Challenge 2023 using Normalizing Flows
AstroAI；Ecole Polytechnique（巴黎综合理工学院）；Institute of Theory and Computation（理论与计算研究所）；Massachusetts Institute of Technology（麻省理工学院）；University of Southampton（南安普顿大学）；Kavli Institute for Astrophysics and Space Research（卡弗里天体物理与空间研究所）
