空间科学中的推理空间空间——天文学、宇宙学与粒子物理中的参数贝叶斯推理

中文摘要 AI 辅助

本文研究了天文学、宇宙学和粒子物理中参数贝叶斯推理应用的样本，并补充了模拟数据集和 toy 问题。这些参数化物理模型的参数空间，以及通过分析特定数据得到的后验分布，可通过以下7个维度表征：(1)模型参数的数量；(2)后验形状是否类似高斯分布；(3)后验具有轻尾还是重尾；(4)后验与先验相比的大小，即数据的信息量；(5)是否部分参数仍未受约束而其他参数高度受约束；(6)后验是否存在多个不相连的模式；(7)推理是否经历相变。这些维度定义了推理问题的参数空间。我们对每个推理问题进行了表征，发现天体物理学中的推理覆盖了整个参数空间，从低维到高维、从单模态到多模态，以及从未信息量到高信息量的各种复杂分布。此外，物理模型的计算成本可从毫秒级到数十秒级。本文将整理后的推理问题样本作为新采样器的标准测试平台，为确保可复现性和易用性，还提供了Docker计算镜像。

英文摘要

A sample of parametric Bayesian inference applications from astronomy, cosmology and particle physics is studied, augmented by mock data sets and toy problems. The parameter spaces of these parametric physical models and their posterior distributions from analysing specific data are characterized by (1) the number of model parameters, (2) whether the posterior shape is similar to a Gaussian, (3) whether the posterior has light or heavy tails, (4) how small the posterior is compared to the prior, i.e., how informative the data are, (5) whether some parameters remain unconstrained while others are highly constrained, (6) whether the posterior has multiple, disconnected modes, and (7) whether the inference undergoes phase transitions. These axis define a parameter space of inference problems. We characterize each of the inference problems and observe that inference in astrophysics spans the entire parameter space, from low to high dimensionality, mono- to multi-modal, and a variety of complex distributions that range from uninformative to highly informative. Furthermore, the computational cost of the physical models can range from milliseconds to dozens of seconds. The collated sample of inference problems is proposed as a standard test bed for new samplers. For reproducibility and ease of use, a Docker compute image is provided.

发表机构

• Max Planck Institute for Extraterrestrial Physics（马克斯·普朗克地外物理学研究所）

机构由 AI 辅助整理，请以论文原文为准。

补充信息

备注

updated in response to referee report