DAGnabbit! 在分层贝叶斯推理中确保噪声与探测的一致性
DAGnabbit! Ensuring Consistency between Noise and Detection in Hierarchical Bayesian Inference
AI总结：
本研究指出分层贝叶斯推理中部分近似方法违背物理探测过程的DAG逻辑会引发偏差，以引力波双星并合星表为例验证了该误差的影响，明确需在模拟中兼顾测量噪声与选择效应，为天体物理族群精确测量提供警示。
摘要：
分层贝叶斯推理可同时兼顾天文星表中的测量不确定性与选择效应。具体而言，所构建的层级结构编码了关于产生观测数据的物理过程之间相互依赖关系的信念。我们表明，文献中已提出的若干近似方法实际上对应的是与任何物理探测过程都不兼容的推理，而物理探测过程可用有向无环图（DAG）描述。这通常会导致偏差，且与“在给定真实源参数的情况下，可探测性与观测数据无关”这一假设相关。我们展示了多个示例，说明该错误会如何影响基于引力波观测到的并合双星星表的天体物理推理，包括错误估计并合率的红移演化，以及在广义相对论并非正确引力理论的情况下仍错误推断其为正确理论。一般而言，人们无法直接拟合“探测分布”并在后处理中“剔除”选择效应。类似地，在将理论预测与观测结果进行比较时，模拟探测数据（同时包含测量噪声和选择效应）要优于比较事件参数的探测分布估计值（这类估计值仅包含选择效应）。尽管对于中等规模的星表（约100个事件），由错误假设导致的模型误设所引入的偏差可能小于统计不确定性，但它们仍将对天体物理族群的精确测量构成重大障碍。
英文摘要：
Hierarchical Bayesian inference can simultaneously account for both measurement uncertainty and selection effects within astronomical catalogs. In particular, the hierarchy imposed encodes beliefs about the interdependence of the physical processes that generate the observed data. We show that several proposed approximations within the literature actually correspond to inferences that are incompatible with any physical detection process, which can be described by a directed acyclic graph (DAG). This generically leads to biases and is associated with the assumption that detectability is independent of the observed data given the true source parameters. We show several examples of how this error can affect astrophysical inferences based on catalogs of coalescing binaries observed through gravitational waves, including misestimating the redshift evolution of the merger rate as well as incorrectly inferring that General Relativity is the correct theory of gravity when it is not. In general, one cannot directly fit for the ``detected distribution'' and ``divide out'' the selection effects in post-processing. Similarly, when comparing theoretical predictions to observations, it is better to simulate detected data (including both measurement noise and selection effects) rather than comparing estimates of the detected distributions of event parameters (which include only selection effects). While the biases introduced by model misspecification from incorrect assumptions may be smaller than statistical uncertainty for moderate catalog sizes (O(100) events), they will nevertheless pose a significant barrier to precision measurements of astrophysical populations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
