When analyzing real-world data it is common to work with event ensembles, which comprise sets of observations that collectively constrain the parameters of an underlying model of interest. Such models often have a hierarchical structure, where "local" parameters impact individual events and "global" parameters influence the entire dataset. We introduce practical approaches for optimal dataset-wide probabilistic inference in cases where the likelihood is intractable, but simulations can be realized via forward modeling. We construct neural estimators for the likelihood(-ratio) or posterior and show that explicitly accounting for the model's hierarchical structure can lead to tighter parameter constraints. We ground our discussion using case studies from the physical sciences, focusing on examples from particle physics (particle collider data) and astrophysics (strong gravitational lensing observations).

翻译：在分析实际数据时，通常需要处理事件集合，这些集合由一组观测数据组成，共同约束所关注的基础模型参数。此类模型往往具有分层结构，其中"局部"参数影响单个事件，而"全局"参数则影响整个数据集。我们针对似然函数难以处理但可通过正向建模实现模拟的情况，引入了实现最优数据集级概率推断的实用方法。我们构建了用于估计似然（比）或后验的神经网络估计器，并证明显式考虑模型的分层结构可以产生更紧致的参数约束。我们通过物理科学中的案例研究来阐述上述讨论，重点聚焦于粒子物理学（粒子对撞机数据）和天体物理学（强引力透镜观测）中的实例。