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 frequentist and Bayesian dataset-wide probabilistic inference in cases where the likelihood is intractable, but simulations can be realized via a hierarchical forward model. We construct neural estimators for the likelihood(-ratio) or posterior and show that explicitly accounting for the model's hierarchical structure can lead to significantly tighter parameter constraints. We ground our discussion using case studies from the physical sciences, focusing on examples from particle physics and cosmology.

翻译：在分析真实世界数据时，通常需要处理事件集合，这些集合由多组观测数据组成，共同约束所关注基础模型的参数。此类模型通常具有分层结构，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计算但可通过分层前向模型实现仿真的情况，引入了频率学派和贝叶斯学派的全数据集概率推断实用方法。我们构建了用于估计似然（比）或后验的神经估计器，并证明明确考虑模型的分层结构可显著收紧参数约束。通过来自物理科学领域的案例研究（重点聚焦粒子物理和宇宙学实例），我们对相关讨论进行了实证支撑。