In both observational data and randomized control trials, researchers select statistical models to articulate how the outcome of interest varies with combinations of observable covariates. Choosing a model that is too simple can obfuscate important heterogeneity in outcomes between covariate groups, while too much complexity risks identifying spurious patterns. In this paper, we propose a novel Bayesian framework for model uncertainty called Rashomon Partition Sets (RPSs). The RPS consists of all models that have posterior density close to the maximum a posteriori (MAP) model. We construct the RPS by enumeration, rather than sampling, which ensures that we explore all models with high evidence in the data, even if they offer dramatically different substantive explanations. We use a l0 prior, which allows the allows us to capture complex heterogeneity without imposing strong assumptions about the associations between effects, showing this prior is minimax optimal from an information-theoretic perspective. We characterize the approximation error of (functions of) parameters computed conditional on being in the RPS relative to the entire posterior. We propose an algorithm to enumerate the RPS from the class of models that are interpretable and unique, then provide bounds on the size of the RPS. We give simulation evidence along with three empirical examples: price effects on charitable giving, heterogeneity in chromosomal structure, and the introduction of microfinance.

翻译：在观测数据和随机对照试验中，研究者选择统计模型来阐明目标结果如何随协变量组合变化。过于简单的模型可能掩盖协变量组间结果的重要异质性，而过于复杂的模型则存在识别虚假模式的风险。本文提出一种新颖的贝叶斯模型不确定性框架——Rashomon分区集（RPS）。RPS包含所有后验密度接近最大后验（MAP）模型的模型。我们通过枚举而非采样构建RPS，这确保我们探索数据中具有高证据的所有模型，即使它们提供截然不同的实质性解释。我们采用l0先验，该先验允许在不施加效应间关联的强假设条件下捕获复杂异质性，并从信息论角度证明该先验具有极小极大最优性。我们刻画了在RPS条件下计算的参数（的函数）相对于整体后验的近似误差。我们提出一种算法，从可解释且唯一的模型类别中枚举RPS，并给出RPS规模的界限。我们提供仿真证据及三个实证案例：价格对慈善捐赠的影响、染色体结构的异质性以及小额信贷的引入。