Likelihood-based inferences have been remarkably successful in wide-spanning application areas. However, even after due diligence in selecting a good model for the data at hand, there is inevitably some amount of model misspecification: outliers, data contamination or inappropriate parametric assumptions such as Gaussianity mean that most models are at best rough approximations of reality. A significant practical concern is that for certain inferences, even small amounts of model misspecification may have a substantial impact; a problem we refer to as brittleness. This article attempts to address the brittleness problem in likelihood-based inferences by choosing the most model friendly data generating process in a discrepancy-based neighbourhood of the empirical measure. This leads to a new Optimistically Weighted Likelihood (OWL), which robustifies the original likelihood by formally accounting for a small amount of model misspecification. Focusing on total variation (TV) neighborhoods, we study theoretical properties, develop inference algorithms and illustrate the methodology in applications to mixture models and regression.

翻译：基于似然的推断在广泛的应用领域中取得了显著成功。然而，即使审慎选择适合当前数据的模型，仍不可避免地存在一定程度的模型误设：异常值、数据污染或不恰当的参数假设（如高斯性）意味着大多数模型充其量只是对现实的粗略近似。一个重要的实际问题是，对于某些推断而言，即使少量模型误设也可能产生重大影响——我们将此问题称为脆弱性。本文尝试通过在选择与经验测度在基于差异的邻域内最友好的数据生成过程，来解决基于似然的推断中的脆弱性问题。这引出了新的乐观加权似然（OWL），该方法通过正式考虑少量模型误设来增强原始似然的稳健性。聚焦于全变差（TV）邻域，我们研究了其理论性质，开发了推断算法，并在混合模型和回归的应用中展示了该方法的有效性。