This paper presents BELLA, a deterministic and model-agnostic posterior explanation method for individual predictions of black-box regression models. To overcome the limitations of existing posterior explanation methods—which rely on synthetic data generation, leading to uncertainty, low reliability, and limited applicability to a small number of data points—BELLA provides explanations in the form of linear models trained in the feature space. BELLA maximizes the size of the neighborhood within which the linear model is applied, generating accurate, simple, general, and robust explanations.