Calibration ensures that predicted uncertainties align with observed uncertainties. While there is an extensive literature on recalibration methods for univariate probabilistic forecasts, work on calibration for multivariate forecasts is much more limited. This paper introduces a novel post-hoc recalibration approach that addresses multivariate calibration for potentially misspecified models. Our method involves constructing local mappings between vectors of marginal probability integral transform values and the space of observations, providing a flexible and model free solution applicable to continuous, discrete, and mixed responses. We present two versions of our approach: one uses K-nearest neighbors, and the other uses normalizing flows. Each method has its own strengths in different situations. We demonstrate the effectiveness of our approach on two real data applications: recalibrating a deep neural network's currency exchange rate forecast and improving a regression model for childhood malnutrition in India for which the multivariate response has both discrete and continuous components.

翻译：校准确保预测的不确定性与观测到的不确定性保持一致。尽管已有大量关于单变量概率预测再校准方法的文献，但针对多变量预测校准的研究则相对有限。本文提出了一种新颖的事后再校准方法，旨在解决可能设定错误模型的多变量校准问题。我们的方法通过构建边际概率积分变换值向量与观测空间之间的局部映射，提供了一种灵活且与模型无关的解决方案，适用于连续、离散及混合型响应变量。我们提出了该方法的两个版本：一种使用K近邻算法，另一种使用标准化流。每种方法在不同情境下各有优势。我们在两个实际数据应用中展示了该方法的有效性：一是对深度神经网络汇率预测的再校准，二是改进印度儿童营养不良的回归模型，该模型的多变量响应同时包含离散和连续分量。