We address the challenge of constructing valid confidence intervals and sets in problems of prediction across multiple environments. We investigate two types of coverage suitable for these problems, extending the jackknife and split-conformal methods to show how to obtain distribution-free coverage in such non-traditional, hierarchical data-generating scenarios. Our contributions also include extensions for settings with non-real-valued responses and a theory of consistency for predictive inference in these general problems. We demonstrate a novel resizing method to adapt to problem difficulty, which applies both to existing approaches for predictive inference with hierarchical data and the methods we develop; this reduces prediction set sizes using limited information from the test environment, a key to the methods' practical performance, which we evaluate through neurochemical sensing and species classification datasets.

在多个环境下进行预测的情况中，我们解决了构建有效置信区间和集合的挑战。通过扩展自助法和分割一致性方法，我们研究了适用于这些问题的两种覆盖类型，展示了如何在这些非传统的分层数据生成场景中获得无分布覆盖。我们还在非实数值响应的设置中进行了扩展，并在这些一般问题中建立了一致性理论。我们演示了一种新的调整方法以适应问题的难度，该方法既适用于具有分层数据的预测推断的现有方法，又适用于我们开发的方法；通过神经化学感应和物种分类数据集，我们评估了方法的实际性能。

多环境场景下的预测推理