Valid Model-Free Spatial Prediction

Predicting the response at an unobserved location is a fundamental problem in spatial statistics. Given the difficulty in modeling spatial dependence, especially in nonstationary cases, model-based prediction intervals are at risk of misspecification bias that can negatively affect their validity. Here we present a new approach for model-free nonparametric spatial prediction based on the <i>conformal prediction</i> machinery. Our key observation is that spatial data can be treated as exactly or approximately exchangeable in a wide range of settings. In particular, under an infill asymptotic regime, we prove that the response values are, in a certain sense, locally approximately exchangeable for a broad class of spatial processes, and we develop a local spatial conformal prediction algorithm that yields valid prediction intervals without strong model assumptions like stationarity. Numerical examples with both real and simulated data confirm that the proposed conformal prediction intervals are valid and generally more efficient than existing model-based procedures for large datasets across a range of nonstationary and non-Gaussian settings.

在空间统计学领域，预测未观测点位的响应值是一项基础性研究问题。鉴于空间依赖关系建模的难点，尤其是非平稳场景下，基于模型的预测区间易陷入设定偏误风险，进而对其有效性产生负面影响。本文提出一种基于共形预测（conformal prediction）框架的无模型非参数空间预测新方法。本文核心观察在于：在诸多实际场景中，空间数据可被视为严格或近似可交换的。具体而言，在填充渐近（infill asymptotic）框架下，本文证明了对于广泛类别的空间过程，响应值在特定意义下具备局部近似可交换性；据此本文构建了局部空间共形预测算法，该算法无需平稳性等严苛模型假设，即可生成有效的预测区间。通过真实数据集与模拟数据集的数值实验验证表明：在各类非平稳、非高斯场景下，针对大规模数据集，本文提出的共形预测区间不仅具备有效性，且整体效率普遍优于现有基于模型的预测流程。