AI 中文总结
该研究提出NNnGP模型，通过扩展NNGP并结合正则化同质性条件与归一化流变分推断，有效捕捉空间数据的非高斯特征，缓解极端事件低估问题，在合成与真实降水数据上验证了其有效性。
AI 中文摘要
我们开发了一类通用的最近邻非高斯过程（NNnGP），用于对地统计数据进行建模。通过将非线性条件均值函数引入Vecchia近似，NNnGP扩展了流行的最近邻高斯过程（NNGP），以有效捕捉复杂的非高斯空间特征。为了确保从单个实现中获得一致的空间预测，我们提出了单变量条件分布间的正则化同质性条件。随后，我们使用高斯过程对条件均值进行贝叶斯非参数构造，并将所得的NNnGP作为非高斯空间先验嵌入分层回归模型中。对于后验计算和预测，我们采用了基于归一化流的变分推断方法。在合成数据和真实世界PRISM降水异常数据上的数值实验表明，NNnGP能够捕捉局部非线性依赖关系，显著缓解极端空间事件的低估问题，同时保持全局预测准确性。
英文摘要
We develop a general class of nearest-neighbor non-Gaussian processes (NNnGP) for modeling geostatistical data. By introducing non-linear conditional mean functions into the Vecchia approximation, NNnGP extends the popular nearest-neighbor Gaussian process (NNGP) to effectively capture complex, non-Gaussian spatial characteristics. To ensure coherent spatial predictions from a single realization, we propose a regularized homogeneity condition across the univariate conditionals. We then formulate a Bayesian non-parametric construction of the conditional mean using Gaussian processes and embed the resulting NNnGP as a non-Gaussian spatial prior within a hierarchical regression model. For posterior computation and prediction, we adopt a normalizing flow-based variational inference approach. Numerical experiments on synthetic data and real-world PRISM precipitation anomalies demonstrate that NNnGP captures local non-linear dependencies and significantly mitigates the underestimation of extreme spatial events, all the while maintaining global predictive accuracy.
