Vecchia Likelihood Approximation for Accurate and Fast Inference with Intractable Spatial Max-Stable Models
提出用Vecchia近似分解高维最大稳定模型的似然函数，通过精心选择的条件集加速推断，在模拟和红海海表温度数据中比传统复合似然方法更高效、更准确。
Max-stable processes are the most popular models for high-impact spatial extreme events, as they arise as the only possible limits of spatially-indexed block maxima.However, likelihood inference for such models suffers severely from the curse of dimensionality, since the likelihood function involves a combinatorially exploding number of terms.In this article, we propose using the Vecchia approximation, which conveniently decomposes the full joint density into a linear number of low-dimensional conditional density terms based on well-chosen conditioning sets designed to improve and accelerate inference in high dimensions.Theoretical asymptotic relative efficiencies in the Gaussian setting and simulation experiments in the maxstable setting show significant efficiency gains and computational savings using the Vecchia likelihood approximation method compared to traditional composite likelihoods.Our application to extreme sea surface temperature data at more than a thousand sites across the entire Red Sea further demonstrates the superiority of the Vecchia likelihood approximation for fitting complex models with intractable likelihoods, delivering significantly better results than traditional composite likelihoods, and accurately capturing the extremal dependence structure at lower computational cost.