标题： 基于时序极端事件的渐近贝叶斯推断：带有自回归的Copula因子模型 显示英文标题

标题： Amortized Bayesian Inference for Spatio-Temporal Extremes: A Copula Factor Model with Autoregression

摘要： 我们开发了一个用于极端值分析的贝叶斯时空框架，该框架通过引入自回归因子来增强分层Copula模型，以捕捉阈值超额值中的剩余时间依赖性。 该因子可以指定为具有空间变化或空间恒定的特性，尺度参数包含具有科学相关性的协变量（例如，经度、纬度、海拔），从而实现对地理异质性的灵活表示。 为了避免完整截断似然的计算负担，我们设计了一个Gibbs采样器，该采样器在每个参数块中嵌入了摊销神经后验估计，从而实现了对参数、预测分位数和重现期的可扩展推断及完整的后验不确定性。 模拟研究显示，与基线规范相比，该方法在使用适度更复杂的网络架构时，能够改善MCMC混合效果和估计准确性，同时保持重尾行为。 我们通过哥斯达黎加瓜纳卡斯特地区的日降水量数据展示了该方法，评估了一系列嵌套模型，并通过样本外诊断选择了表现最佳的因子组合。 所选规范揭示了多年重现期中的连贯空间模式，并为一个受气候因素强烈影响的热带干地区域的基础设施规划和气候风险管理提供了可行的信息。 所提出的Gibbs方案可以推广到其他设置中，在这些设置中参数可以被划分为推断同质块，并通过摊销的、无需似然的方法学习条件分布。 显示英文摘要

摘要： We develop a Bayesian spatio-temporal framework for extreme-value analysis that augments a hierarchical copula model with an autoregressive factor to capture residual temporal dependence in threshold exceedances. The factor can be specified as spatially varying or spatially constant, and the scale parameter incorporates scientifically relevant covariates (e.g., longitude, latitude, altitude), enabling flexible representation of geographic heterogeneity. To avoid the computational burden of the full censored likelihood, we design a Gibbs sampler that embeds amortized neural posterior estimation within each parameter block, yielding scalable inference with full posterior uncertainty for parameters, predictive quantiles, and return levels. Simulation studies demonstrate that the approach improves MCMC mixing and estimation accuracy relative to baseline specifications, particularly when using moderately more complex network architectures, while preserving heavy-tail behavior. We illustrate the methodology with daily precipitation in Guanacaste, Costa Rica, evaluating a suite of nested models and selecting the best-performing factor combination via out-of-sample diagnostics. The chosen specification reveals coherent spatial patterns in multi-year return periods and provides actionable information for infrastructure planning and climate-risk management in a tropical dry region strongly influenced by climatic factors. The proposed Gibbs scheme generalizes to other settings where parameters can be partitioned into inferentially homogeneous blocks and conditionals learned via amortized, likelihood-free methods.