We propose a model to flexibly estimate joint tail properties by exploiting the convergence of an appropriately scaled point cloud onto a compact limit set. Characteristics of the shape of the limit set correspond to key tail dependence properties. We directly model the shape of the limit set using Bezier splines, which allow flexible and parsimonious specification of shapes in two dimensions. We then fit the Bezier splines to data in pseudo-polar coordinates using Markov chain Monte Carlo sampling, utilizing a limiting approximation to the conditional likelihood of the radii given angles. By imposing appropriate constraints on the parameters of the Bezier splines, we guarantee that each posterior sample is a valid limit set boundary, allowing direct posterior analysis of any quantity derived from the shape of the curve. Furthermore, we obtain interpretable inference on the asymptotic dependence class by using mixture priors with point masses on the corner of the unit box. Finally, we apply our model to bivariate datasets of extremes of variables related to fire risk and air pollution.

翻译：我们提出了一种模型，通过利用适当缩放的点云收敛于紧极限集的性质，灵活估计联合尾部特性。极限集形状的特征对应于关键的尾部相依性质。我们使用贝塞尔样条直接对极限集的形状进行建模，该方法允许在二维空间中灵活且简约地指定形状。随后，我们利用马尔可夫链蒙特卡罗采样，在伪极坐标中将贝塞尔样条拟合到数据上，并采用给定角度条件下半径的条件似然的极限近似。通过对贝塞尔样条参数施加适当的约束，我们保证每个后验样本都是有效的极限集边界，从而允许对从曲线形状导出的任何量进行直接后验分析。此外，通过在单位盒角点处使用带点质量的混合先验，我们获得了关于渐近相依类的可解释推断。最后，我们将模型应用于与火灾风险和空气污染相关的极端变量的二元数据集。