论文标题
订单$ m $的广义贝叶斯样品副本
Generalised bayesian sample copula of order $m$
论文作者
论文摘要
在这项工作中，我们提出了一个半参数双变量副群，其密度是由不相交正方形的分段常数函数定义的。我们获得了模型参数的最大似然估计量，并证明它们在特定条件下还原为样品copula。我们进一步建议对模型进行完整的贝叶斯分析，并引入模型参数的空间依赖性先验分布。这一先验允许参数借用各个相邻区域的强度，以产生平滑的后验估计。为了通过完整的条件分布来表征后验分布，我们提出了一种数据增强技术。需要一个大都会危机步骤，我们为随机步行提案分布提出了一种新颖的适应方案。我们实施了模拟研究和对真实数据集的分析，以说明我们的模型和推理算法的性能。
In this work we propose a semiparametric bivariate copula whose density is defined by a piecewise constant function on disjoint squares. We obtain the maximum likelihood estimators of model parameters and prove that they reduce to the sample copula under specific conditions. We further propose to carry out a full Bayesian analysis of the model and introduce a spatial dependent prior distribution for the model parameters. This prior allows the parameters to borrow strength across neighbouring regions to produce smooth posterior estimates. To characterise the posterior distribution, via the full conditional distributions, we propose a data augmentation technique. A Metropolis-Hastings step is required and we propose a novel adaptation scheme for the random walk proposal distribution. We implement a simulation study and an analysis of a real dataset to illustrate the performance of our model and inference algorithms.
