Probability density estimation is a central task in statistics. Copula-based models provide a great deal of flexibility in modelling multivariate distributions, allowing for the specifications of models for the marginal distributions separately from the dependence structure (copula) that links them to form a joint distribution. Choosing a class of copula models is not a trivial task and its misspecification can lead to wrong conclusions. We introduce a novel class of random Bernstein copula functions, and studied its support and the behavior of its posterior distribution. The proposal is based on a particular class of random grid-uniform copulas, referred to as yett-uniform copulas. Alternative Markov chain Monte Carlo algorithms for exploring the posterior distribution under the proposed model are also studied. The methodology is illustrated by means of simulated and real data.

翻译：概率密度估计是统计学的核心任务。基于Copula的模型为多元分布建模提供了极大的灵活性，允许分别设定边际分布模型和连接它们以形成联合分布的相依结构（Copula）。选择一类Copula模型并非易事，其错误设定可能导致错误结论。我们引入了一类新的随机伯恩斯坦Copula函数，并研究了其支撑集及后验分布的行为。该方案基于一类特定的随机网格均匀Copula，称为Yett均匀Copula。我们还研究了在本文模型下探索后验分布的替代马尔可夫链蒙特卡洛算法。通过模拟数据和真实数据验证了该方法的有效性。