We describe a procedure to introduce general dependence structures on a set of Dirichlet processes. Dependence can be in one direction to define a time series or in two directions to define spatial dependencies. More directions can also be considered. Dependence is induced via a set of latent processes and exploit the conjugacy property between the Dirichlet and the multinomial processes to ensure that the marginal law for each element of the set is a Dirichlet process. Dependence is characterised through the correlation between any two elements. Posterior distributions are obtained when we use the set of Dirichlet processes as prior distributions in a bayesian nonparametric context. Posterior predictive distributions induce partially exchangeable sequences defined by generalised P\'olya urs. A numerical example to illustrate is also included.
翻译:我们描述一个程序, 以对一套二流进程引入一般依赖结构。 依赖可以朝着一个方向来定义时间序列或两个方向来定义空间依赖性。 还可以考虑更多的方向。 依赖是通过一系列潜在进程诱发的, 并且利用二流进程与多元进程之间的共性属性, 以确保集的每个元素的边际法是一个二流进程。 依赖是通过任何两个元素的相互关系来定性的。 当我们使用一套二流进程作为先前在海湾非对称背景下的分布时, 就会获得分流分布 。 潜在预测分布会引发由通用 P\' olya urs 定义的可部分互换序列 。 还包含一个要说明的数字示例 。