As a generalization of the Dirichlet process (DP) to allow predictor dependence, we propose a local Dirichlet process (lDP). The lDP provides a prior distribution for a collection of random probability measures indexed by predictors. This is accomplished by assigning stick-breaking weights and atoms to random locations in a predictor space. The probability measure at a given predictor value is then formulated using the weights and atoms located in a neighborhood about that predictor value. This construction results in a marginal DP prior for the random measure at any specific predictor value. Dependence is induced through local sharing of random components. Theoretical properties are considered and a blocked Gibbs sampler is proposed for posterior computation in lDP mixture models. The methods are illustrated using simulated examples and an epidemiologic application.

中文翻译：

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局部狄利克雷过程

作为狄利克雷过程 (DP) 的泛化以允许预测器依赖，我们提出了局部狄利克雷过程 (lDP)。IDP 为由预测变量索引的随机概率度量集合提供先验分布。这是通过将断棒权重和原子分配到预测器空间中的随机位置来实现的。然后使用位于该预测值附近的权重和原子来制定给定预测值的概率度量。这种构造导致随机测量在任何特定预测变量值下的边际 DP 先验。依赖是通过随机组件的本地共享引起的。考虑了理论特性，并提出了一个阻塞的 Gibbs 采样器，用于 LDP 混合模型中的后验计算。