Fully Nonparametric Regression for Bounded Data Using Dependent Bernstein Polynomials
提出一类新的概率模型用于处理有界域上的预测变量依赖概率分布，扩展了狄利克雷-伯恩斯坦先验，并证明了连续性、大支撑等理论性质，通过模拟和真实数据验证了模型表现。
We propose a novel class of probability models for sets of predictor-dependent probability distributions with bounded domain. The proposal extends the Dirichlet–Bernstein prior for single density estimation, by using dependent stick-breaking processes. A general model class and two simplified versions are discussed in detail. Appealing theoretical properties such as continuity, association structure, marginal distribution, large support, and consistency of the posterior distribution are established for all models. The behavior of the models is illustrated using simulated and real-life data. The simulated data are also used to compare the proposed methodology to existing methods. Supplementary materials for this article are available online.