There is a growing interest in learning how the distribution of a response variable changes with a set of predictors. Bayesian nonparametric dependent mixture models provide a flexible approach to address this goal. However, several formulations require computationally demanding algorithms for posterior inference. Motivated by this issue, we study a class of predictor-dependent infinite mixture models, which relies on a simple representation of the stick-breaking prior via sequential logistic regressions. This formulation maintains the same desirable properties of popular predictor-dependent stick-breaking priors, and leverages a recent P\'olya-gamma data augmentation to facilitate the implementation of several computational methods for posterior inference. These routines include Markov chain Monte Carlo via Gibbs sampling, expectation-maximization algorithms, and mean-field variational Bayes for scalable inference, thereby stimulating a wider implementation of Bayesian density regression by practitioners. The algorithms associated with these methods are presented in detail and tested in a toxicology study.

中文翻译：

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通过 logit 破坏先验的可追踪贝叶斯密度回归

人们越来越有兴趣了解响应变量的分布如何随一组预测变量而变化。贝叶斯非参数相关混合模型提供了一种灵活的方法来实现这一目标。然而，一些公式需要计算要求高的算法来进行后验推理。受这个问题的启发，我们研究了一类依赖于预测变量的无限混合模型，该模型依赖于通过顺序逻辑回归对破坏先验的简单表示。该公式保持了流行的依赖预测器的破棒先验的相同理想特性，并利用最近的 P\'olya-gamma 数据增强来促进后验推理的几种计算方法的实现。这些例程包括通过吉布斯采样的马尔可夫链蒙特卡罗，期望最大化算法，以及用于可扩展推理的平均场变分贝叶斯，从而刺激从业者更广泛地实施贝叶斯密度回归。详细介绍了与这些方法相关的算法，并在毒理学研究中进行了测试。