The beta distribution serves as a canonical tool for modeling probabilities in statistics and machine learning. However, there is limited work on flexible and computationally convenient stochastic process extensions for modeling dependent random probabilities. We propose a novel stochastic process called the logistic-beta process, whose logistic transformation yields a stochastic process with common beta marginals. Logistic-beta processes can model dependence on both discrete and continuous domains, such as space or time, and have a flexible dependence structure through correlation kernels. Moreover, its normal variance-mean mixture representation leads to effective posterior inference algorithms. We show how the proposed logistic-beta process can be used to design computationally tractable dependent Bayesian nonparametric models, including dependent Dirichlet processes and extensions. We illustrate the benefits through nonparametric binary regression and conditional density estimation examples, both in simulation studies and in a pregnancy outcome application.

翻译：贝塔分布作为统计学与机器学习中建模概率的经典工具，其地位已得到广泛认可。然而，针对相依随机概率建模的灵活且计算便捷的随机过程扩展研究仍较为有限。本文提出一种称为逻辑-贝塔过程的新型随机过程，其逻辑变换可生成具有公共贝塔边缘分布的随机过程。逻辑-贝塔过程能够对离散域和连续域（如空间或时间）上的相依性进行建模，并通过相关核函数实现灵活的相依结构。此外，其正态方差-均值混合表示形式可导出高效的后验推断算法。我们展示了所提出的逻辑-贝塔过程如何用于构建计算可处理的相依贝叶斯非参数模型，包括相依狄利克雷过程及其扩展。通过非参数二元回归与条件密度估计的实例研究，结合仿真实验与妊娠结局应用，我们验证了该方法的优势。