The beta distribution serves as a canonical tool for modelling probabilities in statistics and machine learning. However, there is limited work on flexible and computationally convenient stochastic process extensions for modelling 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 illustrate the benefits through nonparametric binary regression and conditional density estimation examples, both in simulation studies and in a pregnancy outcome application.
View on arXiv@article{lee2025_2402.07048,
title={ Logistic-beta processes for dependent random probabilities with beta marginals },
author={ Changwoo J. Lee and Alessandro Zito and Huiyan Sang and David B. Dunson },
journal={arXiv preprint arXiv:2402.07048},
year={ 2025 }
}