Logistic-beta processes for dependent random probabilities with beta marginals

• URL: http://arxiv.org/abs/2402.07048v2
• Date: Fri, 10 May 2024 17:17:24 GMT
• Title: Logistic-beta processes for dependent random probabilities with beta marginals
• Authors: Changwoo J. Lee, Alessandro Zito, Huiyan Sang, David B. Dunson,
• Abstract summary: We propose a novel process called the logistic-beta process, whose logistic transformation yields a process with common beta marginals. It can model dependence on both discrete and continuous domains, such as space or time, and has a flexible dependence structure through correlation kernels. We illustrate the benefits through nonparametric binary regression and conditional density estimation examples, both in simulation studies and in a pregnancy outcome application.
• Score: 58.91121576998588
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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