Logistic-beta processes for dependent random probabilities with beta marginals
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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