  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.
