Logistic-beta processes for modeling dependent random probabilities with beta marginals
arxiv(2024)
摘要
The beta distribution serves as a canonical tool for modeling probabilities
and is extensively used in statistics and machine learning, especially in the
field of Bayesian nonparametrics. Despite its widespread use, 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. Similar to the Gaussian
process, the logistic-beta process can model dependence on both discrete and
continuous domains, such as space or time, and has a highly flexible dependence
structure through correlation kernels. Moreover, its normal variance-mean
mixture representation leads to highly effective posterior inference
algorithms. The flexibility and computational benefits of logistic-beta
processes are demonstrated through nonparametric binary regression simulation
studies. Furthermore, we apply the logistic-beta process in modeling dependent
Dirichlet processes, and illustrate its application and benefits through
Bayesian density regression problems in a toxicology study.
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