Logistic-Beta Processes for Dependent Random Probabilities with Beta Marginals

Area of Science:

• Statistics
• Machine Learning
• Bayesian Nonparametrics

Background:

• The beta distribution is widely used for probabilities, but lacks flexible extensions for dependent random probabilities.
• Existing methods for dependent probabilities are often computationally inconvenient.

Purpose of the Study:

• To propose a novel stochastic process, the logistic-beta process, for modeling dependent probabilities.
• To develop a flexible and computationally tractable framework for Bayesian nonparametric models.

Main Methods:

• The logistic-beta process is defined via a logistic transformation, yielding beta marginals.
• It incorporates flexible dependence structures using correlation kernels.
• A normal variance-mean mixture representation facilitates posterior inference.

Main Results:

• The logistic-beta process enables the design of computationally tractable dependent Bayesian nonparametric models.
• Demonstrated effectiveness in dependent Dirichlet processes and extensions.
• Successful application in nonparametric binary regression and conditional density estimation.

Conclusions:

• The logistic-beta process offers a flexible and computationally efficient method for modeling dependent probabilities.
• It provides a valuable tool for advancing Bayesian nonparametric modeling in various domains.
• The approach proved effective in both simulated and real-world applications.