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Logistic-Beta Processes for Dependent Random Probabilities with Beta Marginals.

Changwoo J Lee1, Alessandro Zito2, Huiyan Sang3

  • 1Department of Statistical Science, Duke University.

Bayesian Analysis
|March 4, 2026
PubMed
Summary
This summary is machine-generated.

We introduce the logistic-beta process, a novel statistical method for modeling dependent probabilities. This flexible approach enhances Bayesian nonparametric models for various applications.

Keywords:
Bayesian nonparametricsDependent Dirichlet processMultivariate beta distributionNonparametric binary regressionPólya distribution

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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.