The Dirichlet Process as sampling distribution

2026-07-28

AI Summary

This study presents the first systematic investigation into the statistical properties of the Dirichlet process when employed as a sampling distribution and introduces a Bayesian inference framework for its base measure and concentration parameter. Treating the Dirichlet process as a data-generating mechanism, the authors develop a joint inference approach for these two key parameters by integrating Bayesian nonparametric modeling with Markov chain Monte Carlo algorithms, leveraging observed histogram sequences. The proposed methodology is validated through extensive experiments on both synthetic and real-world datasets, demonstrating its effectiveness and practical utility. This work addresses a notable gap in the literature by providing a principled solution to parameter inference in Dirichlet process models, thereby advancing the theoretical and applied understanding of this foundational Bayesian nonparametric construct.

Abstract

The Dirichlet process (DP) is the most common bayesian nonparametric prior, however, its properties as sampling distribution have not been studied nor inference on its parameters. Here we use the DP as a data generating model and make bayesian inference on its centering measure and precision parameter. We illustrate with a sequence of histograms as observed data. In particular, we consider simulated and real datasets.

Problem

• Dirichlet Process
• sampling distribution
• Bayesian inference
• centering measure
• precision parameter

Innovation

• Dirichlet process
• sampling distribution
• Bayesian inference
• centering measure
• precision parameter