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Related Experiment Video

Updated: May 11, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

The local Dirichlet process.

Yeonseung Chung1, David B Dunson

  • 1Department of Biostatistics, Harvard School of Public Health, 655 Huntington Ave. Bldg 2, Room 435A, Boston, MA 02115, USA.

Annals of the Institute of Statistical Mathematics
|May 7, 2013
PubMed
Summary
This summary is machine-generated.

We introduce the local Dirichlet process (lDP), a novel Bayesian non-parametric method for modeling predictor-dependent random probability measures. This approach enables local sharing of model components, enhancing flexibility in statistical analysis.

Keywords:
Blocked Gibbs samplerDependent Dirichlet processMixture modelNon-parametric BayesStick-breaking representation

Related Experiment Videos

Last Updated: May 11, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Area of Science:

  • Statistics
  • Bayesian Non-parametrics
  • Machine Learning

Background:

  • Dirichlet process (DP) is a foundational tool for Bayesian non-parametric modeling.
  • Existing methods often struggle to incorporate predictor dependence effectively.
  • There is a need for flexible priors that capture complex relationships in data.

Purpose of the Study:

  • To propose the local Dirichlet process (lDP) as a generalization of the DP.
  • To enable modeling of random probability measures that depend on predictors.
  • To develop a computational framework for lDP-based models.

Main Methods:

  • The lDP assigns stick-breaking weights and atoms to random locations in a predictor space.
  • Probability measures are formulated using local neighborhoods in the predictor space.
  • A blocked Gibbs sampler is developed for posterior computation in lDP mixture models.

Main Results:

  • The lDP construction yields a marginal DP prior at specific predictor values.
  • Local sharing of random components induces dependence across the predictor space.
  • The proposed methods are validated through simulated data and an epidemiologic application.

Conclusions:

  • The local Dirichlet process (lDP) offers a powerful and flexible approach for Bayesian non-parametric modeling with predictor dependence.
  • lDP provides a principled way to incorporate local sharing of information in statistical models.
  • The developed computational methods facilitate the application of lDP in practice.