# The Nested Dirichlet Process

@article{Rodrguez2008TheND, title={The Nested Dirichlet Process}, author={Abel Rodr{\'i}guez and David B. Dunson and Alan E. Gelfand}, journal={Journal of the American Statistical Association}, year={2008}, volume={103}, pages={1131 - 1154} }

In multicenter studies, subjects in different centers may have different outcome distributions. This article is motivated by the problem of nonparametric modeling of these distributions, borrowing information across centers while also allowing centers to be clustered. Starting with a stick-breaking representation of the Dirichlet process (DP), we replace the random atoms with random probability measures drawn from a DP. This results in a nested DP prior, which can be placed on the collection of…

## 308 Citations

### Spatial Normalized Gamma Processes

- Computer ScienceNIPS
- 2009

A simple and general framework to construct dependent DPs by marginalizing and normalizing a single gamma process over an extended space is proposed and an empirical study of convergence on a synthetic dataset is reported.

### Posterior Distribution for the Number of Clusters in Dirichlet Process Mixture Models

- Computer Science, MathematicsArXiv
- 2019

This work provides a rigorous study for the posterior distribution of the number of clusters in DPMM under different prior distributions on the parameters and constraints on the distributions of the data.

### The Semi-Hierarchical Dirichlet Process and Its Application to Clustering Homogeneous Distributions

- Mathematics
- 2020

Assessing homogeneity of distributions is an old problem that has received considerable attention, especially in the nonparametric Bayesian literature. To this effect, we propose the…

### Bayesian clustering of distributions in stochastic frontier analysis

- Mathematics
- 2011

In stochastic frontier analysis, firm-specific efficiencies and their distribution are often main variables of interest. If firms fall into several groups, it is natural to allow each group to have…

### BETA-PRODUCT POISSON-DIRICHLET PROCESSES

- Computer Science
- 2011

An efficient Monte Carlo Markov Chain algorithm for posterior computation is provided and a new class of multivariate dependent Dirichlet processes (DDP) is introduced in terms of vector of stick-breaking processes with dependent weights.

### Latent Nested Nonparametric Priors (with Discussion).

- Computer Science, MathematicsBayesian analysis
- 2019

A novel class of latent nested processes is introduced by adding common and group-specific completely random measures and normalizing to yield dependent random probability measures, and a Markov Chain Monte Carlo sampler for Bayesian inferences is developed.

### Functional clustering in nested designs: Modeling variability in reproductive epidemiology studies

- Computer Science
- 2014

A mixture model based on a generalization of the nested Dirichlet process that clusters subjects based on the distribution of their curves induces a much more flexible prior on the partition structure than other popular model-based clustering methods.

### Vectors of two-parameter Poisson-Dirichlet processes

- Mathematics, Computer ScienceJ. Multivar. Anal.
- 2011

### Posterior simulation across nonparametric models for functional clustering

- Computer Science, Mathematics
- 2011

A novel Metropolis-Hastings algorithm for moving between models, with a nested generalized collapsed Gibbs sampler for updating the model parameters, and a Dirichlet process priors approach to the problem of clustering of hormone trajectories are applied.

### The Dependent Dirichlet Process and Related Models

- MathematicsStatistical Science
- 2022

Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of…

## References

SHOWING 1-10 OF 103 REFERENCES

### Order-Based Dependent Dirichlet Processes

- Mathematics, Computer Science
- 2006

This article allows the nonparametric distribution to depend on covariates through ordering the random variables building the weights in the stick-breaking representation and derives the correlation between distributions at different covariate values.

### Modelling Heterogeneity With and Without the Dirichlet Process

- Mathematics
- 2001

We investigate the relationships between Dirichlet process (DP) based models and allocation models for a variable number of components, based on exchangeable distributions. It is shown that the DP…

### Approximate Dirichlet Process Computing in Finite Normal Mixtures

- Mathematics
- 2002

A rich nonparametric analysis of the finite normal mixture model is obtained by working with a precise truncation approximation of the Dirichlet process. Model fitting is carried out by a simple…

### Sampling the Dirichlet Mixture Model with Slices

- Mathematics, Computer ScienceCommun. Stat. Simul. Comput.
- 2007

The key to the algorithm detailed in this article, which also keeps the random distribution functions, is the introduction of a latent variable which allows a finite number of objects to be sampled within each iteration of a Gibbs sampler.

### Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems

- Mathematics
- 1974

process. This paper extends Ferguson's result to cases where the random measure is a mixing distribution for a parameter which determines the distribution from which observations are made. The…

### Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models

- Computer Science, Mathematics
- 2007

This paper designs two novel Markov chain Monte Carlo algorithms which sample from the exact posterior distribution of quantities of interest and shows how the algorithms can obtain samples from functionals of the Dirichlet process.

### Estimating mixture of dirichlet process models

- Computer Science
- 1998

A conceptual framework for computational strategies is proposed that provides a perspective on current methods, facilitates comparisons between them, and leads to several new methods that expand the scope of MDP models to nonconjugate situations.

### A Split-Merge Markov chain Monte Carlo Procedure for the Dirichlet Process Mixture Model

- Computer Science
- 2004

A split-merge Markov chain algorithm is proposed to address the problem of inefficient sampling for conjugate Dirichlet process mixture models by employing a new technique in which an appropriate proposal for splitting or merging components is obtained by using a restricted Gibbs sampling scan.

### Collapsed Variational Dirichlet Process Mixture Models

- Computer ScienceIJCAI
- 2007

A number of variational Bayesian approximations to the Dirichlet process (DP) mixture model are studied and a novel collapsed VB approximation where mixture weights are marginalized out is considered.

### Markov Chain Sampling Methods for Dirichlet Process Mixture Models

- Mathematics
- 2000

Abstract This article reviews Markov chain methods for sampling from the posterior distribution of a Dirichlet process mixture model and presents two new classes of methods. One new approach is to…