The Nested Dirichlet Process

• Published in: Journal of the American Statistical Association Vol. 103; no. 483; pp. 1131 - 1154
• Main Authors: Rodríguez, Abel, Dunson, David B, Gelfand, Alan E
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 01.09.2008; American Statistical Association
• Subjects: Approximation; Atoms; Clustering; Density estimation; Dependent Dirichlet process; Gibbs sampler; Hierarchical model; Inference; Modeling; Mortality; Multilevel models; Nonparametric Bayes; Nonparametric models; Probabilities; Random probability measure; Theory and Methods; Truncation
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214508000000553

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 distributions for the different centers, with centers drawn from the same DP component automatically clustered together. Theoretical properties are discussed, and an efficient Markov chain Monte Carlo algorithm is developed for computation. The methods are illustrated using a simulation study and an application to quality of care in U.S. hospitals.