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The nested Dirichlet process. (English) Zbl 1205.62062

Summary: 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.

MSC:

62G99 Nonparametric inference
65C60 Computational problems in statistics (MSC2010)
62F15 Bayesian inference
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