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Articles by D. B. Dunson
Total Records ( 2 ) for D. B. Dunson
  D. B. Dunson

This paper focuses on the problem of choosing a prior for an unknown random effects distribution within a Bayesian hierarchical model. The goal is to obtain a sparse representation by allowing a combination of global and local borrowing of information. A local partition process prior is proposed, which induces dependent local clustering. Subjects can be clustered together for a subset of their parameters, and one learns about similarities between subjects increasingly as parameters are added. Some basic properties are described, including simple two-parameter expressions for marginal and conditional clustering probabilities. A slice sampler is developed which bypasses the need to approximate the countably infinite random measure in performing posterior computation. The methods are illustrated using simulation examples, and an application to hormone trajectory data.

  A Bhattacharya and D. B. Dunson

Statistical analysis on landmark-based shape spaces has diverse applications in morphometrics, medical diagnostics, machine vision and other areas. These shape spaces are non-Euclidean quotient manifolds. To conduct nonparametric inferences, one may define notions of centre and spread on this manifold and work with their estimates. However, it is useful to consider full likelihood-based methods, which allow nonparametric estimation of the probability density. This article proposes a broad class of mixture models constructed using suitable kernels on a general compact metric space and then on the planar shape space in particular. Following a Bayesian approach with a nonparametric prior on the mixing distribution, conditions are obtained under which the Kullback–Leibler property holds, implying large support and weak posterior consistency. Gibbs sampling methods are developed for posterior computation, and the methods are applied to problems in density estimation and classification with shape-based predictors. Simulation studies show improved estimation performance relative to existing approaches.

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