The local Dirichlet process |
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Authors: | Yeonseung Chung David B Dunson |
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Institution: | (1) Department of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, United Kingdom;(2) Faculty of Business, University of New South Wales, UNSW, Sydney, 2052, Australia;(3) School of Mathematics, University of New South Wales, UNSW, Sydney, 2052, Australia; |
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Abstract: | As a generalization of the Dirichlet process (DP) to allow predictor dependence, we propose a local Dirichlet process (lDP).
The lDP provides a prior distribution for a collection of random probability measures indexed by predictors. This is accomplished
by assigning stick-breaking weights and atoms to random locations in a predictor space. The probability measure at a given
predictor value is then formulated using the weights and atoms located in a neighborhood about that predictor value. This
construction results in a marginal DP prior for the random measure at any specific predictor value. Dependence is induced
through local sharing of random components. Theoretical properties are considered and a blocked Gibbs sampler is proposed
for posterior computation in lDP mixture models. The methods are illustrated using simulated examples and an epidemiologic
application. |
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Keywords: | |
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