Rubbery Polya Tree

Rubbery Polya Tree

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Article ID: iaor2012751
Volume: 39
Issue: 1
Start Page Number: 166
End Page Number: 184
Publication Date: Mar 2012
Journal: Scandinavian Journal of Statistics
Authors: ,
Keywords: statistics: distributions
Abstract:

Polya trees (PT) are random probability measures which can assign probability 1 to the set of continuous distributions for certain specifications of the hyperparameters. This feature distinguishes the PT from the popular Dirichlet process (DP) model which assigns probability 1 to the set of discrete distributions. However, the PT is not nearly as widely used as the DP prior. Probably the main reason is an awkward dependence of posterior inference on the choice of the partitioning subsets in the definition of the PT. We propose a generalization of the PT prior that mitigates this undesirable dependence on the partition structure, by allowing the branching probabilities to be dependent within the same level. The proposed new process is not a PT anymore. However, it is still a tail-free process and many of the prior properties remain the same as those for the PT.

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