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Keywords:

  • Bayes non-parametrics;
  • Markov beta process;
  • partition model;
  • Polya tree;
  • random probability measure;
  • tail-free distribution

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.