Statistical Papers

, Volume 60, Issue 3, pp 849–875 | Cite as

Polya tree priors and their estimation with multi-group data

  • Jianjun Zhang
  • Lei Yang
  • Xianyi WuEmail author
Regular Article


The purpose of this article is in twofold. Firstly, we present new and weaker conditions under which a tail-free or a Polya tree prior can sit on the collection of absolutely continuous probabilities with respect to certain probability measure. Second, we investigate the empirical Bayesian (EB) estimation of the parameters of Polya tree priors with multi-group data. Two types of EB estimates, maximum likelihood estimates and moment estimates, are discussed. We also make an exploratory analysis on the estimability of the parameters and the distribution of the number of estimable parameters.


Tail-free prior Polya tree prior Bayesian nonparametrics Empirical Bayes Maximum likelihood estimate Moment estimate 



This research was partially supported by the Natural Science Foundation of China under Grant No. 71371074 and the 111 Project B14019.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of StatisticsEast China Normal UniversityShanghaiChina
  2. 2.Roche (China) Holding Ltd.ShanghaiChina

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