The nested dirichlet distribution and incomplete categorical data analysis

Kai Wang Ng, Man Lai Tang, Guo Liang Tian, Ming Tan

Research output: Contribution to journalJournal articlepeer-review

9 Citations (Scopus)


The nested Dirichlet distribution (NDD) is an important distribution defined on the closed n-dimensional simplex. It includes the classical Dirichlet distribution and is useful in incomplete categorical data (ICD) analysis. In this article, we develop the distributional properties of NDD. New large-sample likelihood and small-sample Bayesian approaches for analyzing ICD are proposed and compared with existing likelihood/Bayesian strategies. We show that the new approaches have at least three advantages over existing approaches based on the traditional Dirichlet distribution in both frequentist and conjugate Bayesian inference for ICD. The new methods possess closed-form expressions for both the maximum likelihood and Bayes estimates when the likelihood function is in NDD form; produce computationally efficient EM and data augmentation algorithms when the likelihood is not in NDD form; and provide exact sampling procedures for some special cases. The methodologies are illustrated with simulated and real data.

Original languageEnglish
Pages (from-to)251-271
Number of pages21
JournalStatistica Sinica
Issue number1
Publication statusPublished - Jan 2009

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Data augmentation
  • Dirichlet distribution
  • EM
  • Incomplete categorical data
  • Matrix rate of convergence
  • Mixing rate of a markov chain
  • Nested dirichlet distribution


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