A note on the binomial model with simplex constraints

Guo-Liang TIAN, Kai Wang NG, Leung Ho Philip YU

Research output: Contribution to journalArticlespeer-review

2 Citations (Scopus)


Liu (2000) considered maximum likelihood estimation and Bayesian estimation in a binomial model with simplex constraints using the expectationmaximization (EM) and data augmentation (DA) algorithms. By introducing latent variables {Zij}and {Yij} (to be defined later), he formulated the constrained parameter problem into a missing data problem. However, the derived DA algorithm does not work because he actually assumed that the {Yij} are known. Furthermore, although the final results from the derived EM algorithm are correct, his findings are based on the assumption that the {Yij} are observable. This note provides a correct DA algorithm. In addition, we obtained the same E-step and M-step under the assumption that the {Yij} are unobservable. A real example is used for illustration. Copyright © 2011 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)3381-3385
JournalComputational Statistics and Data Analysis
Issue number12
Early online dateJun 2011
Publication statusPublished - Dec 2011


Tian, G.-L., Ng, K. W., & Yu, P. L. H. (2011). A note on the binomial model with simplex constraints. Computational Statistics and Data Analysis, 55(12), 3381-3385. doi: 10.1016/j.csda.2011.06.005


  • Constrained binomial model
  • DA algorithm
  • EM algorithm
  • Simplex constraints


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