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A note on the binomial model with simplex constraints


  • Tian, Guo-Liang
  • Ng, Kai Wang
  • Yu, Philip L.H.


Liu (2000) considered maximum likelihood estimation and Bayesian estimation in a binomial model with simplex constraints using the expectation-maximization (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.

Suggested Citation

  • Tian, Guo-Liang & Ng, Kai Wang & Yu, Philip L.H., 2011. "A note on the binomial model with simplex constraints," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3381-3385, December.
  • Handle: RePEc:eee:csdana:v:55:y:2011:i:12:p:3381-3385

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