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Algorithmic Construction of Bayesian Optimal Block Designs Using the Linear Mixed Effects Model

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  • Dibaba B. Gemechu
  • Legesse K. Debusho
  • Linda M. Haine

Abstract

In this paper a numerical method for construction of optimal Bayesian block designs of size two is considered. The main focus is on implementing prior information on the unknown error variance and variance of random block effects to calculate the A- and D-optimal designs. It is noted from the numerical results that the A- and D-optimal Bayesian block designs are insensitive to the shape of the prior distributions.

Suggested Citation

  • Dibaba B. Gemechu & Legesse K. Debusho & Linda M. Haine, 2025. "Algorithmic Construction of Bayesian Optimal Block Designs Using the Linear Mixed Effects Model," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 14(1), pages 1-50, April.
    • Handle: RePEc:ibn:ijspjl:v:14:y:2025:i:1:p:50
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    References listed on IDEAS

    as
    1. R. A. Bailey, 2007. "Designs for two‐colour microarray experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(4), pages 365-394, August.
    2. Landgrebe, Jobst & Bretz, Frank & Brunner, Edgar, 2006. "Efficient design and analysis of two colour factorial microarray experiments," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 499-517, January.
    3. Ernst Wit & Agostino Nobile & Raya Khanin, 2005. "Near‐optimal designs for dual channel microarray studies," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(5), pages 817-830, November.
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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