Bayesian A-Optimal Designs for Gamma and Poisson Regression Models: An Algorithmic Approach
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Authors
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Mahesh Kumar Panda
Department of Statistics, Ravenshaw University, Cuttack
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Tofan Kumar Biswal
Department of Statistics, Central University of Odisha, Sunabeda
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V.K. Gupta
Formerly at ICAR-IASRI, New Delhi
Keywords:
Fisher information matrix; Bayesian A-optimal design; Gamma regression model; Poisson regression model; Prior information.Abstract
Bayesian design approaches leverage prior information about unknown parameters to improve the efficiency of experimental designs. In this study,
we propose two algorithms for deriving Bayesian A-optimal designs for Gamma and Poisson regression models involving two explanatory factors.
The experimental region is assumed to be a unit rectangle. The present work focuses specifically on vertex-type designs, where the support points of
the initial designs are restricted to the vertices of the experimental region. Initially, the Fisher information matrix is computed based on the support
points of the proposed locally optimal designs. Subsequently, Bayesian A-optimal designs are determined by incorporating prior distributions-namely,
Uniform, Normal, Beta, and Gamma-on the unknown parameters. The corresponding optimal weights for each design are computed using MATLAB.
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