Bayesian A- and D-optimal designs for gamma regression model with inverse link function

ABSTRACT

Bayesian optimal designs have received increasing attention in recent years, especially in biomedical and clinical trials. Bayesian design procedures can utilize the available prior information of the unknown parameters so that a better design can be achieved. With this in mind, this article considers the Bayesian A- and D-optimal designs of the two- and three-parameter Gamma regression model. In this regard, we first obtain the Fisher information matrix of the proposed model and then calculate the Bayesian A- and D-optimal designs assuming various prior distributions such as normal, half-normal, gamma, and uniform distribution for the unknown parameters. All of the numerical calculations are handled in R software. The results of this article are useful in medical and industrial researches.

KEYWORDS:

• Bayesian A- and D-optimal design
• Equivalence theorem
• Gamma regression
• Locally optimal design
• Prior information

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62F10
• Secondary 62C12