Bayesian D-optimal design for a quadratic beta regression model with a known nuisance parameter considering prior uniform and normal distributions for parameters

One of the practical and important issue in statistics is the fitness of regression models. Optimal design is a way to obtain suitable fitness of this type of models. In addition, we need to use some criteria for attaining optimal design in regression models. The D-optimality criterion is one of the most famous criteria which is used here. An appropriate method to obtain the optimal designs is the Bayesian method that need to the prior distribution for the parameters of the model (coefficient regression). In this paper, by using Bayesian methods, D-optimal designs are obtained for quadratic beta regression model. Also, uniform and normal distributions are considered as the prior distributions and obtained results are analyzed.

Keywords:

Bayesian D-optimal design , Beta regression model , D-optimality criterion , Fisher information matrix