Bayesian D-optimal designs on a fixed number of design points for heteroscedastic polynomial models

We consider design issues in a polynomial regression model where the variance of the response depends on the independent variable exponentially. However, this dependence is not known precisely and additional parameters are required in the model. Our design criteria permit various subsets of the parameters to be estimated with different emphasis. Bayesian D-optimal designs on a compact interval, with the number of support points restricted to be one more than the degree of the polynomial, are found analytically for a large class of priors. These designs may or may not be optimal within the class of all designs, depending on the prior distribution.