Bayesian minimally supported D-optimal designs for an exponential regression model

We consider the problem of obtaining static (i.e., nonsequential), approximate optimal designs for a nonlinear regression model with response E[Y\x] exp(theta(0) + theta(1)x + (...) + theta(k)x(k)). The problem can be transformed to the design problem for a heteroscedastic polynomial regression model, where the variance function is of an exponential form with unknown parameters. Under the assumption that sufficient prior information about these parameters is available, minimally supported Bayesian D-optimal designs are obtained. A general procedure for constructing Such designs is provided; as well the analytic forms of these designs are derived for some special priors. The theory of canonical moments and the theory of continued fractions are applied for these purposes.