  Optimal designs are required to make efficient statistical experiments.
D-optimal designs for some models are calculated by using canonical moments. On
the other hand, integrable systems are dynamical systems whose solutions can be
written down concretely. In this paper, polynomial regression models with prior
information are discussed. In order to calculate D-optimal designs for these
models, a useful relationship between canonical moments and discrete integrable
systems is used. By using canonical moments and discrete integrable systems, an
algorithm for calculating D-optimal designs for these models is proposed. Then
some examples of applications of the algorithm are introduced.
