Designing an optimal experiment for Bayesian estimation: application to the kinetics of iodine thyroid uptake.

We consider the problem of designing an optimal experiment for Bayesian estimation of the parameters of a non-linear model. When their distribution is known, the Bayesian approach allows individual estimation from a small number of measurements; the design determines the accuracy of the estimates. We propose to optimize this design by maximizing a general criterion: the expectation of the information supplied by the experiment. This approach is applied to optimize the two sampling times for Bayesian estimation of the kinetics of radioiodine thyroid uptake from an estimated non-parametric prior distribution.