Algorithms for constructing D-optimal designs of experiments
Radoslav Harman (Comenius University in Bratislava)
Friday 18th November, 2011 15:00-16:00 Maths 203
An optimal design is a rule for performing trials in a way that provides the maximum amount of information about the unknown parameters of the underlying statistical model. For a given number of trials, the construction of an optimal design is in general a difficult integer optimization problem. However, if the number of trials is large and the observations are uncorrelated, we can use the so-called “approximate” optimal designs, which can be computed by continuous convex optimization methods. In the talk we will focus on the most common D-optimal designs of experiments, which minimize the volume of the confidence ellipsoid for the unknown parameter. We will describe two classes of algorithms for computing D-optimal approximate designs: the steepest descent algorithms and the multiplicative algorithms. We will also mention recent methods of mathematical programming that can be used to compute D-optimal approximate designs. Finally, we will give a brief survey of heuristics for constructing D-efficient designs with a specified number of trials.