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D-optimal design of experiments

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If you have a question about this talk, please contact Elena Yudovina.

Consider an experiment consisting of a series of linear regression trials. The question is: How should we choose the trials in order to obtain “as much information as possible” from the experiment? The most classic answer is to choose the trials such that the resulting confidence ellipsoid for the unknown regression parameter has minimum achievable volume, which leads to the so-called D-optimal design. In the talk we will define the basic notions of exact and approximate designs and prove the fundamental “equivalence theorem” for D-optimality. We will also give several concrete examples of D-optimal exact and approximate designs for various linear regression models, relating the design problems to areas as different as the theory of Brownian motion and the number of spanning trees of graphs.

This talk is part of the Statistical Laboratory Graduate Seminars series.

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