Optimal design: methods and applications

14.07.2021, 15:00!  –  Online Kolloquium
Institutskolloquium

Holger Dette (Ruhr-Universität Bochum, Germany) and John Stufken (UNC Greensboro, US)

Bitte geänderte Zeit beachten! Please mind the later starting time!

3 pm Holger Dette (Ruhr-Universität Bochum, Germany): Statistics, Geometry und Pharmacokinetics

4:15 pm John Stufken (UNC Greensboro, US): Design selection for factor screening experiments

Abstracts:

Holger Dette (Ruhr-Universität Bochum, Germany): Statistics, Geometry und Pharmacokinetics

This talks gives a careful introduction into the theory of optimal design for regression using concrete examples from the pharmaceutical industry. We demonstrate how geometric methods can be used to determine optimal designs for concrete applications. In particular, the talk shows how the - on a first glance - very different areas of geometry, convex optimization and statistics can be used to determine optimal designs for the analysis of dose-response curves.

John Stufken (UNC Greensboro, US): Design selection for factor screening experiments

An important step when planning an experiment is the selection of a design. An appropriate design can depend on, for example, the number of experimental units that are available, the cost of obtaining observations, and the objective of the experiment. It will typically also consist of statistical considerations. An "optimal design" is a design that, under specified constraints, optimizes a criterion that is based on statistical considerations. Such optimality criteria for design selection are used across many areas of application. However, the commonly used criteria are inadequate for some situations.
One such situation is for factor screening experiments in which the number of observations is smaller than the number of model parameters to be estimated. Such problems belong to the "small n, large p" problems, where n refers to the number of observations and p to the number of model parameters. Designs for such problems are called supersaturated designs.
There is an extensive literature on alternative optimality criteria for supersaturated designs. Most of these criteria are rather ad hoc and are not directly related to the primary goal of these experiments, which is factor screening. Especially, unlike almost any other optimal design problem, the criteria are not directly related to the method of analysis.
An assumption needed for the analysis of supersaturated designs is the assumption of effect sparsity. Under this assumption, a popular method of analysis for 2-level supersaturated designs is the Gauss-Dantzig Selector (GDS), which shrinks many parameter estimates to zero. We have developed new design selection criteria inspired by the GDS and establish that designs that are better under these criteria tend to perform better as factor screening designs than designs obtained using existing criteria.

This presentation is based on joint work with Rakhi Singh, University of North Carolina at Greensboro.

If you wish to attend the talks,  please contact Sylvie Paycha paycha@math.uni-potsdam.de for the login details.