Statistics Seminar: Multi-objective optimal design of experiments

Dates

Tuesday, March 2, 2021 - 14:00 to 15:00

Speaker: Steven Gilmour (King’s College London)

Title: Multi-objective optimal design of experiments

Abstract:

The statistical design of experiments has developed over the last 100 years to deal with different structures of experiments and data collected from them. Historically there have been two different approaches. Optimal design involves defining a mathematical function, which depends on the particular sets of treatments used in the experiment, and then choosing the treatments to optimise this function. This has the advantage of being easily understood to be directly related to the properties of the data analysis, e.g. choose a design to minimise the variance of the estimate of some important quantity. However, it has the disadvantage of oversimplifying the multiple objectives that experimenters actually have in practice. Classical design, on the other hand, chooses designs with attractive mathematical structures (usually based on symmetries) which can make the designs fairly good for many objectives. However, classical designs can be difficult or impossible to find for some experimental structures and there is no guarantee that they will be very good for the objectives of any particular experiment. We develop and implement methods which will get the best of both optimal and classical designs, namely multi-objective optimal designs (MOODs). MOODs use the idea of optimising a mathematical function, but that function represents a compromise between the many different objectives that experimenters have in practice. Some of the objectives can be used to restrict the set of designs over which we search for an optimum, e.g. in some cases we might restrict the search to designs which allow us to obtain uncorrelated estimates of the main effects of factors. Other objectives are combined in a compound optimality criterion, which defines a weighted geometric mean of several individual simple criteria. We discuss the use of MOODs in the context of multifactor response surface designs