Optimal regression designs with previous observations

Abstract

SUMMARY A method is developed for constructing D -optimal designs in a linear regression context with k explanatory variables, when previous observations are available and a fixed number of new sets of values of the explanatory variables are to be chosen within the unit sphere. The effect of previous observations on the relationship between D -optimality and E -opti-mality is discussed. The relationship between designs constructed sequentially to be optimum for each new set of values and fully optimal designs is also discussed. Some brief comment is made on the relevance of the ideas to Bayesian design.