Statistical foundations of deep generative models
Abstract:
Experimental designs for response surface models are often constructed in a way that facilitates sequential operation. This is a sensible approach to practical sequential experimentation, allowing for an early stop if the preliminary first-order result does not look promising. Here, we consider an analogous strategy for factorial experiments in which factors have qualitative levels. We examine three-level orthogonal arrays to find subsets of runs that constitute good two-level designs. Our assumption is that the experimenter's tentative plan is to complete a three-level factorial experiment, but would like the option of early termination if a small preliminary experiment using two levels of each factor does not provide promising results. For this purpose, we systematically examine the complete collections of three-level orthogonal arrays of strength two and three generated by Schoen, Eendebak and Nguyen (2009), along with a new set of 36-run arrays, to find the most promising two-level subset designs. From this collection, we identify nested designs that are Pareto-admissible with respect to four criteria that characterize overall precision and bias for both the preliminary (2-level) and final (3-level) analyses. Three minor modifications of the nested plans that improve the efficiency of the final designs are also considered.