Such foundations have to include not assuming that we always know what in fact we never know --the exact probability structure involved. We have to face up to bouquets of alternative challenges --of alternative probability structures that are relevant, yet extreme. And we have to focus on bouquets of alternative procedures, most, if not all, of which are not the results of formal optimisation. To select a procedure for use on a given sort of data set most carefully, we need to assess performance over combinations of procedures and challenges, often minimaxing over challenges. Such assessment will rarely be possible without simulation, perhaps of an analogous situation.
Selection of bouquets of challenges will involve experience, direct and extrapolated, as will selection of bouquets of procedures. Thus it will not be wrong for different experts of the greatest experience to choose different analyses of the same data. Moreover, the bouquets conventionally considered for any class of problem will evolve over time, thus changing preferred procedures. These are customary characteristics of other branches of engineering data analysis, to be practical, has to be engineering, not science. Model development, for real world description, not for inference, is a procedure of successive approximations where assumptions can be vital. Sound inference, on the other hand, demands facing alternative possibilities, as illustrated by diverse challenges.