  As datasets grow it becomes infeasible to process them completely with a
desired model. For giant datasets, we frame the order in which computation is
performed as a decision problem. The order is designed so that partial
computations are of value and early stopping yields useful results. Our
approach comprises two related tools: a decision framework to choose the order
to perform computations, and an emulation framework to enable estimation of the
unevaluated computations. The approach is applied to the problem of computing
similarity matrices, for which the cost of computation grows quadratically with
the number of objects. Reasoning about similarities before they are observed
introduces difficulties as there is no natural space and hence comparisons are
difficult. We solve this by introducing a computationally convenient form of
multidimensional scaling we call `data directional scaling'. High quality
estimation is possible with massively reduced computation from the naive
approach, and can be scaled to very large matrices. The approach is applied to
the practical problem of assessing genetic similarity in population genetics.
The use of statistical reasoning in decision making for large scale problems
promises to be an important tool in applying statistical methodology to Big
Data.
