Items are characterized by a set of attributes (T) and a collection of covariates (ℝ5X) associated with those attributes. The authors wish to screen for acceptable items (T∈CT), but T is expensive to measure. They envisage a two-stage screen in which observation of ℝ5X is used as a filter at the first stage to sentence most items. The second stage involves the observation of T for those items for which the first stage is indecisive. The authors adopt a Bayes decision-theoretic approach to the development of optimal two-stage screens within a general framework for costs and stochastic structure. They also consider the important question of how much screens need to be modified in the light of resource limitations that bound the proportion of items that can be passed to the second stage.
