Needed data expenditure for an ambiguous decision problem

The amount worth spending to collect and analyze data depends on the uses of the data. We consider the determination of the optimal expenditure in some simple situations when only some aspects of the data use are known. In particular, we consider uses where an action is taken if a statistic exceeds a threshold τ, which is unknown at the time of data planning and collection (though its value will not depend on the value of the statistic). We analyze the sensitivity of the optimal expenditure to the a priori uncertainty in τ. For many decision problems, the optimal expenditure decreases with increasing uncertainty about τ, but we identify some uses for which the optimal expenditure increases with increasing uncertainty about τ. We also study the effects of other forms of ambiguity. Uncertainty about whether the data will be used typically decreases the optimal expenditure, as does uncertainty about the preferences represented in the decision making.