  Statistical estimation in many contemporary settings involves the
acquisition, analysis, and aggregation of datasets from multiple sources, which
can have significant differences in character and in value. Due to these
variations, the effectiveness of employing a given resource (e.g., a sensing
device or computing power) for gathering or processing data from a particular
source depends on the nature of that source. As a result, the appropriate
division and assignment of a collection of resources to a set of data sources
can substantially impact the overall performance of an inferential strategy. In
this expository article, we adopt a general view of the notion of a resource
and its effect on the quality of a data source, and we describe a framework for
the allocation of a given set of resources to a collection of sources in order
to optimize a specified metric of statistical efficiency. We discuss several
stylized examples involving inferential tasks such as parameter estimation and
hypothesis testing based on heterogeneous data sources, in which optimal
allocations can be computed either in closed form or via efficient numerical
procedures based on convex optimization.
