  To improve the precision of inferences and reduce costs there is considerable
interest in combining data from several sources such as sample surveys and
administrative data. Appropriate methodology is required to ensure satisfactory
inferences since the target populations and methods for acquiring data may be
quite different. To provide improved inferences we use methodology that has a
more general structure than the ones in current practice. We start with the
case where the analyst has only summary statistics from each of the sources. In
our primary method, uncertain pooling, it is assumed that the analyst can
regard one source, survey $r$, as the single best choice for inference. This
method starts with the data from survey $r$ and adds data from those other
sources that are shown to form clusters that include survey $r$. We also
consider Dirichlet process mixtures, one of the most popular nonparametric
Bayesian methods. We use analytical expressions and the results from numerical
studies to show properties of the methodology.
