Ordered designs and Bayesian inference in survey sampling

Many sampling designs, such as simple random sampling without replacement, can in principle be extended in a natural way so that the units continue to be selected until the population is exhausted. These designs impose a random order on the population. Here we show how such ordered designs can be used to define prior distributions over the population. For such priors the Bayesian analysis uses information that in standard frequentist methods is incorporated in the sampling design. The resulting methods will often have good frequentist properties.