Objective stepwise Bayes weights in survey sampling

Although weights are widely used in survey sampling their ultimate justification from the design perspective is often problematical. Here we will argue for a stepwise Bayes justification for weights that does not depend explicitly on the sampling design. This approach will make use of the standard kind of information present in auxiliary variables however it will not assume a model relating the auxiliary variables to the characteristic of interest. The resulting weight for a unit in the sample can be given the usual interpretation as the number of units in the population which it represents.