Bayesian Inference for a Finite Population Total Using Linked Data

We consider the problem of estimating the total (or the mean) of a continuous variable in a finite population setting, using the auxiliary information provided by a covariate which is available in a different file. However the matching steps between the two files is uncertain due to a lack of identification code for the single unit. We propose a fully Bayesian approach which merges the record linkage step with the subsequent estimation procedure.