Beyond objective priors for the Bayesan bootstrap analysis of survey data

This article provides reasonable answers to the problems left unsolved in Aitkin (2008), a recent paper on the Bayesian bootstrap in finite population inference. These problems are essentially two: the choice of the population parameter cannot be discussed from within the Aitkin’s Bayesian bootstrap approach, which is based on a multinomial likelihood with unconstrained parameters; assumptions such as model constraints on the multinomial probabilities are difficult to implement in such a Bayesian framework. The answers are obtained by assigning suitable informative priors to the population proportions involved in the analysis.