Subjective Bayesian Models in Sampling Finite Populations

Summary A general and basic model for inference about characteristics of a finite population of distinguishable elements is presented from a subjectivistic–Bayesian point of view. A subjectivist analogue to simple random sampling, based on the notion of exchangeable random variables, is discussed and the inputs and assumptions underlying the model are shown to involve nothing more than is required for inference under Bayesian models for infinite populations. The model is illustrated by a number of particular examples including one based on the multinomial distribution which incorporates a prior distribution representing an extreme position of initial ignorance. Inferences under this particular model are shown to agree closely in several respects with usual “classical” results. Finally, an extension of the results is presented involving the use of concomitant measurements, and under this Bayesian model several common ratio and regression estimators are shown to arise as means of posterior distributions.