Subjective Bayesian Models in Sampling Finite Populations

Abstract

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.

A Bayesian Superpopulation Approach to Inference for Finite Populations Based on Imperfect Diagnostic Outcomes

“…Following the prescription of Ericson (1969), we "place a prior" on the population values {X 1 , . .…”

“…Little (2004) provides an overview of the arguments and suggests that they can be reconciled from a Bayesian perspective. In fact, Ericson (1969) gave an explicit analysis of this relationship, showing the correspondence between simple random sampling in design-based inference and the use of an exchangeable distribution for the finite population values {X 1 , . .…”

A Decision-Theoretic Approach to Defining Variables Sampling Plans for Finite Lots: Single Sampling for Exponential and Gaussian Processes

“…is minimized, where r is a prior distribution of lc and R ( k , 6) is the usual risk function (the expected value of the loss function) with respect to 6(x) for each x. Alinimizing (1.3) rather than r(6, T) is strictly valid only when the change in the order of integration is allowable and when all the appropriate integrals exist. However, this is not the case for the integrals encountered in this article.…”

A Varying Coefficients Model For Estimating Finite Population Totals: A Hierarchical Bayesian Approach

“…Clearly, the distribution of the total summarizes several sources of uncertainty such as the sampling distribution and the prior distributions. (For details on model-based and design-based approaches, see Little 2004;Gregoire 1998;Sarndal et al 1992;Ericson 1969Ericson , 1988Basu 2011;Scott 1977;Binder 1982;Ghosh and Meeden 1997. ) We propose a model-based Bayesian approach appropriate for estimating totals based on samples collected using any type of sampling design.…”