A generalisation of bayesian inference : with applications to finite population sampling theory

Abstract

This thesis is concerned with the foundations of statistics and how they interact with the practical needs of finite population sampling theory. The current competing foundations are critically examined and compared. New foundations, which are a generalisation of the Bayesian foundations, are presented. They are applied to populations of random variables which are independently generated from Bernoulli, multiple Bernoulli, Poisson, normal, rectangular, Laplace and gamma distributions. The case of multiple linear regression is treated with and without the assumption of normal errors. Populations of independent variables of no particular parametric form are also treated under various assumptions which reflect realistic situations which occur in survey sampling. These include situations analogous to simple random sampling, , stratification, within stratum ratio estimation, across stratum ratio estimation, probability proportional to size sampling and multistage sampling. Multistage sampling is examined in the case of methodology used in designing the monthly Labour Force Survey run by the Australian Bureau of Statistics. The foundations presented here are compared with the current established foundations. The occurrence and impact of internal inconsistencies in these foundations is one criterion for comparison. Further criteria are their versatility to cope with varied situations, their practicality and their intuitive appeal. Show more