| Ranked Set Sampling (RSS) is a data collection technique that combines measurement with judgment ranking for statistical inference. After a brief review of the basics of RSS, this dissertation lays out a formal and natural Bayesian framework for RSS that is analogous to its frequentist justification, and that does not require the assumption of perfect ranking or use of any imperfect ranking models. Prior beliefs about the judgment order statistic distributions and their interdependence are embodied by a nonparametric prior distribution. Posterior inference is carried out by means of Markov Chain Monte Carlo (MCMC) techniques, and yields estimators of the judgment order statistic distributions (and of functionals of those distributions). Because of non-conjugacy, different MCMC algorithms are used for continuous and discrete data. Judgment post-stratification is introduced to answer questions about handling information from multiple rankers, the quality of judgment ranking, and the role of set size. Finally, a more specific model is proposed for RSS with judgment ranking via a concomitant variable. |
