Bayesian nonparametric models for ranked set sampling
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Ranked set sampling (RSS) is a data collection technique that combines measurement with judgment ranking for statistical inference. This paper 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 techniques, and yields estimators of the judgment order statistic distributions (and of functionals of those distributions).
KeywordsANOVA decomposition Dependent Dirichlet process Imperfect ranking Judgment order statistics Judgment post-stratification Markov chain Monte Carlo
The authors would like to thank Professor Steve Mac Eachern for invaluable discussions and advice that helped lead them to the results in this paper.
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