Bayesian mixture modelling with ranked set samples

• Published in: Statistics in medicine Vol. 43; no. 19; pp. 3723 - 3741
• Main Authors: Alvandi, Amirhossein, Omidvar, Sedigheh, Hatefi, Armin, Jafari Jozani, Mohammad, Ozturk, Omer, Nematollahi, Nader
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 30.08.2024; Wiley Subscription Services, Inc
• Subjects: Aged; Algorithms; Bayes Theorem; Bone diseases; bone mineral data; Computer Simulation; EM algorithm; Female; finite mixture models; Gibbs sampling; Humans; imperfect ranking; Likelihood Functions; Markov Chains; Mathematical models; metropolis‐Hastings; Middle Aged; misplacement probability model; Models, Statistical; Monte Carlo Method; Older people; ranked set sampling; Sampling; Womens health; bone mineral data; imperfect ranking; misplacement probability model; metropolis‐Hastings; ranked set sampling; Gibbs sampling; finite mixture models; EM algorithm
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.10144

We consider the Bayesian estimation of the parameters of a finite mixture model from independent order statistics arising from imperfect ranked set sampling designs. As a cost‐effective method, ranked set sampling enables us to incorporate easily attainable characteristics, as ranking information, into data collection and Bayesian estimation. To handle the special structure of the ranked set samples, we develop a Bayesian estimation approach exploiting the Expectation‐Maximization (EM) algorithm in estimating the ranking parameters and Metropolis within Gibbs Sampling to estimate the parameters of the underlying mixture model. Our findings show that the proposed RSS‐based Bayesian estimation method outperforms the commonly used Bayesian counterpart using simple random sampling. The developed method is finally applied to estimate the bone disorder status of women aged 50 and older.