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Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest. Among the various sampling methods used by...
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Bayesian mixture modelling with ranked set samples.

Amirhossein Alvandi1, Sedigheh Omidvar2, Armin Hatefi3

  • 1Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts, USA.

Statistics in Medicine
|June 18, 2024
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Summary
This summary is machine-generated.

This study introduces a Bayesian estimation method using ranked set sampling (RSS) for finite mixture models. The RSS-based Bayesian approach offers improved parameter estimation compared to simple random sampling.

Keywords:
EM algorithmGibbs samplingbone mineral datafinite mixture modelsimperfect rankingmetropolis‐Hastingsmisplacement probability modelranked set sampling

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Area of Science:

  • Statistics
  • Statistical Modeling
  • Computational Statistics

Background:

  • Ranked set sampling (RSS) is a cost-effective data collection technique.
  • Incorporating ranking information enhances data analysis and Bayesian estimation.
  • Finite mixture models are widely used for data clustering and density estimation.

Purpose of the Study:

  • To develop a Bayesian estimation approach for finite mixture models using imperfect ranked set samples.
  • To compare the performance of the proposed RSS-based Bayesian method against traditional simple random sampling methods.
  • To apply the developed method for estimating bone disorder status in older women.

Main Methods:

  • Utilizing the Expectation-Maximization (EM) algorithm for estimating ranking parameters in RSS data.
  • Employing Metropolis within Gibbs Sampling for estimating mixture model parameters.
  • Developing a Bayesian framework tailored for the unique structure of ranked set samples.

Main Results:

  • The proposed ranked set sampling-based Bayesian estimation method demonstrates superior performance over simple random sampling.
  • The Expectation-Maximization (EM) algorithm effectively estimates ranking parameters.
  • Metropolis within Gibbs Sampling efficiently estimates mixture model parameters.

Conclusions:

  • The developed Bayesian estimation method using ranked set sampling provides a more accurate and cost-effective alternative for finite mixture models.
  • The method is successfully applied to a real-world health study on bone disorder status.
  • Ranked set sampling significantly improves the efficiency of Bayesian parameter estimation.