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A hierarchical Bayesian analysis for bivariate Weibull distribution under left-censoring scheme.

Danielle Peralta1, Ricardo Puziol de Oliveira2, Jorge Alberto Achcar1

  • 1Ribeir ao Preto Medical School, University of Sao Paulo (USP), Ribeirao Preto, Brazil.

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Summary

This study introduces a new Bayesian method for analyzing paired positive data with missing values and covariates. The hierarchical model accurately captures dependencies, offering reliable inference for complex datasets.

Keywords:
Bayesian analysisTobit modelWeibull distributionleft-censored datastellar data

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Area of Science:

  • Statistics
  • Astronomy

Background:

  • Analyzing bivariate positive data with covariates and left-censored observations presents statistical challenges.
  • Existing methods may not fully capture the dependence structure in such complex datasets.

Purpose of the Study:

  • To develop a novel hierarchical Bayesian analysis for bivariate positive data with covariates and left-censored observations.
  • To incorporate a latent variable to account for potential correlations between bivariate responses.
  • To compare Weibull and Weibull-Tobit likelihood approaches within the proposed framework.

Main Methods:

  • A hierarchical Bayesian framework assuming marginal Weibull distributions.
  • Inclusion of a latent variable (frailty) to model dependence between bivariate responses.
  • Application of Markov Chain Monte Carlo (MCMC) methods for posterior inference.
  • Utilizing Weibull or Weibull-Tobit likelihood functions.

Main Results:

  • The proposed bivariate model with a latent factor accurately infers dependencies in stellar astronomy data.
  • The hierarchical Bayesian approach provides reliable results for left-censored bivariate data with covariates.
  • Comparison of Weibull and Weibull-Tobit likelihoods demonstrated the model's flexibility.

Conclusions:

  • The novel hierarchical Bayesian analysis is effective for bivariate positive data with left-censored observations and covariates.
  • The inclusion of a latent factor is crucial for capturing response dependence.
  • This methodology offers a promising tool for analyzing complex scientific data.