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

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.