Bayes analysis of some important lifetime models using MCMC based approaches when the observations are left truncated and right censored

The paper considers the Bayes analysis of important lifetime models such as the Weibull, the gamma, and the lognormal distributions when the available data are left truncated and right-censored. Weakly informative prior distributions are employed for the purpose. Two well-known Markov chain Monte Carlo based approaches, namely, the Metropolis algorithm and the Hamiltonian Monte Carlo technique are used to draw samples from analytically intractable posterior distributions. Besides, the paper does a comparative study of the three entertained models using Bayes factor. The paper has considered calculating the marginal likelihood using bridge sampler algorithm for evaluating the necessary Bayes factor. Finally, a numerical illustration based on a real dataset compares the two algorithms and draws relevant conclusions appropriately.

Automated summary

This paper examines the Bayes analysis of important lifetime models like Weibull, gamma, and lognormal distributions, considering left-truncated and right-censored data, with weakly informative prior distributions. It uses Markov chain Monte Carlo methods such as the Metropolis algorithm and the Hamiltonian Monte Carlo technique to sample from analytically intractable posterior distributions. Additionally, a comparative study of the models is done using Bayes factor, and the bridge sampler algorithm is employed to calculate marginal likelihood for evaluating the necessary Bayes factor. Finally, a numerical illustration based on a real dataset compares the two algorithms and draws relevant conclusions.