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

Highlights: • Bayesian analysis of the Weibull, lognormal and gamma models is considered. • The entertained data are in the form of left truncated and right censored. • The Metropolis and Hamiltonian Monte Carlo algorithms are employed and subsequently compared. • Model comparison using bridge sampler is another important focus of the work. 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.