Bayesian Inference for a Birnbaum-Saunders Regression Model Based on the Centered Skew Normal Distribution

In this paper, we developed Bayesian inference tools for a log Birnbaum-Saunders regression model based on the skew normal distribution under the centered parameterization. Parameter estimation, model t assessment, model comparison, residual analysis and Bayesian case in uence diagnostics were developed through MCMC algorithms. Also, a comparison with the maximum likelihood, previously proposed in the literature, was performed, in terms of parameter recovery. We noticed that the results are quite similar, but the Bayesian approach is more easily implemented and for developing in uence diagnostics tools, which also allows incorporating prior information. Finally, a real data
set is analyzed. The results indicate that our model outperforms the usual log Birnbaum-Saunders regression model in terms of model t.