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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Bayesian inference for the Birnbaum-Saunders nonlinear regression model

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Author(s):
Farias, Rafael B. A. [1, 2] ; Lemonte, Artur J. [1, 2]
Total Authors: 2
Affiliation:
[1] Univ Sao Paulo, Dept Estat, BR-05508090 Sao Paulo - Brazil
[2] Univ Sao Paulo, Dept Stat, BR-05508090 Sao Paulo - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Statistical Methods and Applications; v. 20, n. 4, p. 423-438, NOV 2011.
Web of Science Citations: 9
Abstract

We develop a Bayesian analysis for the class of Birnbaum-Saunders nonlinear regression models introduced by Lemonte and Cordeiro (Comput Stat Data Anal 53:4441-4452, 2009). This regression model, which is based on the Birnbaum-Saunders distribution (Birnbaum and Saunders in J Appl Probab 6:319-327, 1969a), has been used successfully to model fatigue failure times. We have considered a Bayesian analysis under a normal-gamma prior. Due to the complexity of the model, Markov chain Monte Carlo methods are used to develop a Bayesian procedure for the considered model. We describe tools for model determination, which include the conditional predictive ordinate, the logarithm of the pseudo-marginal likelihood and the pseudo-Bayes factor. Additionally, case deletion influence diagnostics is developed for the joint posterior distribution based on the Kullback-Leibler divergence. Two empirical applications are considered in order to illustrate the developed procedures. (AU)