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Bayesian inference for the Birnbaum-Saunders nonlinear regression model

机译：Birnbaum-Saunders非线性回归模型的贝叶斯推断

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摘要

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.
机译：我们开发了由Lemonte和Cordeiro引入的Birnbaum-Saunders非线性回归模型的贝叶斯分析（Comput Stat Data Anal 53：4441-4452，2009）。这种基于Birnbaum-Saunders分布的回归模型（Birnbaum和Saunders在J Appl Probab 6：319-327，1969a中）已成功地用于疲劳破坏时间建模。我们考虑了先验法线下的贝叶斯分析。由于模型的复杂性，马尔可夫链蒙特卡罗方法用于为所考虑的模型开发贝叶斯程序。我们描述了用于模型确定的工具，其中包括条件预测纵坐标，伪边际似然的对数和伪贝叶斯因子。此外，基于Kullback-Leibler散度，针对关节后部分布开发了案例删除影响诊断程序。为了说明开发的程序，考虑了两个经验应用。

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