Baves Local Influence For Log-BS Linear Regression Models

In the analysis of life data,the description of fatigue life data distribution is important component, and log-Birnbaum - Saunders distribution (log-BS distribution) is an important distribution to describe the fatigue life data. The often-used life distribution such as Weibull,gamma and log-normal models fail to deliver a good tail fitting. Because of considering the basic characteristics of the fatigue process,the log-BS distribution provide a good fit at the tails where only a few observations are available.In this paper, we intend to develop a Bayes local influence analysis method to diagnose the log-BS linear regression model with non-censored and censored response data respectively,which aim to assess the effect of minor perturbations to the prior and the data,and detect the influential observations. Specifically, for the log-BS linear regression model with non-censor and censor response data: First, this paper present a simultaneous perturbation model to char-acterize perturbations to the prior and the data. Then, based on the objective function of bayes factor, first-order local influence measures and first-order adjustment local influence measures are developed, which can be used in local influence analysis for data or prior or both of them.Finally, MCMC methods are used to complete the computation of influence measures, and three real data sets and simulation computations of the following four aspects are conduct-ed to show the effects of above local influence measures: (1) perturbation to response data;(2) simultaneous perturbations to the prior distribution and response data; (3) perturbation to explanatory data; (4) and the joint perturbation to explanatory data and the prior distribution.The main innovation point of this paper is that the local influence measures for log-BS linear model with non-censored and censored response are developed and algorithm based on MCMC methods is applied to execute related computations.