Modified Influential Observation Detection in Bayesian Regression Using Conjugate Prior Distribution

The influential observations has long been one of the most concern in the statistical structure to researchers. A Bayesian approach to multivariate linear regression is known as Bayesian multivariate linear regression analysis in which the predicted outcome is a vector of correlated random variables rather than a single scalar random variable. In this study, influential observation diagnostics based on case deletion approach with the ith case deleted are examined for the Bayesian regression analysis. For this aim, Welsch-Kuh distance, Cook’s distance, and the Hadi measure which are major case deletion diagnostics in linear regression is modified for the Bayesian regression using conjugate prior distribution. To show the performance of proposed diagnostics on detection influential observations in the Bayesian regression analysis using conjugate prior distribution, the pavement data is used.