Some Bayesian Inferences for a Changing Linear Model

This paper is a generalization of earlier studies by Ferreira (1975) and Holbert and Broemeling (1977), who used improper prior distributions in order to make informal Bayesian inferences for the shift point and other parameters of a changing linear model. In this study, normal-gamma distributions are employed as prior distributions for the regression parameters of the model and, as a result, the posterior distribution of the regression parameters are mixtures of t distributions, while a mixture of gamma distributions is the posterior distribution of the precision parameter. Point and interval estimators of the regression parameters and the residual precision are based on the appropriate marginal and conditional posterior distributions and are illustrated with data generated from a known model.