AbstractsMathematics

A Bayesian approach to the analysis of a two-phase linear regression model is given. It is assumed that the regression model is continuous at the change point. The likelihood function is expressed in a form which explicitly contains the continuity restriction. The natural conjugate prior distribution for the likelihood function is used, and the form of the prior constrained mean vector and dispersion matrix is developed for the situation where prior knowledge only exists on an unconstrained model. The situation where the join point is unknown is approached by discretizing the possible values of the join point, and assuming a discrete prior distribution for the join point. The marginal posterior probability of the join point is determined, and the various posterior conditional and marginal distributions of the unknown parameters are shown. Numerical examples are considered which show the similarities and differences which exist between the Bayesian approach and the more common least squares approach. The situation of vague prior knowledge is briefly considered.