We prove the weak consistency of the posterior distribution and that of the
Bayes estimator for a two-phase piecewise linear regression mdoel where the
break-point is unknown. The non-differentiability of the likelihood of the
model with regard to the break- point parameter induces technical difficulties
that we overcome by creating a regularised version of the problem at hand. We
first recover the strong consistency of the quantities of interest for the
regularised version, using results about the MLE, and we then prove that the
regularised version and the original version of the problem share the same
asymptotic properties
