We consider the problem of outlier detection in bivariate exponential data fitted using the generalized linear model via Bayesian approach. We follow closely the work outlined by Unnikrishnan (2010) and present every step of the detection procedure in details. Due to the complexity of the resulting joint posterior distribution, we obtain the information on the posterior distribution from samples generated by Markov Chain Monte Carlo sampling, in particular, using either the Gibbs sampler or the Metropolis-Hastings algorithm. We use local breast cancer patients’ data to illustrate the implementation of the method.