Bayesian Computation for the Superposition ofNonhomogeneous Poisson

Bayesian inference for the superposition of nonhomogeneous Poisson processes is studied. A Markov chain Monte Carlo method with data augmentation is developed to compute the features of the posterior distribution. For each observed failure epoch, a latent variable is introduced that indicates which component of the superposition model gives rise to the failure. This data augmentation approach facilitates speciication of the transitional kernel in the Markov chain. Moreover, new Bayesian tests are developed for the full superposition model against simpler submodels. Model determination by a predictive likelihood approach is studied. A numerical example based on a real data set is given.