Bayesian prediction for a jump diffusion process - With application to crack growth in fatigue experiments

Simone Hermann, Katja Ickstadt, Christine H. Müller

Abstract: Highlights•A new statistical model for the damage process of prestressed concrete under low cyclic load with ability for prediction.•Bayesian inference for a jump diffusion process based on a nonhomogeneous Poisson process.•Two-stage modeling because of observed jumps: 1) the counting process is modeled,2) the jump diffusion process itself.•For prediction of crack width process, the uncertainties of parameters and the latent Poisson process are included.