Approximate Bayesian computation (ABC) method for estimating parameters of the gamma process using noisy data

The stochastic gamma process (GP) has emerged as a versatile model of degradation processes affecting the performance of engineering structures and components. The GP model captures the temporal uncertainty in the degradation process, whereas the Bayesian approach is used to account for uncertainty in the model parameters. Although the conceptual approach to GP parameter estimation is straightforward, its practical implementation is quite challenging. The reason is that degradation data required for parameter estimation are invariably contaminated by measurement noise, which turns the likelihood function into a high-dimensional multivariate integral. To circumvent this difficulty, the paper presents a novel and practical approach based on the approximate Bayesian computation (ABC) technique. The ABC method is a simulation-based approach that does not require an explicit formulation of the likelihood function. Instead, ABC uses an “accept-reject†mechanism to perform the posterior computation. To reduce the rejection rate, the Markov chain Monte Carlo (MCMC) approach is used within the ABC algorithm. The proposed ABC-MCMC algorithm is shown to be computationally more efficient than the traditional likelihood-based method without compromising the numerical accuracy. A case study involving the modelling of corrosion in nuclear piping systems is presented, which confirms the practical usefulness of the proposed method.