On Alternative Monte Carlo Methods for Parameter Estimation in Gamma Process Models With Intractable Likelihood

Due to stochastic gamma processes adaptability, they are now widely used to mimic a variety of degradation events. However, in certain situations, measurement errors are present in degradation data, and an intractable probability setting is emerging. When completing inference tasks, its intractableness causes significant practical difficulty. In order to overcome the difficulty of producing MLEs and the related confidence intervals for the model parameters, we propose a new technique. The rare-event problem, which has a significant influence on the estimator efficiency and, consequently, on the whole inference process, plagues previously employed Monte Carlo approaches for intractable likelihood estimation. We suggest using an alternative Monte Carlo method to address this, while avoiding the establishment of a rare-event issue. The cross-entropy optimization approach, which can handle objective functions that are tainted by noise, is then added to this technique. We demonstrate that the suggested mix can be implemented within an acceptable computation time and lays the foundation for efficient, generic, and scalable inference processes under the intractable likelihood scenario. Our results show that, given the stochastic gamma process degradation model assumption, the proposed technique may yield high-quality inference results.