Improved likelihood estimation for noisy gamma degradation processes via sequential Monte Carlo

The use of Gamma processes for modeling various degradation phenomena has recently gained extensive attention. In many cases, the degradation data contain measurement errors and an intractable likelihood phenomenon comes into sight. Therefore, in order to perform efficient statistical inference, one must obtain high-quality estimates of the corresponding likelihood. Our findings indicate that the crude Monte Carlo method, which is the de facto state-of-the-art method, is not adequate in practice for efficient likelihood estimation. To cope with this problem, we propose to employ the sequential Monte Carlo approach, which shows promise for improved reliability compared to the current state of the art. Our approach leads to efficient variance minimization and opens the way for effective and scalable inference procedures.