This paper presents an approach for making inference on the mean and variance of a Gaussian distribution in the presence of resolution errors. The approach is based on the principle of fiducial inference and requires a Monte Carlo method for computing uncertainty intervals. A small simulation study is carried out to evaluate the performance of the proposed procedure and compare it with some of the existing procedures. The results show that the fiducial procedure is competitive with the best of the competing procedures for inference on the mean. However, unlike the competing procedures, the same Monte Carlo calculations also provide inference for the variance and many other related quantities of interest.
Pub Type: Journals
fiducial inference, Markov chain Monte Carlo, resolution error.