Bayesian analysis with consideration of data uncertainty in a specific scenario

In this paper data uncertainty in a specific scenario is modeled with Berkson and Classical errors. With consideration of uncertainty three methods within Bayesian framework are presented to update the failure probability with Beta-Binomial model. It shows that the three methods have their posteriors in the same form of weighted Beta distributions, but the weights are different for each method. Approximation to the mixed posteriors has been proposed and demonstrated by computation results. Moreover, comparison and illustration of the three methods are made based on case study and analytical analysis, which suggest that the LO method with Classical error model be more appropriate in similar applications.