Post-silicon validation has become essential in catching hard-to-detect, rarely-occurring bugs that have slipped through pre-silicon verification. Post-silicon validation flows, however, are challenged by limited signal observability, which impacts their ability of diagnosing and detecting bugs. Indeed, bug manifestations during the execution of constrained-random tests may be masked and be unobservable from the test's outputs. The ability to evaluate the bug-masking rate of a test provides great value in generating and/or selecting effective tests for high coverage regressions. To this end, we propose an efficient, static bug-masking analysis solution, called BugMAPI. BugMAPI tracks the information flow in a test program, and it estimates the probability that bugs go undetected by the checking mechanisms in place in the post-silicon platform. To achieve this goal, we leverage static code analysis and a novel, lightweight, probability estimation algorithm. We evaluated BugMAPI on a range of industrial constrained-random tests and a range of bug injection models, and we found that it can estimate bug-masking rates with an accuracy of 77% in 3 orders-of-magnitude less time, compared to an ideal dynamic analysis solution.