Probabilistic database systems have successfully established themselves as a tool for managing uncertain data. However, much of the research in this area has focused on efficient query evaluation and has largely ignored two key issues that commonly arise in uncertain data management: First, how to provide explanations for query results, e.g., “Why is this tuple in my result?” or “Why does this output tuple have such high probability?”. Second, the problem of determining the sensitive input tuples for the given query, e.g., users are interested to know the input tuples that can substantially alter the output, when their probabilities are modified (since they may be unsure about the input probability values). Existing systems provide the lineage/provenance of each of the output tuples in addition to the output probabilities, which is a boolean formula indicating the dependence of the output tuple on the input tuples. However, lineage does not immediately provide a quantitative...