Static slicing is a popular program analysis used in software engineering to find which parts of a program affect other parts. Unfortunately, static slicing often produces large and imprecise results because of its conservative nature. Dynamic slicing can be an alternative in some cases, but it requires detailed runtime information that can be hard or impossible to obtain or re-create. This is often the case when users report bugs in deployed software. In this paper, we significantly improve the precision of static slicing through PRIOSLICE, a novel technique that exploits the insight that not all statements in a static slice are equally likely to affect another statement such as a failing point. PRIOSLICE first computes a probabilistic model of the dependencies in the program. In this model, some data dependencies are more likely to occur than others and control dependencies are less likely than data dependencies to propagate effects (e.g., errors). PRIOSLICE then traverses the program backwards, like static slicing, but in an order defined by the computed dependence probabilities. Our study of fault localization on various Java subjects indicates that PRIOSLICE can help localize faults much more effectively than existing static-slicing approaches. (c) 2015 Elsevier Inc. All rights reserved.