Runtime verification encompasses several lightweight techniques for checking whether a system’s current execution satisfies a given specification. We focus on runtime verification for Linear Temporal Logic (LTL). Previous work describes monitors which produce, at every time step one of three outputs - true, false, or inconclusive - depending on whether the observed execution prefix definitively determines satisfaction of the formula. However, for many LTL formulas, such as liveness properties, satisfaction cannot be concluded from any finite prefix. For these properties traditional monitors will always output inconclusive. In this work, we propose a novel monitoring approach that replaces hard verdicts with probabilistic predictions and an associated confidence score. Our method guarantees eventual correctness of the prediction and ensures that confidence increases without bound from that point on.