Temporal information extraction is a challenging but important area of automatic natural language understanding. Existing approaches annotate and extract various parts of the temporal information conveyed in language like relative event order, temporal expressions, or event durations. Most schemes focus primarily on annotation of temporally certain (often explicit) information, resulting in partial annotation, and underrepresentation of implicit information. In this paper, we propose an approach towards extraction of more complete (implicit and explicit) temporal information for all events, and obtain probabilistic absolute event timelines by modeling temporal uncertainty with information bounds. As a case study, we use our scheme to annotate a set of English clinical reports, and propose and evaluate a multi-regression model for predicting probabilistic absolute timelines, obtaining promising results.