Assessing Small Probabilities in Extreme Hazard Event Trees When Limited Information Is Available

Event trees are often used to assess the risks associated with geoextreme events caused by natural hazards and choose the appropriate risk-management strategy. However, because the frequencies of interest for these extreme events can be as small as once per 1,000–10,000 years, there is limited information available to assess them. This paper proposes a methodology for assessing the probabilities of rare events. The methodology utilizes the possibility of fractional occurrences in a random process to represent estimates of small frequencies in limited lengths of historical record and a decision-based approach to establish noninformative probabilities to be updated with the available information. A case study of a risk-based rehabilitation decision for major rockfill dam demonstrates that realistically representing the uncertainty in assessing small frequencies is important, both in deciding whether or not to rehabilitate the dam and in assessing the value of obtaining additional information about the risk.