Metrics, Bayes, and BOGSAT: Recognizing and Assessing Uncertainties in Earthquake Hazard Maps

Abstract:

Recent damaging earthquakes in areas predicted to be relatively safe illustrate the need to assess how seismic hazard maps perform. At present, there is no agreed way of assessing how well a map performed. The metric implicit in current maps, that during a time interval predicted shaking will be exceeded only at a specific fraction of sites, is useful but permits maps to be nominally successful although they significantly underpredict or overpredict shaking, or nominally unsuccessful but predict shaking well. We explore metrics that measure the effects of overprediction and underprediction. Although no single metric fully characterizes map behavior, using several metrics can provide useful insight for comparing and improving maps. A related question is whether to regard larger-than-expected shaking as a low-probability event allowed by a map, or to revise the map to show increased hazard. Whether and how much to revise a map is complicated, because a new map that better describes the past may or may not better predict the future. The issue is like deciding after a coin has come up heads a number of times whether to continue assuming that the coin is fair and the run is a low-probability event, or to change to a model in which the coin is assumed to be biased. This decision can be addressed using Bayes’ Rule, so that how much to change depends on the degree of one’s belief in the prior model. Uncertainties are difficult to assess for hazard maps, which require subjective assessments and choices among many poorly known or unknown parameters. However, even rough uncertainty measures for estimates/predictions from such models, sometimes termed BOGSATs (Bunch Of Guys Sitting Around Table) by risk analysts, can give users useful information to make better decisions. We explore the extent of uncertainty via sensitivity experiments on how the predicted hazard depends on model parameters.