Model Selection in Seismic Hazard Analysis: An Information-Theoretic Perspective

Abstract

Abstract Although the methodological framework of probabilistic seismic hazard analysis is well established, the selection of models to predict the ground motion at the sites of interest remains a major challenge. Information theory provides a powerful theoretical framework that can guide this selection process in a consistent way. From an information-theoretic perspective, the appropriateness of models can be expressed in terms of their relative information loss (Kullback–Leibler distance) and hence in physically meaningful units (bits). In contrast to hypothesis testing, information-theoretic model selection does not require ad hoc decisions regarding significance levels nor does it require the models to be mutually exclusive and collectively exhaustive. The key ingredient, the Kullback–Leibler distance, can be estimated from the statistical expectation of log-likelihoods of observations for the models under consideration. In the present study, data-driven ground-motion model selection based on Kullback–Leibler-distance differences is illustrated for a set of simulated observations of response spectra and macroseismic intensities. Information theory allows for a unified treatment of both quantities. The application of Kullback–Leibler-distance based model selection to real data using the model generating data set for the Abrahamson and Silva (1997) ground-motion model demonstrates the superior performance of the information-theoretic perspective in comparison to earlier attempts at data-driven model selection (e.g., Scherbaum et al. , 2004).