This dissertation addresses three different earthquake engineering prediction problems and draws heavily from other fields, especially statistics. The great uncertainty associated with each prediction requires statistics to rigorously address the problem. Conventional wisdom within the geotechnical engineering field often assumes that there is too much uncertainty in the material property estimates to use statistics. This assumption reflects a limited understanding of the role and value of statistics: if there was no uncertainty then we would not need statistics. In fact, statistics provides a quantitative framework for analyzing and understanding the uncertainty that is so prevalent in the natural world. This dissertation focuses on (i) the likelihood of large earthquakes, (ii) spatial interpolation of seismic properties, and (iii) the theoretical formulation of site response prediction. The accuracy of the predictions in each problem is limited for fundamentally different reasons. By properly accounting for the unique limitations in each situation, I hope to improve our understanding of the problem and help the field develop more accurate models.
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