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prediction equations, building stock and infrastructure exposure, and vul-
nerability of infrastructure (e.g. Crowley et al. 2005; Kwona and Elnashai
2006; Goda and Hong 2008). Models and input parameters used in quantify-
ing risk are subject to assumptions, validity/quality of underlying data, and
data scarcity/variability (Walley 1996). Thus, consideration of uncertainty in
any risk analysis is unavoidable. Typology and defi nition of uncertainty
within the engineering community are broad and often confl icting. In risk
analysis, uncertainty can be categorized into aleatory and epistemic uncer-
tainty. Aleatory uncertainty (variability) is due to natural heterogeneity or
stochasticity of a physical process and it cannot be reduced, while epistemic
uncertainty is due to ignorance or subjectivity, which can be reduced with
availability of more information. In the context of earthquake disasters,
various uncertainty propagation methodologies have been discussed in the
literature (e.g. Kaplan 1981; Paté-Cornell 1996; Baker and Cornell 2008;
Bradley et al. 2009; Ching et al. 2009). Modeling and treatment of epistemic
uncertainties are critically important.
One of the major challenges in seismic risk analysis is the treatment and
characterization of uncertainty associated with earthquake risks. Our expe-
rience and knowledge are insuffi cient to envisage possible earthquake sce-
narios completely and comprehensively. In future disasters, there will always
be surprises and new lessons will be learned. Recent examples for such
surprises include damaging ground shaking and widespread liquefaction
due to the February 22 2011 Christchurch (New Zealand) earthquake
(despite the fact that the earthquake size was moderate) and devastating
tsunami damage due to the March 11 2011 Tohoku (Japan) earthquake.
These cases clearly show that our capability for predicting what might
happen in a future earthquake disaster, the chance of its happening, and
extent of its consequences needs to be improved. This highlights importance
of extending the current approaches/methods for risk analysis and manage-
ment by broadening the scope/perspective on epistemic uncertainties.
Potential remedies for quantifying epistemic uncertainties are to adopt a
broader formalism of uncertainties in comparison with the current defi ni-
tion of risk/uncertainty in probabilistic seismic risk analysis (where all pos-
sible events are considered to be captured comprehensively). For such
purposes, imprecise interval probability theory (Walley 1996) and evidence
theory (Dempster 1967; Shafer 1976) may be adopted. These uncertainty
theories relax some of the axioms of classical probability (e.g. total sum of
the event probabilities equals one) and thus are able to capture vagueness
and ambiguity (to which numerical probability values may not be assigned
with full confi dence). An introduction to several uncertainty theories will
be given in Section 6.2. The aim of this introduction is to broaden our
knowledge basis beyond the conventional defi nition of uncertainty in prob-
abilistic seismic risk analysis. An application of the interval probability