Bayesian updating of earthquake vulnerability functions with application to mortality rates

Vulnerability functions often rely on data from expert opinion, postearthquake investigations, or analytical simulations. Combining the information can be particularly challenging. In this paper, a Bayesian statistical framework is presented to combining disparate information. The framework is illustrated through application to earthquake mortality data obtained from the 2005 Pakistan earthquake and from PAGER. Three different models are tested including an exponential, a combination of Bernoulli and exponential and Bernoulli and gamma fit to model respectively zero and non-zero mortality rates. A novel Bayesian model for the Bernoulli-exponential and Bernoulli-gamma probability densities is introduced. It is found that the exponential distribution represents the zero casualties very poorly. The Bernoulli-exponential and Bernoulli-gamma models capture the data for both the zero and non-zero mortality rates. It is also shown that the Bernoulli-gamma model fits the 2005 Pakistan data the best and has uncertainties that are smaller than either the ones from the 2005 Pakistan data or the PAGER data.